A flight lifesaving equipment posture tracking control method based on low-frequency learning and event triggering mechanism

Abstract

The application provides a flight lifesaving equipment posture tracking control method based on low-frequency learning and event triggering mechanism, and belongs to the technical field of unmanned aerial vehicle posture control. The application establishes a simplified posture dynamics model under a small angle assumption, unifies model coupling terms, parameter perturbation, unmodeled dynamics, simplified modeling errors and external disturbances into total uncertain terms; adopts RBF neural network to online approximate the total uncertain terms, and introduces a low-frequency weight learning mechanism to constrain fast weight update and suppress high-frequency estimation oscillation; designs an event triggering maintenance mechanism to reduce control update frequency; constructs an actuator amplitude saturation model and an auxiliary dynamic system to compensate for actuator constraints; and further generates an event-triggered actuator-constrained posture tracking control law. Based on Lyapunov stability theory, it is proved that all signals of the closed-loop system are uniformly ultimately bounded, the posture tracking error converges to a small neighborhood around the origin, and there is no Zeno behavior.

Description

Technical Field

[0001] This invention relates to the fields of unmanned aerial vehicle control, maritime emergency rescue equipment control, intelligent control, event-triggered control, actuator constraint control, and neural network adaptive control. In particular, it relates to an attitude tracking control method for flight rescue equipment based on a low-frequency learning and event-triggered mechanism. Background Technology

[0002] With the rapid development of unmanned systems, maritime emergency equipment, and intelligent rescue technologies, quadcopter-based rescue vehicles, with their advantages of vertical takeoff and landing, hovering maneuverability, flexible deployment, and low operating costs, have been widely applied in tasks such as search and monitoring, target identification, material delivery, and emergency response. They have become an important technological carrier for building a collaborative sea, air, land, and submarine rescue system. In maritime search and rescue scenarios, quadcopter-based rescue vehicles can rapidly conduct search and initial rescue operations in areas that are difficult to reach in a timely manner using traditional lifeboats, thereby significantly improving rescue response efficiency.

[0003] However, the marine environment is often accompanied by adverse factors such as gusts of wind, surges, platform sway, limited communication, and physical constraints on actuators. This makes flight rescue equipment prone to amplified attitude fluctuations, limited control inputs, and strained communication resources when performing hovering search, trajectory tracking, and pinpoint delivery missions. Therefore, researching high-performance attitude tracking control methods for flight rescue equipment under complex constraints has significant theoretical and engineering value. In such missions, attitude control is the inner-loop foundation for hovering, approach, and delivery operations, and the execution of upper-level motion commands ultimately depends on the stable and accurate response of roll, pitch, and yaw attitudes.

[0004] Existing methods for quadrotor attitude and trajectory control have evolved from dynamic modeling and classical nonlinear control to robust control, adaptive control, observer-aided control, and intelligent control. Although significant progress has been made in improving the speed, accuracy, and disturbance rejection of quadrotor systems, most methods still focus on control design under conditions without significant network constraints or considering only a single constraint. Communication and transmission constraints under networked implementation conditions are increasingly becoming unavoidable issues in the control design of flight rescue equipment; if the controller updates and transmits control commands at every sampling moment, it will increase the communication burden and cause frequent actuator movements.

[0005] Meanwhile, the actual flight rescue equipment has physical limits on motor thrust, control torque, and power supply capacity. Actuator amplitude constraints often manifest as control input saturation and may cause a decline in control performance under large disturbances or rapid maneuvers, even disrupting closed-loop stability in severe cases. Furthermore, flight equipment in maritime rescue missions is inevitably affected by model uncertainties, coupling terms, and external disturbances. While RBF neural networks can be used for online approximation of unknown nonlinearities, in the complex maritime environment, sea state and airflow disturbances often contain significant high-frequency components. If the neural network weight updates are too sensitive to high-frequency error information, it may still cause estimation oscillations and control input chattering.

[0006] Therefore, it is necessary to propose an attitude tracking control method for flight rescue equipment that can simultaneously handle model uncertainty, external disturbances, actuator amplitude constraints, event-triggered update constraints, and high-frequency oscillations of neural network weights within a unified control framework. Summary of the Invention

[0007] To address the aforementioned technical problems of decreased attitude control accuracy, frequent control input updates, neural network estimation oscillations, and insufficient actuator constraint compensation for flight rescue equipment in maritime emergency rescue scenarios under conditions of model uncertainty, external disturbances, actuator saturation, and limited communication resources, this invention provides an attitude tracking control method for flight rescue equipment based on a low-frequency learning and event-triggered mechanism. This invention establishes a simplified attitude dynamics model of the flight rescue equipment under the small-angle assumption, unifying model coupling terms, parameter perturbations, unmodeled dynamics, simplified modeling errors, and external disturbances into a total uncertainty term. It defines the attitude tracking error and sliding mode surface, and uses an RBF neural network to approximate the total uncertainty term online. Low-frequency learning technology is introduced to quickly update weights through low-frequency weight estimation constraints. An event-triggered control mechanism is designed to reduce control updates and signal transmission. An actuator saturation model and auxiliary dynamic system compensation actuator constraints are constructed. Finally, an event-triggered actuator constraint control law is generated, and the stability of the closed-loop system and the absence of Zeno behavior are proven using Lyapunov stability theory.

[0008] The technical means employed in this invention are as follows: A method for attitude tracking control of flight rescue equipment based on low-frequency learning and event-triggered mechanisms, comprising: S1. Under the assumption of small angle, establish a simplified attitude dynamics model of the flight rescue equipment, obtain the attitude angle vector, body angular velocity vector, moment of inertia matrix, control input signal and external disturbance torque of the flight rescue equipment, and combine the model coupling terms, parameter perturbation, unmodeled dynamics, simplified modeling error and external disturbance into the total uncertainty term; S2. Define the attitude tracking error based on the actual attitude angle and the desired attitude trajectory, construct a linear sliding surface, and obtain the dynamic equation of the sliding surface that includes the total uncertainty term, control input, and reference trajectory acceleration. S3. Construct an RBF neural network to approximate the total uncertainty term online, define the ideal weight matrix, basis function vector, approximation error and estimated weight matrix, and introduce a low-frequency weight estimation matrix and design a low-frequency learning adaptive law. S4. Design an event trigger holding mechanism, define the event trigger error and the channel trigger threshold, so that the control input remains unchanged between adjacent trigger times, and the control input is updated when the trigger error reaches the threshold. S5. Establish an actuator amplitude saturation model, define the saturation error caused by actuator constraints, and construct an auxiliary dynamic system to compensate for the adverse effects of actuator saturation on closed-loop attitude control performance. S6. Define intermediate variables for the control law, and combine the estimated values ​​of the RBF neural network, the robust hyperbolic tangent term, the event-triggered error compensation term, and the auxiliary dynamic system state to generate the event-triggered actuator constrained attitude tracking control law. S7. Based on the Lyapunov stability theory, construct a Lyapunov function that includes the sliding surface, neural network weight estimation error, low-frequency weight estimation error and auxiliary dynamic system state. Prove that all signals in the closed-loop system are consistent and eventually bounded and that the attitude tracking error converges to a small neighborhood near the origin. S8. Based on the boundedness of the derivative of the event triggering error, it is proved that there is a positive lower bound between any two adjacent triggering times, thus excluding Zeno behavior; S9. Set the moment of inertia, initial state, control parameters, RBF neural network parameters, event trigger threshold, actuator saturation upper and lower bounds, external disturbances, and reference attitude trajectory of the flight rescue equipment. Verify the effectiveness of the flight rescue equipment attitude tracking control method through attitude tracking and attitude stabilization tasks.

[0009] Further, step S1 includes: S11. Define the inertial coordinate system of the flight rescue equipment. and the body coordinate system fixed at the center of mass of the flight rescue equipment Define roll angle Pitch angle and yaw angle Define the lift generated by the four rotors as follows: Adjacent rotors rotate in opposite directions to balance the counter-torque and achieve attitude adjustment; S12. Establish the kinematic equations for the posture as follows:

[0010] in, The attitude angle vector, The angular velocity vector of the machine system. Here is the attitude kinematics transformation matrix; S13. Establish the attitude dynamics equations as follows:

[0011] in For the rotational inertia matrix of flight rescue equipment, For system control input signals, External disturbance torque; S14. Based on the fact that flight rescue equipment mainly serves low-altitude delivery, close-range hovering, and fixed-point rescue missions, and that the system typically operates within a relatively stable small attitude angle range without involving violent rolls or large maneuvers, the small-angle assumption is adopted without sacrificing the main control characteristics, and the attitude kinematic equations are simplified as follows:

[0012] S15. Define the state vector as follows:

[0013] in, For the roll angular velocity, The pitch angular velocity, Yaw angular velocity; S16. Expand the attitude dynamics equations as follows:

[0014] S17. The attitude system of flight rescue equipment shall be written as:

[0015] in, To control the efficiency matrix, This represents the control efficiency coefficient of the roll channel. This represents the control efficiency coefficient of the pitch channel. The control efficiency coefficient for the yaw channel; To account for lumped nonlinear terms and model uncertainties, This represents parameter perturbation, unmodeled dynamics, and simplified modeling errors; External disturbance term; S18. Combine the model coupling terms, parameter perturbations, unmodeled dynamics, simplified modeling errors, and external disturbances into a total uncertainty term to obtain an equivalent second-order attitude model, as follows:

[0016] in, This is the total uncertainty term; S19. Set the desired attitude trajectory as follows:

[0017] in, For the desired roll angle, For the desired pitch angle, The desired yaw angle; S110. The desired attitude trajectory is set to be at least three times continuously differentiable, and satisfies the following conditions: Both are bounded, meaning they have positive constants. , so that:

[0018] in, Let be the desired attitude trajectory vector. Let the first derivative of the desired attitude trajectory be . Let the second derivative of the desired attitude trajectory be... Let the third derivative of the desired attitude trajectory be... All are positive numbers, representing the upper bounds of their respective derivatives.

[0019] Further, step S2 includes: S21. Based on the actual attitude angle and the desired attitude trajectory, define the tracking error as follows:

[0020] in, Let be the attitude tracking error vector. Let the desired attitude trajectory vector be denoted as . S22. Based on the attitude kinematics relationship under the small angle assumption, the derivative of the tracking error is defined as follows:

[0021] S23. Based on the defined tracking error and its derivative, construct the linear sliding surface as follows:

[0022] in, For the selected positive definite diagonal matrix, , For the sliding surface of the rolling channel, For pitch channel sliding surface, For yaw channel sliding surface; S24. Differentiating the constructed linear sliding surface, we obtain:

[0023] S25. Define the total uncertainty term and write the total uncertainty term into the sliding surface dynamics:

[0024] in, For the total uncertain term, This is the input vector for the RBF neural network; S26. Define the hyperbolic tangent vector as follows:

[0025] in, , , All are robust term boundary parameters; S27. Expand the product term in the dynamics of the sliding surface as follows:

[0026] in, Design the parameter matrix for the control law. For robust compensation gain vector, These are the boundary parameters for the robust term.

[0027] Further, step S3 includes: S31, Compact set in a closed-loop system Above, define the total uncertainty term. It is continuous, and its online approximation is achieved using the general approximation property of RBF neural networks; S32. Assume that an ideal weight matrix exists. and RBF basis function vectors , so that:

[0028] in, For neural network approximation error, ; S33. Set the neural network approximation error It satisfies the element-bounded condition, i.e., there exists a vector of normal numbers. , making At the same time, it is set that there are normal numbers. , so that:

[0029] S34, the first The RBF basis functions are set as follows:

[0030] in, For the neural network input vector, For the first The center of each hidden layer node, The width of the Gaussian function; S35. Using the estimated weight matrix The estimated value of the total uncertainty term is constructed as follows:

[0031] S36. Define the ideal weight estimation error as follows:

[0032] S37. Considering ideal weights This is unavailable, and traditional direct weight estimation is easily affected by high-frequency disturbances at sea, resulting in estimation oscillations and control input chattering, introducing low-frequency weight estimation errors, as follows:

[0033] Low-frequency weight estimation matrix As The first-order low-pass filter output is used to constrain the rapidly changing direct weight estimation, thereby suppressing the impact of high-frequency disturbances in the marine environment on neural network estimation and control response; S38. Design a low-frequency learning adaptive law for neural network weights, as follows:

[0034] in, For design constants, It is a positive definite symmetric diagonal parameter matrix; S39. In the low-frequency learning adaptive law of the neural network weights, As a leakage correction term to suppress weight drift, As a low-frequency coupling term to constrain fast weight estimation Low-frequency weight estimation The difference between them weakens the high-frequency oscillations caused by weight updates.

[0035] Further, step S4 includes: S41. To save on input signal communication, an event-triggered hold strategy is designed so that the control input retains the control command from the previous trigger moment between adjacent trigger moments:

[0036] in, To retain input for event triggering, For the first The control law value is calculated at each trigger moment. For the first The event is triggered at the time. For the next event trigger time, The time interval between two consecutive triggers; S42. Based on the design-based event-triggered persistence strategy, define the event-triggered error as follows:

[0037] S43. Set the channel trigger threshold vector And determine the next trigger time:

[0038] S44, when When, set ;when When no new control input signal is transmitted, the controller value remains unchanged to reduce unnecessary signal transmission and control execution; when any channel meets the trigger threshold, the current moment is determined as the next trigger moment and the control input is updated. S45. Introducing a continuously time-varying coefficient vector To satisfy:

[0039] And we obtain the equivalent form of triggering the hold input, as follows:

[0040] in, This is the Hadamard product, used to represent the element-wise multiplication between the channel trigger threshold and the continuously time-varying coefficients.

[0041] Further, step S5 includes: S51. Based on the motor output limit and the allowable control torque range, establish the actuator amplitude saturation model as follows:

[0042] in, This is the actual control input vector. It is a saturation function. To retain input for event triggering, This is the upper limit of the actuator control torque. This is the lower bound of the actuator control torque; S52. Define the saturation error caused by actuator constraints as follows:

[0043] in, The actuator saturation error vector. This is for the saturation error of the roll channel. For pitch channel saturation error, This refers to the yaw channel saturation error. S53. Assume that the saturation error is bounded within the compact set of the closed-loop system, i.e., there exists a normal vector. , so that:

[0044] S54. To compensate for the impact of actuator constraints on the control input, design auxiliary dynamic system states for each attitude channel:

[0045] in, To assist the state vector of the dynamic system, To assist in the dynamic system status of the roll channel, To assist in the dynamic system status of the pitch channel, Provide dynamic system status for yaw channels; S55. Construct an auxiliary dynamic system and differentiate the state of the auxiliary dynamic system as follows:

[0046] in, Nonlinear functions that assist in dynamic systems; S56, For any attitude channel The auxiliary dynamic system is defined element by element as follows:

[0047] in, To assist in the design parameters of dynamic systems, For small design constants; S57. Combining the event-triggered holding mechanism and the actuator saturation model, the actual control input is represented as:

[0048] S58. The actual input is equivalently represented as:

[0049] in, It is a continuously time-varying coefficient vector. This is the trigger threshold vector for each channel.

[0050] Further, step S6 includes: S61. Define the intermediate variables of the control law as follows:

[0051] S62. Obtained from the intermediate variables of the defined control law:

[0052] in, This is the RBF neural network estimate of the total uncertainty term; S63. Define the neural network estimation error as follows:

[0053] S64. Based on the defined neural network estimation error, the sliding surface dynamics are written as:

[0054] S65. Using the property of the hyperbolic tangent function: for any real number... and any positive constant ,have:

[0055] S66. Define the robustness term for each attitude channel, as follows:

[0056] in, For the first Robust compensation gain for each attitude channel For the first Sliding surface variables for each attitude channel For the first The width parameter of the hyperbolic tangent function for each attitude channel. Let be the hyperbolic tangent lemma constant; S67. The vector form of the robust term for each attitude channel after definition is as follows:

[0057] S68. Because the neural network approximation error satisfies... ,but:

[0058] S69, Order ,when When the condition holds true by element:

[0059] S610. Set the dynamic upper limit of the sliding surface as follows:

[0060] S611, Set Event Trigger Threshold Compensation Vector and define:

[0061] S612, Generate event-triggered actuator constraint control law, as follows:

[0062] in, To assist the dynamic system feedback gain matrix, Design parameters for the auxiliary dynamic system of the roll channel. Design parameters for the pitch channel auxiliary dynamic system. Design parameters for the yaw channel auxiliary dynamic system; S613, Constrain the control law of the event-triggered actuator. Input event triggers the hold to get The actual control input is then obtained through the actuator saturation stage. This forms a complete event-triggered actuator constrained attitude tracking closed-loop control structure.

[0063] Further, step S7 includes: S71, For any and any positive constant ,have:

[0064] S72, if Then for any vector The following matrix eigenvalue inequalities are used:

[0065] S73. Employ low-frequency learning weight error relationship: when At that time, there are positive numbers. ,make:

[0066] S74, Set controller parameters to meet requirements Valid by element; Setting auxiliary dynamic system parameters satisfies... and make the matrix ,in, To assist in the analysis of dynamic systems, For auxiliary analysis parameters of the roll channel, To provide auxiliary analysis parameters for the pitch channel, Parameters for auxiliary analysis of yaw channels; S75. Construct the Lyapunov function as follows:

[0067] S76. Calculate the constructed Lyapunov function. The derivative is obtained by:

[0068] S77, Substitute the control law and combine it with the actual input. ,get:

[0069] in, For an effective robust gain vector, For parameters hyperbolic tangent vector function; S78, Utilizing the hyperbolic tangent boundary and get:

[0070] Therefore, we get:

[0071] in, The hyperbolic tangent width parameter vector; S79, Calculation and The derivative is as follows:

[0072]

[0073] in, Let be the positive definite symmetric parameter matrix of the adaptive law. Design a constant for the leakage correction term. Design constants for low-frequency coupling terms. For negative definite terms related to the sliding surface, For leak correction items, This is a low-frequency coupling term; S710, will and By merging, we get:

[0074] S711, due to Then we have:

[0075] S712, Using Inequalities ,get:

[0076] therefore, ; S713. For the auxiliary dynamic system, define the total analysis term for the auxiliary dynamic system as follows:

[0077] in, For the first The auxiliary dynamic system analysis items of the channel, For the first Channel actuator saturation error; S714, when Then:

[0078] Thus obtain ,in, For the first The control efficiency coefficient of the channel; S715, when hour, And:

[0079] in, To assist in the convergence parameters of the dynamic system, For the bounded aggregation constant term, For the first Upper bound of channel saturation error; S716, Define auxiliary dynamic system analysis parameters and take ,get:

[0080] S717, Order and ,get:

[0081] in, To assist the convergence rate matrix of the dynamic system, The rolling channel is used to assist the convergence parameters of the dynamic system. To provide convergence parameters for the dynamic system auxiliary in the pitch channel, The convergence parameters for the yaw channel auxiliary dynamic system are provided. To assist the total aggregate constant term of the dynamic system, For the constant term in the auxiliary dynamic system analysis of the roll channel, For the constant term in the dynamic system analysis of the pitch channel, The constant term is used to assist in the dynamic system analysis of the yaw channel; S718. Combining all the terms, the Lyapunov derivative is obtained as follows:

[0082] in, ; S719, Take ,get:

[0083] S720, utilizing the low-frequency learning weight error relationship, has ,make:

[0084] in, This is the sum of the Lyapunov energy terms corresponding to the neural network weight estimation error and the low-frequency weight estimation error. ; S721, Take ,get:

[0085] in, The attenuation coefficient related to the sliding surface. The weight estimation error is related to the attenuation coefficient. To assist in the state-related attenuation coefficient of the dynamic system; S722. Solving the differential inequality yields:

[0086] S723, taking the limit yields:

[0087] This proves that all signals in a closed-loop system are consistent and eventually bounded, and Finally entered by The determined bounded neighborhood; S724. According to the definition of sliding surface, the error dynamics satisfy:

[0088] because and Consistency is ultimately bounded, therefore It is also consistent that it eventually becomes bounded, and the attitude tracking error converges to a small neighborhood near the origin.

[0089] Further, step S8 includes: S81. Define the RBF basis functions. Continuously differentiable, and The system is bounded within a bounded set of closed-loop systems, and the attitude trajectory is expected to satisfy the conditions of third-order continuous differentiability and boundedness. S82, due to the auxiliary dynamic system To avoid singular terms and because the closed-loop signal is bounded, therefore Bounded; S83, in the interval Internally, it is obtained through an event-triggered persistence mechanism:

[0090] S84, derived from the definition of event triggering error:

[0091] S85, obtained from the control law:

[0092] in, ; S86, Yes Taking the derivative, we get:

[0093] in,

[0094] S87, by Learned and Bounded, obtained from the total uncertainty estimate:

[0095] It can be known from the consistent eventual boundedness of closed loops. Bounded; this is known from the RBF basis function assumption. Bounded; as can be seen from the adaptive law. Bounded, therefore Bounded; S88. Combining the boundedness condition of the desired trajectory and the boundedness of the auxiliary dynamic system. Both are bounded, therefore they have positive constants. ,make ,therefore:

[0096] S89. After updating at the trigger time, the trigger error satisfies... Define the minimum trigger threshold as follows:

[0097] S810, According to the triggering mechanism, at the next triggering moment At least one channel reaches the threshold, therefore:

[0098] Therefore, we obtain Therefore:

[0099] make Then any adjacent triggering times satisfy The event will not be triggered an unlimited number of times within a limited time, thus eliminating Zeno behavior.

[0100] Further, step S9 includes: S91. Set the moment of inertia of the flight rescue equipment as follows:

[0101] Therefore, ; S92. Set the total simulation time and sampling time. The initial system state is as follows:

[0102] S93. Set the controller parameters as follows:

[0103]

[0104]

[0105]

[0106] S94. Construct an RBF network for each attitude channel, with the network input set as follows:

[0107] in, and These are the attitude estimates and angular velocity estimates for the corresponding channels, respectively. S95. Set the number of hidden layer nodes. The basis function centers are uniformly distributed in Set the RBF width; S96. Set initial estimated weights Simultaneously set the parameter matrix and low-frequency learning parameters; S97. Set event trigger parameters ; S98. Set the upper and lower limits of the actuator control torque as follows:

[0108]

[0109] S99. Set the initial state and singularity avoidance parameters of the auxiliary dynamic system as follows:

[0110] S910. Select the state-dependent bounded function and the external disturbance as follows:

[0111]

[0112] S911. In the attitude tracking task, the desired attitude trajectory corresponding to the dynamic rescue target is set as follows:

[0113] S912. In the attitude stabilization mission, the desired attitude command for the static rescue target is set as follows:

[0114] S913. The attitude tracking performance, uncertainty estimation smoothness, communication update saving effect, actuator saturation compensation effect, and Zeno-free behavior of the attitude tracking control method of the flight rescue equipment are verified by using attitude angle tracking curve, angular velocity tracking curve, tracking error curve, RBF uncertainty estimation curve, event trigger interval, and actuator saturation control input curve.

[0115] Compared with the prior art, the present invention has the following advantages: 1. The present invention provides an attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism. By establishing a simplified attitude dynamics model under the assumption of small angle, and uniformly representing the model coupling terms, parameter perturbations, unmodeled dynamics, simplified modeling errors and external disturbances as the total uncertainty term, it realizes the centralized characterization and integrated compensation of multi-source uncertainty factors, and provides a unified approximation object for subsequent neural network adaptive control design.

[0116] 2. The present invention provides an attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism. By constructing an RBF neural network to approximate the total uncertainty online, and introducing a low-frequency weight estimation matrix to constrain the fast weight update process, the method suppresses neural network estimation oscillation and control input chattering caused by high-frequency disturbances at sea, and significantly improves the smoothness of uncertainty estimation and control input quality.

[0117] 3. The present invention provides an attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism. By designing an event triggering and holding mechanism and defining event triggering error and channel triggering threshold, the control input is kept unchanged between adjacent triggering moments. This realizes on-demand updating of control commands instead of transmitting them at every sampling moment, which significantly reduces the communication burden and actuator operation frequency.

[0118] 4. The present invention provides an attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism. By establishing an actuator amplitude saturation model and constructing an auxiliary dynamic system to compensate for the adverse effects caused by actuator constraints, the method achieves online compensation for saturation error and closed-loop performance recovery under limited control input conditions, thereby improving the feasibility of the control scheme in practical engineering.

[0119] 5. The present invention provides an attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism. By constructing an event triggering actuator to constrain the attitude tracking control law and the corresponding adaptive law, and rigorously proving it based on Lyapunov stability theory, it achieves the theoretical guarantee that all signals of the closed-loop system are consistent and eventually bounded, the attitude tracking error converges to a small neighborhood near the origin, and the event triggering mechanism does not have Zeno behavior.

[0120] In summary, by applying the technical solution of this invention, and addressing the problems of decreased control accuracy, frequent control input updates, neural network estimation oscillations, and insufficient actuator constraint compensation in existing technologies for flight rescue equipment under maritime emergency rescue scenarios, where model uncertainty, external disturbances, actuator saturation, and limited communication resources all contribute to the challenges. This invention effectively suppresses high-frequency estimation chattering, reduces unnecessary control transmissions, and compensates for actuator saturation effects through a collaborative design of low-frequency learning, event-triggered control, and auxiliary dynamic system compensation. Therefore, the technical solution of this invention solves the problem in existing technologies of simultaneously handling model uncertainty, external disturbances, actuator amplitude constraints, event-triggered update constraints, and high-frequency oscillations of neural network weights within a unified framework.

[0121] Based on the above reasons, this invention can be widely applied in fields such as attitude control of unmanned aerial vehicles, control of maritime emergency rescue equipment, intelligent control, event-triggered control, actuator constraint control, and neural network adaptive control. Attached Figure Description

[0122] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0123] Figure 1 This is a flowchart of the method of the present invention.

[0124] Figure 2 A schematic diagram of the airframe structure of a flight rescue system.

[0125] Figure 3 This is a block diagram of the controller design for the present invention.

[0126] Figure 4 This is a diagram showing the attitude angle tracking results in one embodiment.

[0127] Figure 5 This is a diagram showing the angular velocity tracking results in one embodiment.

[0128] Figure 6This is a graph showing the tracking error results in one embodiment.

[0129] Figure 7 This is a comparison chart showing the estimation of uncertainties in an RBF neural network with and without low-frequency learning in one embodiment.

[0130] Figure 8 This is a diagram showing the event triggering result in one embodiment.

[0131] Figure 9 This is a diagram showing the control input results under actuator constraints in one embodiment.

[0132] Figure 10 This is a diagram showing the attitude angle stabilization result in another embodiment.

[0133] Figure 11 This is a diagram showing the angular velocity stabilization results in another embodiment.

[0134] Figure 12 This is a diagram showing the stabilization error results in another embodiment.

[0135] Figure 13 This is a comparison chart showing the estimation of uncertainties in the RBF neural network with and without low-frequency learning in another embodiment.

[0136] Figure 14 This is a diagram showing the event triggering result in another embodiment.

[0137] Figure 15 This is a diagram showing the control input results under actuator constraints in another embodiment. Detailed Implementation

[0138] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0139] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product or device.

[0140] This implementation method breaks down the technical solution into a series of implementation steps according to the original logic of the paper's technical content. Each set of steps corresponds to a specific modeling, controller design, event triggering, actuator constraint compensation, stability proof, and simulation verification process.

[0141] like Figure 1 As shown, this invention provides a flight rescue equipment attitude tracking control method based on a low-frequency learning and event-triggered mechanism, comprising: S1. Under the assumption of small angle, establish a simplified attitude dynamics model of the flight rescue equipment, obtain the attitude angle vector, body angular velocity vector, moment of inertia matrix, control input signal and external disturbance torque of the flight rescue equipment, and combine the model coupling terms, parameter perturbation, unmodeled dynamics, simplified modeling error and external disturbance into the total uncertainty term; S2. Define the attitude tracking error based on the actual attitude angle and the desired attitude trajectory, construct a linear sliding surface, and obtain the dynamic equation of the sliding surface that includes the total uncertainty term, control input, and reference trajectory acceleration. S3. Construct an RBF neural network to approximate the total uncertainty term online, define the ideal weight matrix, basis function vector, approximation error and estimated weight matrix, and introduce a low-frequency weight estimation matrix and design a low-frequency learning adaptive law. S4. Design an event trigger holding mechanism, define the event trigger error and the channel trigger threshold, so that the control input remains unchanged between adjacent trigger times, and the control input is updated when the trigger error reaches the threshold. S5. Establish an actuator amplitude saturation model, define the saturation error caused by actuator constraints, and construct an auxiliary dynamic system to compensate for the adverse effects of actuator saturation on closed-loop attitude control performance. S6. Define intermediate variables for the control law, and combine the estimated values ​​of the RBF neural network, the robust hyperbolic tangent term, the event-triggered error compensation term, and the auxiliary dynamic system state to generate the event-triggered actuator constrained attitude tracking control law. S7. Based on the Lyapunov stability theory, construct a Lyapunov function that includes the sliding surface, neural network weight estimation error, low-frequency weight estimation error and auxiliary dynamic system state. Prove that all signals in the closed-loop system are consistent and eventually bounded and that the attitude tracking error converges to a small neighborhood near the origin. S8. Based on the boundedness of the derivative of the event triggering error, it is proved that there is a positive lower bound between any two adjacent triggering times, thus excluding Zeno behavior; S9. Set the moment of inertia, initial state, control parameters, RBF neural network parameters, event trigger threshold, actuator saturation upper and lower bounds, external disturbances, and reference attitude trajectory of the flight rescue equipment. Verify the effectiveness of the flight rescue equipment attitude tracking control method through attitude tracking and attitude stabilization tasks.

[0142] In a specific implementation, as a preferred embodiment of the present invention, step S1 includes: S11, such as Figure 2 As shown, the airframe structure, coordinate system, and rotor force relationships of the flight rescue equipment are defined. Specifically, the inertial coordinate system of the flight rescue equipment is defined. and the body coordinate system fixed at the center of mass of the flight rescue equipment Define roll angle Pitch angle and yaw angle Define the lift generated by the four rotors as follows: Adjacent rotors rotate in opposite directions to balance the counter-torque and achieve attitude adjustment. In this embodiment, the attitude control problem of the flight rescue equipment under limited maneuvering conditions is considered, and its attitude channel is described by the Euler angle kinematic equation and the rotational dynamics equation. To facilitate subsequent controller design, the focus is on the attitude subsystem composed of the three attitude angles of roll, pitch, and yaw and their angular velocities.

[0143] S12. Establish the kinematic equations for the posture as follows:

[0144] in, The attitude angle vector, The angular velocity vector of the machine system. Here is the attitude kinematics transformation matrix; S13. Establish the attitude dynamics equations as follows:

[0145] in For the rotational inertia matrix of flight rescue equipment, For system control input signals, External disturbance torque; S14. Based on the fact that flight rescue equipment mainly serves low-altitude delivery, close-range hovering, and fixed-point rescue missions, and that the system typically operates within a relatively stable small attitude angle range without involving violent rolls or large maneuvers, the small-angle assumption is adopted without sacrificing the main control characteristics, and the attitude kinematic equations are simplified as follows:

[0146] S15. Define the state vector as follows:

[0147] in, For the roll angular velocity, The pitch angular velocity, Yaw angular velocity; S16. Expand the attitude dynamics equations as follows:

[0148] S17. The attitude system of flight rescue equipment shall be written as:

[0149] in, To control the efficiency matrix, This represents the control efficiency coefficient of the roll channel. This represents the control efficiency coefficient of the pitch channel. The control efficiency coefficient for the yaw channel; To account for lumped nonlinear terms and model uncertainties, This represents parameter perturbation, unmodeled dynamics, and simplified modeling errors; External disturbance term; S18. Combine the model coupling terms, parameter perturbations, unmodeled dynamics, simplified modeling errors, and external disturbances into a total uncertainty term to obtain an equivalent second-order attitude model, as follows:

[0150] in, This is the total uncertainty term; S19. Set the desired attitude trajectory as follows:

[0151] in, For the desired roll angle, For the desired pitch angle, The desired yaw angle; S110. The desired attitude trajectory is set to be at least three times continuously differentiable, and satisfies the following conditions: Both are bounded, meaning they have positive constants. , so that:

[0152] in, Let be the desired attitude trajectory vector. Let the first derivative of the desired attitude trajectory be . Let the second derivative of the desired attitude trajectory be... Let the third derivative of the desired attitude trajectory be... All are positive numbers, representing the upper bounds of their respective derivatives.

[0153] In a specific implementation, as a preferred embodiment of the present invention, step S2 includes: S21. Based on the actual attitude angle and the desired attitude trajectory, define the tracking error as follows:

[0154] in, Let be the attitude tracking error vector. Let the desired attitude trajectory vector be denoted as . S22. Based on the attitude kinematics relationship under the small angle assumption, the derivative of the tracking error is defined as follows:

[0155] S23. Based on the defined tracking error and its derivative, construct the linear sliding surface as follows:

[0156] in, For the selected positive definite diagonal matrix, , For the sliding surface of the rolling channel, For pitch channel sliding surface, For yaw channel sliding surface; S24. Differentiating the constructed linear sliding surface, we obtain:

[0157] S25. Define the total uncertainty term and write the total uncertainty term into the sliding surface dynamics:

[0158] in, For the total uncertain term, This is the input vector for the RBF neural network; S26. Define the hyperbolic tangent vector as follows:

[0159] in, , , All are robust term boundary parameters; S27. Expand the product term in the dynamics of the sliding surface as follows:

[0160] in, Design the parameter matrix for the control law. For robust compensation gain vector, These are the boundary parameters for the robust term.

[0161] In a specific implementation, as a preferred embodiment of the present invention, step S3 includes: S31, Compact set in a closed-loop system Above, define the total uncertainty term. It is continuous, and its online approximation is achieved using the general approximation property of RBF neural networks; S32. Assume that an ideal weight matrix exists. and RBF basis function vectors , so that:

[0162] in, For neural network approximation error, ; S33. Set the neural network approximation error It satisfies the element-bounded condition, i.e., there exists a vector of normal numbers. , making At the same time, it is set that there are normal numbers. , so that:

[0163] S34, the first The RBF basis functions are set as follows:

[0164] in, For the neural network input vector, For the first The center of each hidden layer node, The width of the Gaussian function; S35. Using the estimated weight matrix The estimated value of the total uncertainty term is constructed as follows:

[0165] S36. Define the ideal weight estimation error as follows:

[0166] S37. Considering ideal weights This is unavailable, and traditional direct weight estimation is easily affected by high-frequency disturbances at sea, resulting in estimation oscillations and control input chattering, introducing low-frequency weight estimation errors, as follows:

[0167] Low-frequency weight estimation matrix As The first-order low-pass filter output is used to constrain the rapidly changing direct weight estimation, thereby suppressing the impact of high-frequency disturbances in the marine environment on neural network estimation and control response; S38. Design a low-frequency learning adaptive law for neural network weights, as follows:

[0168] in, For design constants, It is a positive definite symmetric diagonal parameter matrix; S39. In the low-frequency learning adaptive law of the neural network weights, As a leakage correction term to suppress weight drift, As a low-frequency coupling term to constrain fast weight estimation Low-frequency weight estimation The difference between them weakens the high-frequency oscillations caused by weight updates.

[0169] In a specific implementation, as a preferred embodiment of the present invention, step S4 includes: S41. To save on input signal communication, an event-triggered hold strategy is designed so that the control input retains the control command from the previous trigger moment between adjacent trigger moments:

[0170] in, To retain input for event triggering, For the first The control law value is calculated at each trigger moment. For the first The event is triggered at the time. For the next event trigger time, The time interval between two consecutive triggers; S42. Based on the design-based event-triggered persistence strategy, define the event-triggered error as follows:

[0171] S43. Set the channel trigger threshold vector And determine the next trigger time:

[0172] S44, when When, set ;when When no new control input signal is transmitted, the controller value remains unchanged to reduce unnecessary signal transmission and control execution; when any channel meets the trigger threshold, the current moment is determined as the next trigger moment and the control input is updated. S45. Introducing a continuously time-varying coefficient vector To satisfy:

[0173] And we obtain the equivalent form of triggering the hold input, as follows:

[0174] in, This is the Hadamard product, used to represent the element-wise multiplication between the channel trigger threshold and the continuously time-varying coefficients.

[0175] In a specific implementation, as a preferred embodiment of the present invention, step S5 includes: S51. Based on the motor output limit and the allowable control torque range, establish the actuator amplitude saturation model as follows:

[0176] in, This is the actual control input vector. It is a saturation function. To retain input for event triggering, This is the upper limit of the actuator control torque. This is the lower bound of the actuator control torque; S52. Define the saturation error caused by actuator constraints as follows:

[0177] in, The actuator saturation error vector. This is for the saturation error of the roll channel. For pitch channel saturation error, This refers to the yaw channel saturation error. S53. Assume that the saturation error is bounded within the compact set of the closed-loop system, i.e., there exists a normal vector. , so that:

[0178] S54. To compensate for the impact of actuator constraints on the control input, design auxiliary dynamic system states for each attitude channel:

[0179] in, To assist the state vector of the dynamic system, To assist in the dynamic system status of the roll channel, To assist in the dynamic system status of the pitch channel, Provide dynamic system status for yaw channels; S55. Construct an auxiliary dynamic system and differentiate the state of the auxiliary dynamic system as follows:

[0180] in, Nonlinear functions that assist in dynamic systems; S56, For any attitude channel The auxiliary dynamic system is defined element by element as follows:

[0181] in, To assist in the design parameters of dynamic systems, For small design constants; S57. Combining the event-triggered holding mechanism and the actuator saturation model, the actual control input is represented as:

[0182] S58. The actual input is equivalently represented as:

[0183] in, The event-triggered actuator constraint control law, It is a continuously time-varying coefficient vector. This is the trigger threshold vector for each channel.

[0184] In a specific implementation, as a preferred embodiment of the present invention, step S6 includes: S61. Define the intermediate variables of the control law as follows:

[0185] S62. Obtained from the intermediate variables of the defined control law:

[0186] in, This is the RBF neural network estimate of the total uncertainty term; S63. Define the neural network estimation error as follows:

[0187] S64. Based on the defined neural network estimation error, the sliding surface dynamics are written as:

[0188] S65. Using the property of the hyperbolic tangent function: for any real number... and any positive constant ,have:

[0189] S66. Define the robustness term for each attitude channel, as follows:

[0190] in, For the first Robust compensation gain for each attitude channel For the first Sliding surface variables for each attitude channel For the first The width parameter of the hyperbolic tangent function for each attitude channel. Let be the hyperbolic tangent lemma constant; S67. The vector form of the robust term for each attitude channel after definition is as follows:

[0191] S68. Because the neural network approximation error satisfies... ,but:

[0192] S69, Order ,when When the condition holds true by element:

[0193] S610. Set the dynamic upper limit of the sliding surface as follows:

[0194] S611, Set Event Trigger Threshold Compensation Vector and define:

[0195] S612, Generate event-triggered actuator constraint control law, as follows:

[0196] in, To assist the dynamic system feedback gain matrix, Design parameters for the auxiliary dynamic system of the roll channel. Design parameters for the pitch channel auxiliary dynamic system. Design parameters for the yaw channel auxiliary dynamic system; S613, Constrain the control law of the event-triggered actuator. Input event triggers the hold to get The actual control input is then obtained through the actuator saturation stage. This forms a complete event-triggered actuator-constrained attitude tracking closed-loop control structure, such as... Figure 3 As shown.

[0197] In a specific implementation, as a preferred embodiment of the present invention, step S7 includes: S71, For any and any positive constant ,have:

[0198] S72, if Then for any vector The following matrix eigenvalue inequalities are used:

[0199] S73. Employ low-frequency learning weight error relationship: when At that time, there are positive numbers. ,make:

[0200] S74, Set controller parameters to meet requirements Valid by element; Setting auxiliary dynamic system parameters satisfies... and make the matrix ,in, To assist in the analysis of dynamic systems, For auxiliary analysis parameters of the roll channel, To provide auxiliary analysis parameters for the pitch channel, Parameters for auxiliary analysis of yaw channels; S75. Construct the Lyapunov function as follows:

[0201] S76. Calculate the constructed Lyapunov function. The derivative is obtained by:

[0202] S77, Substitute the control law and combine it with the actual input. ,get:

[0203] in, For an effective robust gain vector, For parameters hyperbolic tangent vector function; S78, Utilizing the hyperbolic tangent boundary and get:

[0204] Therefore, we get:

[0205] in, The hyperbolic tangent width parameter vector; S79, Calculation and The derivative is as follows:

[0206]

[0207] in, Let be the positive definite symmetric parameter matrix of the adaptive law. Design a constant for the leakage correction term. Design constants for low-frequency coupling terms. For negative definite terms related to the sliding surface, For leak correction items, This is a low-frequency coupling term; S710, will and By merging, we get:

[0208] S711, due to Then we have:

[0209] S712, Using Inequalities ,get:

[0210] therefore, ; S713. For the auxiliary dynamic system, define the total analysis term for the auxiliary dynamic system as follows:

[0211] in, For the first The auxiliary dynamic system analysis items of the channel, For the first Channel actuator saturation error; S714, when Then:

[0212] Thus obtain ,in, For the first The control efficiency coefficient of the channel; S715, when hour, And:

[0213] in, To assist in the convergence parameters of the dynamic system, For the bounded aggregation constant term, For the first Upper bound of channel saturation error; S716, Define auxiliary dynamic system analysis parameters and take ,get:

[0214] S717, Order and ,get:

[0215] in, To assist the convergence rate matrix of the dynamic system, The rolling channel is used to assist the convergence parameters of the dynamic system. To provide convergence parameters for the dynamic system auxiliary in the pitch channel, The convergence parameters for the yaw channel auxiliary dynamic system are provided. To assist the total aggregate constant term of the dynamic system, For the constant term in the auxiliary dynamic system analysis of the roll channel, For the constant term in the dynamic system analysis of the pitch channel, The constant term is used to assist in the dynamic system analysis of the yaw channel; S718. Combining all the terms, the Lyapunov derivative is obtained as follows:

[0216] in, ; S719, Take ,get:

[0217] S720, utilizing the low-frequency learning weight error relationship, has ,make:

[0218] in, This is the sum of the Lyapunov energy terms corresponding to the neural network weight estimation error and the low-frequency weight estimation error. ; S721, Take ,get:

[0219] in, The attenuation coefficient related to the sliding surface. The weight estimation error is related to the attenuation coefficient. To assist in the state-related attenuation coefficient of the dynamic system; S722. Solving the differential inequality yields:

[0220] S723, taking the limit yields:

[0221] This proves that all signals in a closed-loop system are consistent and eventually bounded, and Finally entered by The determined bounded neighborhood; S724. According to the definition of sliding surface, the error dynamics satisfy:

[0222] because and Consistency is ultimately bounded, therefore It is also consistent that it eventually becomes bounded, and the attitude tracking error converges to a small neighborhood near the origin.

[0223] In a specific implementation, as a preferred embodiment of the present invention, step S8 includes: S81. Define the RBF basis functions. Continuously differentiable, and The system is bounded within a bounded set of closed-loop systems, and the attitude trajectory is expected to satisfy the conditions of third-order continuous differentiability and boundedness. S82, due to the auxiliary dynamic system To avoid singular terms and because the closed-loop signal is bounded, therefore Bounded; S83, in the interval Internally, it is obtained through an event-triggered persistence mechanism:

[0224] S84, derived from the definition of event triggering error:

[0225] S85, obtained from the control law:

[0226] in, ; S86, Yes Taking the derivative, we get:

[0227] in,

[0228] S87, by Learned and Bounded, obtained from the total uncertainty estimate:

[0229] It can be known from the consistent eventual boundedness of closed loops. Bounded; this is known from the RBF basis function assumption. Bounded; as can be seen from the adaptive law. Bounded, therefore Bounded; S88. Combining the boundedness condition of the desired trajectory and the boundedness of the auxiliary dynamic system. Both are bounded, therefore they have positive constants. ,make ,therefore:

[0230] S89. After updating at the trigger time, the trigger error satisfies... Define the minimum trigger threshold as follows:

[0231] S810, According to the triggering mechanism, at the next triggering moment At least one channel reaches the threshold, therefore:

[0232] Therefore, we obtain Therefore:

[0233] make Then any adjacent triggering times satisfy The event will not be triggered an unlimited number of times within a limited time, thus eliminating Zeno behavior.

[0234] In a specific implementation, as a preferred embodiment of the present invention, in order to verify the effectiveness of the proposed event-triggered actuator constrained attitude tracking control method based on RBF neural network, step S9 includes: S91. Using flight rescue equipment as the simulation object, set the moment of inertia of the flight rescue equipment as follows:

[0235] Therefore, ; S92. Set the total simulation time (40s) and sampling time (0.001s). The initial system state is as follows:

[0236] S93. Set the controller parameters as follows:

[0237]

[0238]

[0239]

[0240] S94. Construct an RBF network for each attitude channel, with the network input set as follows:

[0241] in, and These are the attitude estimates and angular velocity estimates for the corresponding channels, respectively. S95. Set the number of hidden layer nodes. The basis function centers are uniformly distributed in Set the RBF widths to 0.55 and 0.95 respectively; S96. Set initial estimated weights Simultaneously, parameter matrices and low-frequency learning parameters are set; among them, The diagonal element is 0.8. The diagonal element is 0.05. ; S97. Set event trigger parameters ; S98. Set the upper and lower limits of the actuator control torque as follows:

[0242]

[0243] S99. Set the initial state and singularity avoidance parameters of the auxiliary dynamic system as follows:

[0244] S910. Select a state-dependent bounded function as follows:

[0245] S911. Select the external disturbance as follows:

[0246] S912. In one embodiment, to simulate a dynamic rescue target, a person who has fallen into the water or a floating rescue target may continue to drift under the influence of wind, waves, and currents. The upper guidance module generates slowly changing attitude commands. Therefore, in the attitude tracking task, the desired attitude trajectory corresponding to the dynamic rescue target is set as follows:

[0247] The results of the examples show that, as Figure 4 , 5 As shown in Figure 6, when there is a deviation between the initial attitude and the desired attitude, the actual attitude angle can converge to the neighborhood of the desired trajectory in a short time and maintain good tracking consistency in subsequent simulations; the angular velocity can track the desired angular velocity well without obvious oscillation or divergence; the attitude error RMSE is 0.039, and the angular velocity error RMSE is 0.051. Figure 7 As shown, the uncertainty estimation results indicate that after introducing low-frequency learning, the estimation curve is smoother and approaches the true uncertainty faster; the RMSE of the neural network estimation error is 0.335 without low-frequency learning, but decreases to 0.124 after introducing low-frequency learning. Figure 8 As shown, the event triggering mechanism does not trigger continuously at every sampling moment, but updates as needed based on changes in control input and error; the number of triggers during the simulation was 202, the communication saving rate was 99.50%, and the minimum event interval was 0.04s, indicating that the event triggering mechanism effectively avoids Zeno behavior. Figure 9 As shown, the nominal control input, actual control input under actuator constraints, and auxiliary dynamic system state indicate that in the initial stage, due to the large attitude error, the nominal control input may briefly approach or reach the actuator constraint boundary. As the error decreases, the control input gradually changes within a smaller range, and both the saturation error and the auxiliary system state gradually converge to the zero neighborhood, indicating that the auxiliary dynamic system can effectively compensate for the adverse effects of actuator constraints.

[0248] S913. In another embodiment, to simulate a static rescue target, when the sea state is relatively calm or the drift of the rescue target is negligible, the main task of the flight rescue equipment is to maintain a stable attitude near the rescue location for hovering, observation, or precise delivery. Therefore, in the attitude stabilization task, the desired attitude command corresponding to the static rescue target is set as follows:

[0249] S914. The attitude tracking performance, uncertainty estimation smoothness, communication update saving effect, actuator saturation compensation effect, and Zeno-free behavior of the attitude tracking control method of the flight rescue equipment are verified by using attitude angle tracking curve, angular velocity tracking curve, tracking error curve, RBF uncertainty estimation curve, event trigger interval, and actuator saturation control input curve.

[0250] The results of this embodiment show that, as Figure 10 , 11 As shown, when the initial attitude angle deviates significantly from the zero reference command, the proposed control law enables the roll, pitch, and yaw angles to converge rapidly to near zero and remain stable after a brief transient. Although the angular velocity exhibits a brief peak in the initial stage due to the large initial attitude error and actuator constraints, it subsequently decays rapidly to the zero neighborhood without sustained oscillation or divergence. Figure 12 As shown, the overall attitude error RMSE is 0.032 rad, and the overall angular velocity error RMSE is 0.040 rad / s; within the steady-state range of 10s to 40s, the attitude error RMSE is 0.00145 rad, and the angular velocity error RMSE is 0.00118 rad / s, indicating that the system has high steady-state stabilization accuracy. Figure 13 As shown, the RMSE of the neural network estimation error is 0.340 without low-frequency learning, and drops to 0.107 after introducing low-frequency learning. This indicates that the low-frequency learning mechanism can suppress unnecessary high-frequency fluctuations in the estimation process and improve the robustness of the uncertainty approximation. Figure 14 As shown, the total number of triggered events was 216, the communication saving rate was 99.46%, and the minimum event interval was 0.04s; all adjacent trigger intervals were positive, indicating that the event triggering mechanism significantly reduced the control update frequency while avoiding Zeno behavior. Figure 15 As shown, the nominal control input may temporarily exceed the actuator constraint in the initial transient phase due to the large initial deviation, but the actuator saturation module keeps the actual control torque within the allowable range; the saturation induced error and the auxiliary system state gradually converge to near zero, indicating that the auxiliary dynamic system can compensate for the actuator saturation effect and maintain the stability of the closed-loop system.

[0251] In summary, this invention addresses the attitude tracking control problem of maritime flight rescue equipment under conditions of model uncertainty, external disturbances, actuator constraints, and limited communication resources. It establishes a simplified attitude model under the small-angle assumption, treating coupling effects, parameter perturbations, unmodeled dynamics, and external disturbances as total uncertainties. An RBF neural network with low-frequency learning is used to improve uncertainty compensation and constrain the rapid weight update process, reducing high-frequency estimation fluctuations and improving control input smoothness. An event-triggered actuator-constrained control scheme is designed, and the saturation effect caused by actuator limitations is compensated through an auxiliary dynamic system. Theoretical analysis shows that all signals in the closed-loop system are uniformly bounded, the attitude tracking error converges to a small neighborhood near the origin, and the event-triggered mechanism does not exhibit Zeno behavior. Simulation results further demonstrate that this invention can achieve accurate attitude and angular velocity tracking, smoother uncertainty estimation, fewer control update cycles, and effective actuator constraint compensation.

[0252] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for attitude tracking control of flight rescue equipment based on low-frequency learning and event triggering mechanisms, characterized in that, include: S1. Under the assumption of small angle, establish a simplified attitude dynamics model of the flight rescue equipment, obtain the attitude angle vector, body angular velocity vector, moment of inertia matrix, control input signal and external disturbance torque of the flight rescue equipment, and combine the model coupling terms, parameter perturbation, unmodeled dynamics, simplified modeling error and external disturbance into the total uncertainty term; S2. Define the attitude tracking error based on the actual attitude angle and the desired attitude trajectory, construct a linear sliding surface, and obtain the dynamic equation of the sliding surface that includes the total uncertainty term, control input, and reference trajectory acceleration. S3. Construct an RBF neural network to approximate the total uncertainty term online, define the ideal weight matrix, basis function vector, approximation error and estimated weight matrix, and introduce a low-frequency weight estimation matrix and design a low-frequency learning adaptive law. S4. Design an event trigger holding mechanism, define the event trigger error and the channel trigger threshold, so that the control input remains unchanged between adjacent trigger times, and the control input is updated when the trigger error reaches the threshold. S5. Establish an actuator amplitude saturation model, define the saturation error caused by actuator constraints, and construct an auxiliary dynamic system to compensate for the adverse effects of actuator saturation on closed-loop attitude control performance. S6. Define intermediate variables for the control law, and combine the estimated values ​​of the RBF neural network, the robust hyperbolic tangent term, the event-triggered error compensation term, and the auxiliary dynamic system state to generate the event-triggered actuator constrained attitude tracking control law. S7. Based on the Lyapunov stability theory, construct a Lyapunov function that includes the sliding surface, neural network weight estimation error, low-frequency weight estimation error and auxiliary dynamic system state. Prove that all signals in the closed-loop system are consistent and eventually bounded and that the attitude tracking error converges to a small neighborhood near the origin. S8. Based on the boundedness of the derivative of the event triggering error, it is proved that there is a positive lower bound between any two adjacent triggering times, thus excluding Zeno behavior; S9. Set the moment of inertia, initial state, control parameters, RBF neural network parameters, event trigger threshold, actuator saturation upper and lower bounds, external disturbances, and reference attitude trajectory of the flight rescue equipment. Verify the effectiveness of the flight rescue equipment attitude tracking control method through attitude tracking and attitude stabilization tasks.

2. The attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism according to claim 1, characterized in that, Step S1 includes: S11. Define the inertial coordinate system of the flight rescue equipment. and the body coordinate system fixed at the center of mass of the flight rescue equipment Define roll angle Pitch angle and yaw angle Define the lift generated by the four rotors as follows: Adjacent rotors rotate in opposite directions to balance the counter-torque and achieve attitude adjustment; S12. Establish the kinematic equations for the posture as follows: in, The attitude angle vector, The angular velocity vector of the machine system. Here is the attitude kinematics transformation matrix; S13. Establish the attitude dynamics equations as follows: in For the rotational inertia matrix of flight rescue equipment, For system control input signals, External disturbance torque; S14. Based on the fact that flight rescue equipment mainly serves low-altitude delivery, close-range hovering, and fixed-point rescue missions, and that the system typically operates within a relatively stable small attitude angle range without involving violent rolls or large maneuvers, the small-angle assumption is adopted without sacrificing the main control characteristics, and the attitude kinematic equations are simplified as follows: S15. Define the state vector as follows: in, For the roll angular velocity, The pitch angular velocity, Yaw angular velocity; S16. Expand the attitude dynamics equations as follows: S17. The attitude system of flight rescue equipment shall be written as: in, To control the efficiency matrix, This represents the control efficiency coefficient of the roll channel. This represents the control efficiency coefficient of the pitch channel. The control efficiency coefficient for the yaw channel; To account for lumped nonlinear terms and model uncertainties, This represents parameter perturbation, unmodeled dynamics, and simplified modeling errors; External disturbance term; S18. Combine the model coupling terms, parameter perturbations, unmodeled dynamics, simplified modeling errors, and external disturbances into a total uncertainty term to obtain an equivalent second-order attitude model, as follows: in, This represents the total uncertainty term; S19. Set the desired attitude trajectory as follows: in, For the desired roll angle, For the desired pitch angle, The desired yaw angle; S110. The desired attitude trajectory is set to be at least three times continuously differentiable, and satisfies the following conditions: Both are bounded, meaning they have positive constants. , so that: in, Let be the desired attitude trajectory vector. Let the first derivative of the desired attitude trajectory be . Let the second derivative of the desired attitude trajectory be... Let the third derivative of the desired attitude trajectory be... All are positive numbers, representing the upper bounds of their respective derivatives.

3. The attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism according to claim 1, characterized in that, Step S2 includes: S21. Based on the actual attitude angle and the desired attitude trajectory, define the tracking error as follows: in, Let be the attitude tracking error vector. Let the desired attitude trajectory vector be denoted as . S22. Based on the attitude kinematics relationship under the small angle assumption, the derivative of the tracking error is defined as follows: S23. Based on the defined tracking error and its derivative, construct the linear sliding surface as follows: in, For the selected positive definite diagonal matrix, , For the sliding surface of the rolling channel, For pitch channel sliding surface, For yaw channel sliding surface; S24. Differentiating the constructed linear sliding surface, we obtain: S25. Define the total uncertainty term and write the total uncertainty term into the sliding surface dynamics: in, For the total uncertain term, This is the input vector for the RBF neural network; S26. Define the hyperbolic tangent vector as follows: in, , , All are robust term boundary parameters; S27. Expand the product term in the dynamics of the sliding surface as follows: in, Design the parameter matrix for the control law. For robust compensation gain vector, These are the boundary parameters for the robustness term.

4. The attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism according to claim 1, characterized in that, Step S3 includes: S31, Compact set in a closed-loop system Above, define the total uncertainty term. It is continuous, and its online approximation is achieved using the general approximation property of RBF neural networks; S32. Assume that an ideal weight matrix exists. and RBF basis function vectors , so that: in, For neural network approximation error, ; S33. Set the neural network approximation error It satisfies the element-bounded condition, i.e., there exists a vector of normal numbers. , making At the same time, it is set that there are normal numbers. , so that: S34, the first The RBF basis functions are set as follows: in, For the neural network input vector, For the first The center of each hidden layer node, The width of the Gaussian function; S35. Using the estimated weight matrix The estimated value of the total uncertainty term is constructed as follows: S36. Define the ideal weight estimation error as follows: S37. Considering ideal weights This is unavailable, and traditional direct weight estimation is easily affected by high-frequency disturbances at sea, resulting in estimation oscillations and control input chattering, introducing low-frequency weight estimation errors, as follows: Low-frequency weight estimation matrix As The first-order low-pass filter output is used to constrain the rapidly changing direct weight estimation, thereby suppressing the impact of high-frequency disturbances in the marine environment on neural network estimation and control response; S38. Design a low-frequency learning adaptive law for neural network weights, as follows: in, For design constants, It is a positive definite symmetric diagonal parameter matrix; S39. In the low-frequency learning adaptive law of the neural network weights, As a leakage correction term to suppress weight drift, As a low-frequency coupling term to constrain fast weight estimation Low-frequency weight estimation The difference between them weakens the high-frequency oscillations caused by weight updates.

5. The attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism according to claim 1, characterized in that, Step S4 includes: S41. To save on input signal communication, an event-triggered hold strategy is designed so that the control input retains the control command from the previous trigger moment between adjacent trigger moments: in, To retain input for event triggering, For the first The control law value is calculated at each trigger moment. For the first The event is triggered at the time. For the next event trigger time, The time interval between two consecutive triggers; S42. Based on the design-based event-triggered persistence strategy, define the event-triggered error as follows: S43. Set the channel trigger threshold vector And determine the next trigger time: S44, when When, set ;when When no new control input signal is transmitted, the controller value remains unchanged to reduce unnecessary signal transmission and control execution; when any channel meets the trigger threshold, the current moment is determined as the next trigger moment and the control input is updated. S45. Introducing a continuously time-varying coefficient vector To satisfy: And we obtain the equivalent form of triggering the hold input, as follows: in, This is the Hadamard product, used to represent the element-wise multiplication between the channel trigger threshold and the continuously time-varying coefficients.

6. The attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism according to claim 1, characterized in that, Step S5 includes: S51. Based on the motor output limit and the allowable control torque range, establish the actuator amplitude saturation model as follows: in, This is the actual control input vector. It is a saturation function. To retain input for event triggering, This is the upper limit of the actuator control torque. This is the lower bound of the actuator control torque; S52. Define the saturation error caused by actuator constraints as follows: in, The actuator saturation error vector, This is for the saturation error of the roll channel. For pitch channel saturation error, This refers to the yaw channel saturation error. S53. Assume that the saturation error is bounded within the compact set of the closed-loop system, i.e., there exists a normal vector. , so that: S54. To compensate for the impact of actuator constraints on the control input, design auxiliary dynamic system states for each attitude channel: in, To assist the state vector of the dynamic system, To assist in the dynamic system status of the roll channel, To assist in the dynamic system status of the pitch channel, Provide dynamic system status for yaw channels; S55. Construct an auxiliary dynamic system and differentiate the state of the auxiliary dynamic system as follows: in, Nonlinear functions that assist in dynamic systems; S56, For any attitude channel The auxiliary dynamic system is defined element by element as follows: in, To assist in the design parameters of dynamic systems, For small design constants; S57. Combining the event-triggered holding mechanism and the actuator saturation model, the actual control input is represented as: S58. The actual input is equivalently represented as: in, It is a continuously time-varying coefficient vector. This is the trigger threshold vector for each channel.

7. The attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism according to claim 1, characterized in that, Step S6 includes: S61. Define the intermediate variables of the control law as follows: S62. Obtained from the intermediate variables of the defined control law: in, This is the RBF neural network estimate of the total uncertainty term; S63. Define the neural network estimation error as follows: S64. Based on the defined neural network estimation error, the sliding surface dynamics are written as: S65. Using the property of the hyperbolic tangent function: for any real number... and any positive constant ,have: S66. Define the robustness term for each attitude channel, as follows: in, For the first Robust compensation gain for each attitude channel For the first Sliding surface variables for each attitude channel For the first The width parameter of the hyperbolic tangent function for each attitude channel. Let be the hyperbolic tangent lemma constant; S67. The vector form of the robust term for each attitude channel after definition is as follows: S68. Because the neural network approximation error satisfies... ,but: S69, Order ,when When the condition holds true by element: S610. Set the dynamic upper limit of the sliding surface as follows: S611, Set Event Trigger Threshold Compensation Vector and define: S612, Generate event-triggered actuator constraint control law, as follows: in, To assist the dynamic system feedback gain matrix, Design parameters for the auxiliary dynamic system of the roll channel. Design parameters for the pitch channel auxiliary dynamic system. Design parameters for the yaw channel auxiliary dynamic system; S613, Constrain the control law of the event-triggered actuator. Input event triggers the hold to get The actual control input is then obtained through the actuator saturation stage. This forms a complete event-triggered actuator constrained attitude tracking closed-loop control structure.

8. The attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism according to claim 1, characterized in that, Step S7 includes: S71, For any and any positive constant ,have: S72, if Then for any vector The following matrix eigenvalue inequalities are used: S73. Employ low-frequency learning weight error relationship: when At that time, there are positive numbers. ,make: S74, Set controller parameters to meet requirements Valid by element; Setting auxiliary dynamic system parameters satisfies... and make the matrix ,in, To assist in the analysis of dynamic systems, For auxiliary analysis parameters of the roll channel, To provide auxiliary analysis parameters for the pitch channel, Parameters for auxiliary analysis of yaw channels; S75. Construct the Lyapunov function as follows: S76. Calculate the constructed Lyapunov function. The derivative is obtained by: S77, Substitute the control law and combine it with the actual input. ,get: in, For an effective robust gain vector, For parameters hyperbolic tangent vector function; S78, Utilizing the hyperbolic tangent boundary and get: Therefore, we get: in, The hyperbolic tangent width parameter vector; S79, Calculation and The derivative is as follows: in, Let be the positive definite symmetric parameter matrix of the adaptive law. Design a constant for the leakage correction term. Design constants for low-frequency coupling terms. For negative definite terms related to the sliding surface, For leak correction items, This is a low-frequency coupling term; S710, will and By merging, we get: S711, due to Then we have: S712, Using Inequalities ,get: therefore, ; S713. For the auxiliary dynamic system, define the total analysis term for the auxiliary dynamic system as follows: in, For the first The auxiliary dynamic system analysis items of the channel, For the first Channel actuator saturation error; S714, when Then: Thus obtain ,in, For the first The control efficiency coefficient of the channel; S715, when hour, And: in, To assist in the convergence parameters of the dynamic system, For the bounded aggregation constant term, For the first Upper bound of channel saturation error; S716, Define auxiliary dynamic system analysis parameters and take ,get: S717, Order and ,get: in, To assist the convergence rate matrix of the dynamic system, The rolling channel is used to assist the convergence parameters of the dynamic system. The pitch channel is used to assist the convergence parameters of the dynamic system. The convergence parameters for the yaw channel auxiliary dynamic system are provided. To assist the total aggregate constant term of the dynamic system, For the constant term in the auxiliary dynamic system analysis of the roll channel, For the constant term in the dynamic system analysis of the pitch channel, The constant term is used to assist in the dynamic system analysis of the yaw channel; S718. Combining all the terms, the Lyapunov derivative is obtained as follows: in, ; S719, Take ,get: S720, utilizing the low-frequency learning weight error relationship, has ,make: in, This is the sum of the Lyapunov energy terms corresponding to the neural network weight estimation error and the low-frequency weight estimation error. ; S721, Take ,get: in, The attenuation coefficient related to the sliding surface. The weight estimation error is related to the attenuation coefficient. To assist in the state-related attenuation coefficient of the dynamic system; S722. Solving the differential inequality yields: S723, taking the limit yields: This proves that all signals in a closed-loop system are consistent and eventually bounded, and Finally entered by The determined bounded neighborhood; S724. According to the definition of sliding surface, the error dynamics satisfy: because and Consistency is ultimately bounded, therefore It is also consistent that it eventually becomes bounded, and the attitude tracking error converges to a small neighborhood near the origin.

9. The attitude tracking control method for flight rescue equipment based on low-frequency learning and event triggering mechanism according to claim 1, characterized in that, Step S8 includes: S81. Define the RBF basis functions Continuously differentiable, and The system is bounded within a bounded set of closed-loop systems, and the attitude trajectory is expected to satisfy the conditions of third-order continuous differentiability and boundedness. S82, due to the auxiliary dynamic system To avoid singular terms and because the closed-loop signal is bounded, therefore Bounded; S83, in the interval Internally, it is obtained through an event-triggered persistence mechanism: S84, derived from the definition of event triggering error: S85, obtained from the control law: in, ; S86, Yes Taking the derivative, we get: in, S87, by Learned and Bounded, obtained from the total uncertainty estimate: It can be known from the consistent eventual boundedness of closed loops. Bounded; this is known from the RBF basis function assumption. Bounded; as can be seen from the adaptive law. Bounded, therefore Bounded; S88. Combining the boundedness condition of the desired trajectory and the boundedness of the auxiliary dynamic system. Both are bounded, therefore they have positive constants. ,make ,therefore: S89. After updating at the trigger time, the trigger error satisfies... Define the minimum trigger threshold as follows: S810, According to the triggering mechanism, at the next triggering moment At least one channel reaches the threshold, therefore: Therefore, we obtain Therefore: make Then any adjacent triggering times satisfy The event will not be triggered an unlimited number of times within a limited time, thus eliminating Zeno behavior.

10. The attitude tracking control method for flight rescue equipment based on a low-frequency learning and event-triggered mechanism according to claim 1, characterized in that, Step S9 includes: S91. Set the moment of inertia of the flight rescue equipment as follows: Therefore, ; S92. Set the total simulation time and sampling time. The initial system state is as follows: S93. Set the controller parameters as follows: S94. Construct an RBF network for each attitude channel, with the network input set as follows: in, and These are the attitude estimates and angular velocity estimates for the corresponding channels, respectively. S95. Set the number of hidden layer nodes. The basis function centers are uniformly distributed in Set the RBF width; S96. Set initial estimated weights Simultaneously set the parameter matrix and low-frequency learning parameters; S97. Set event trigger parameters ; S98. Set the upper and lower limits of the actuator control torque as follows: S99. Set the initial state and singularity avoidance parameters of the auxiliary dynamic system as follows: S910. Select the state-dependent bounded function and the external disturbance as follows: S911. In the attitude tracking task, the desired attitude trajectory corresponding to the dynamic rescue target is set as follows: S912. In the attitude stabilization mission, the desired attitude command for the static rescue target is set as follows: S913. The attitude tracking performance, uncertainty estimation smoothness, communication update saving effect, actuator saturation compensation effect, and Zeno-free behavior of the attitude tracking control method of the flight rescue equipment are verified by using attitude angle tracking curve, angular velocity tracking curve, tracking error curve, RBF uncertainty estimation curve, event trigger interval, and actuator saturation control input curve.

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