Trajectory tracking control method and system based on predefined time observer and neural network

Abstract

The invention relates to a trajectory tracking control method and system based on a predefined time observer and a neural network. The method comprises the following steps: defining a trajectory tracking error and deriving to obtain an error derivative; constructing a predefined time observer, estimating a state and composite disturbance which cannot be directly measured by the controlled system, and converging an observation error within a preset time to obtain a state estimation result; constructing a non-singular fast terminal sliding mode variable; carrying out online approximation by adopting a neural network, updating the weight of the neural network in real time based on the sliding mode variable, and outputting a compensation item through the neural network; and combining the state estimation result, the sliding mode variable and the compensation item to construct a trajectory tracking control law, and applying the trajectory tracking control law to a controlled system, so that a trajectory tracking error is converged to zero or a preset neighborhood within a preset time. The stable convergence of the trajectory tracking error within the predefined time can be realized, and the dynamic response performance and the tracking precision of the system are improved.

Description

Technical Field

[0001] This invention relates to the field of robot trajectory tracking technology, and in particular to a trajectory tracking control method and system based on a predefined time observer and a neural network. Background Technology

[0002] Trajectory tracking control, as one of the core research directions in the field of automatic control, has been widely used in many key scenarios such as autonomous flight of UAVs, navigation and obstacle avoidance of unmanned vessels, collaborative operation of robots, and precision operation of complex electromechanical equipment due to its precise control over motion paths. It has become an important technical support for promoting the development of intelligent equipment. However, in actual engineering environments, the controlled systems mentioned above face complex problems such as model parameter uncertainty, unmodeled dynamics, and unknown external disturbances. This makes it difficult to achieve high-precision and fast trajectory tracking control while ensuring system stability, which seriously restricts the application efficiency of the system in complex scenarios. To improve the robustness of the system, sliding mode control has been widely studied and applied due to its strong ability to suppress model uncertainty and external disturbances. This method designs discontinuous control inputs to force the system state to move along a preset sliding surface, thereby effectively suppressing the influence of disturbances and uncertainties. However, traditional sliding mode control can only achieve asymptotic stability of the system, that is, the error needs to converge to zero over an infinite amount of time. Moreover, the discontinuity of the control input is prone to chattering, which not only affects the control accuracy but may also cause wear and tear on the actuator, which is not conducive to the stable and reliable operation of the system.

[0003] To address the slow convergence speed, terminal sliding mode control and fast terminal sliding mode control methods have emerged. These methods introduce nonlinear terminal terms to enable the system state to converge within a finite time, significantly improving the dynamic response speed. However, when the trajectory tracking error approaches zero, these methods often exhibit singularity problems, leading to abnormal surges in control input. This not only compromises the system's control stability but may also cause equipment failure, severely limiting their feasibility in engineering practice. Meanwhile, in practical engineering applications, due to limitations in sensor measurement range, accuracy, and cost, some key system state variables and external complex disturbances are difficult to obtain directly, requiring indirect estimation using state observers. Currently, most mainstream observation methods employ asymptotic convergence or finite-time convergence mechanisms. Their convergence speed and final convergence time are highly dependent on the system's initial state, making it impossible to pre-set the convergence time according to engineering requirements. This hinders precise constraints on the system's transient performance and fails to meet scenarios with strict response time requirements.

[0004] In recent years, adaptive approximation techniques such as neural networks have been widely used to compensate for unknown nonlinear characteristics and external disturbances in systems due to their powerful nonlinear fitting capabilities, providing new ideas for solving model uncertainty problems. However, in practical applications, if an efficient state estimation mechanism is lacking to provide accurate state information, and a stable and fast control framework is not constructed as support, the approximation accuracy of neural networks is easily affected by observation errors and measurement noise, and its compensation effect will be greatly reduced, making it difficult to fully realize its adaptive advantages.

[0005] Therefore, traditional trajectory tracking control methods often suffer from low tracking accuracy and dynamic response performance in complex environments due to significant shortcomings in convergence time controllability, singularity avoidance, and robustness improvement. Summary of the Invention

[0006] In order to solve the above-mentioned technical problems, a trajectory tracking control method and system based on a predefined time observer and a neural network is provided. This method can achieve stable convergence of trajectory tracking error within a predefined time and improve the dynamic response performance and tracking accuracy of the system.

[0007] A trajectory tracking control method based on a predefined time observer and a neural network, the method comprising:

[0008] Obtain the actual state vector and the desired trajectory state vector of the controlled system, define the trajectory tracking error based on the actual state vector and the desired trajectory state vector, and obtain the error derivative by taking the derivative of the trajectory tracking error;

[0009] Based on the controlled system, a predefined time observer is constructed for the system state and composite disturbance, and the observation error is defined; the state and composite disturbance of the controlled system that cannot be directly measured are estimated through the predefined time observer, and the observation error is made to converge within a preset time to obtain the state estimation result;

[0010] Using the trajectory tracking error and error derivative, a non-singular fast terminal sliding mode variable is constructed;

[0011] A neural network is used to approximate the unknown nonlinearity and external disturbances in the controlled system online, and the weights of the neural network are updated in real time based on the sliding mode variables. The compensation term is output through the neural network.

[0012] The trajectory tracking control law is constructed by combining the state estimation results, sliding mode variables, and compensation terms, and then applied to the controlled system so that the trajectory tracking error converges to zero or a preset neighborhood within a preset time.

[0013] In one embodiment, the actual state vector and the desired trajectory state vector of the controlled system are obtained, and a trajectory tracking error is defined based on the actual state vector and the desired trajectory state vector. The derivative of the trajectory tracking error is obtained by taking the derivative of the error, including:

[0014] The system's real-time operating data is collected by the sensors of the controlled system, and the real-time operating data is preprocessed to form an actual state vector containing the system's motion state; the desired trajectory state vector of the controlled system is obtained, and the desired trajectory state vector and its first derivative are known and bounded.

[0015] Calculate the difference between the actual state vector and the desired trajectory state vector, and define the difference as the trajectory tracking error;

[0016] The difference between the first derivative of the actual state vector and the first derivative of the desired trajectory state vector is obtained by taking the derivative of the trajectory tracking error, and the difference is used as the error derivative.

[0017] In one embodiment, a predefined time observer of the system state and composite disturbances is constructed based on the controlled system, and the observation error is defined, including:

[0018] A dual-channel observer framework comprising a state estimation channel and a composite perturbation estimation channel is constructed. The state estimation channel constructs the state estimation dynamic equation based on the known dynamic equations of the system and introduces a continuous nonlinear error feedback function related to predefined time parameters. The composite perturbation estimation channel constructs the composite perturbation estimation equation using the observation error as input. The construction of the predefined time observer is then completed.

[0019] Set the convergence time of the observation error and design the observer gain parameters;

[0020] The observation error is defined as the difference between the actual state of the controlled system, which cannot be directly measured, and the state estimate output by the observer, forming an error vector.

[0021] Construct a Lyapunov function for the observation error and verify the derivative of the Lyapunov function. Observation errors that pass the verification converge within a predefined time.

[0022] In one embodiment, the state and composite disturbances of the controlled system that cannot be directly measured are estimated using the predefined time observer, and the observation error is converged within a pre-set time to obtain the state estimation result, including:

[0023] Start the predefined time observer and initialize the state estimate, composite disturbance estimate and various design parameters;

[0024] After initializing the parameters, the time observer takes the real-time measurement data and control input of the controlled system as inputs, and dynamically adjusts the state estimation value through the state estimation channel and tracks the dynamic changes of the composite disturbance in real time through the composite disturbance estimation channel until a predefined time is reached.

[0025] After a predefined time is reached, the observation error converges to zero or a preset neighborhood, the disturbance estimate is updated, and the state estimation result is obtained.

[0026] In one embodiment, the non-singular fast terminal sliding mode variables are constructed using the trajectory tracking error and the error derivative, including:

[0027] Obtain control parameters and terminal index parameters, and select a sign function that represents the conformity of the variables;

[0028] Calculate the non-singular fast terminal sliding mode variable based on the trajectory tracking error, error derivative, control parameters, terminal type exponential parameter, and sign function.

[0029] In one embodiment, a neural network is used to approximate the unknown nonlinearities and external disturbances in the controlled system online, and the neural network weights are updated in real time based on the sliding mode variables. The neural network outputs a compensation term, including:

[0030] Select a suitable feedforward neural network and initialize the parameters in the neural network;

[0031] The system status data is collected and preprocessed in real time and used as the input to the neural network to initiate online approximation;

[0032] Based on the sliding mode variable feedback after online approximation, the neural network weights are adjusted in real time through adaptive updates; the neural network calculates and outputs the compensation term based on the adjusted neural network weights.

[0033] In one embodiment, a trajectory tracking control law is constructed by combining the state estimation results, sliding mode variables, and compensation terms, including:

[0034] The state estimation results, sliding mode variables, and compensation terms are verified to ensure that the information dimensions of the state estimation results, sliding mode variables, and compensation terms are consistent, the timing is synchronized, and they are effective.

[0035] Based on the verified state estimation results, sliding mode variables, compensation terms, and positive definite control gain matrix, a trajectory tracking control law is constructed.

[0036] In one embodiment, the trajectory tracking control law is applied to the controlled system so that the trajectory tracking error converges to zero or a preset neighborhood within a preset time period, including:

[0037] The control cycle is acquired, and the trajectory tracking control law is applied to the controlled system according to the control cycle;

[0038] The neural network weights, trajectory tracking error, state estimation results, and trajectory tracking control law are iteratively updated, and the trajectory tracking error convergence process is dynamically monitored, converging to zero or a preset neighborhood within a preset time.

[0039] A trajectory tracking control system based on a predefined time observer and a neural network, the system comprising:

[0040] The trajectory tracking error construction module is used to obtain the actual state vector and the desired trajectory state vector of the controlled system, define the trajectory tracking error based on the actual state vector and the desired trajectory state vector, and obtain the error derivative by taking the derivative of the trajectory tracking error.

[0041] The time observer construction and state estimation module is used to construct a predefined time observer for the system state and composite disturbances based on the controlled system, and define the observation error; estimate the state and composite disturbances of the controlled system that cannot be directly measured through the predefined time observer, and make the observation error converge within a preset time to obtain the state estimation result;

[0042] The sliding mode variable construction module is used to construct non-singular fast terminal sliding mode variables using the trajectory tracking error and error derivative;

[0043] The online approximation and compensation module is used to approximate the unknown nonlinearity and external disturbances in the controlled system online using a neural network, and to update the neural network weights in real time based on the sliding mode variables, and output compensation terms through the neural network.

[0044] The trajectory tracking control module is used to construct a trajectory tracking control law by combining the state estimation results, sliding mode variables, and compensation terms, and to apply the trajectory tracking control law to the controlled system so that the trajectory tracking error converges to zero or a preset neighborhood within a preset time.

[0045] The trajectory tracking control method and system described above, based on a predefined time observer and a neural network, can achieve rapid estimation of system state and complex disturbances by introducing a predefined time observer; it can accelerate error convergence and avoid the terminal sliding mode singularity problem by using a non-singular fast terminal sliding mode structure; and it can significantly improve the robustness of the control system and trajectory tracking accuracy under uncertain environments by combining the neural network for online compensation of unknown nonlinearities. Attached Figure Description

[0046] Figure 1This is an application environment diagram of a trajectory tracking control method based on a predefined time observer and a neural network in one embodiment;

[0047] Figure 2 This is a flowchart illustrating a trajectory tracking control method based on a predefined time observer and a neural network in one embodiment.

[0048] Figure 3 This is a schematic diagram of a trajectory tracking control framework based on a predefined time observer and a neural network in one embodiment;

[0049] Figure 4 This is a schematic diagram of the coordinate system of an unmanned vessel in one embodiment;

[0050] Figure 5 This is a schematic diagram of the framework for trajectory tracking control of a non-singular fast terminal sliding mode unmanned surface vessel based on a predefined time observer and a neural network in one embodiment.

[0051] Figure 6 This is a schematic diagram of the observation results of velocity error in a trajectory tracking control method based on a predefined time observer and a neural network in one embodiment;

[0052] Figure 7 This is a schematic diagram illustrating the online estimation effect of a neural network on unknown nonlinear terms of a system in one embodiment;

[0053] Figure 8 This is a schematic diagram comparing the system trajectory tracking position error under different control methods in one embodiment;

[0054] Figure 9 This is a schematic diagram comparing the system trajectory tracking speed error under different control methods in one embodiment;

[0055] Figure 10 This is a schematic diagram illustrating the process of changing the system control input signal in one embodiment;

[0056] Figure 11 This is a block diagram of a trajectory tracking control system based on a predefined time observer and a neural network in one embodiment;

[0057] Figure 12 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0059] The trajectory tracking control method based on a predefined time observer and a neural network provided in this application can be applied to, for example... Figure 1 The application environment shown. For example... Figure 1 As shown, the application environment includes computer device 110. Computer device 110 can acquire the actual state vector and the desired trajectory state vector of the controlled system, define the trajectory tracking error based on the actual state vector and the desired trajectory state vector, and obtain the error derivative by differentiating the trajectory tracking error. Computer device 110 can construct a predefined time observer of the system state and composite disturbances based on the controlled system, and define the observation error. It estimates the unmeasurable state and composite disturbances of the controlled system through the predefined time observer, and makes the observation error converge within a pre-set time to obtain the state estimation result. Computer device 110 can construct a non-singular fast terminal sliding mode variable using the trajectory tracking error and the error derivative. Computer device 110 can use a neural network to approximate the unknown nonlinearities and external disturbances in the controlled system online, and update the neural network weights in real time based on the sliding mode variable, outputting a compensation term through the neural network. Computer device 110 can combine the state estimation result, the sliding mode variable, and the compensation term to construct a trajectory tracking control law, and apply the trajectory tracking control law to the controlled system, making the trajectory tracking error converge to zero or a preset neighborhood within a preset time. Among them, computer equipment 110 may include, but is not limited to, various personal computers, laptops, smartphones, robots, unmanned aerial vehicles, tablets, and other devices.

[0060] In one embodiment, such as Figure 2 As shown, a trajectory tracking control method based on a predefined time observer and a neural network is provided, applied to nonlinear dynamic systems with model uncertainties and external disturbances, to achieve stable convergence of trajectory tracking errors within a predefined time and improve the dynamic response performance and engineering applicability of the system; the method includes the following steps:

[0061] Step 202: Obtain the actual state vector and the desired trajectory state vector of the controlled system, define the trajectory tracking error based on the actual state vector and the desired trajectory state vector, and obtain the error derivative by taking the derivative of the trajectory tracking error.

[0062] First, it is necessary to clarify the method for measuring the deviation between the actual state and the expected state, so as to provide a clear target for subsequent error suppression.

[0063] In one embodiment, the provided trajectory tracking control method based on a predefined time observer and a neural network may further include a process of trajectory error modeling and control target definition. Specifically, this process includes: acquiring real-time operating data of the controlled system through sensors, preprocessing the real-time operating data to form an actual state vector containing the system's motion state; obtaining the desired trajectory state vector of the controlled system, where the desired trajectory state vector and its first derivative are known and bounded; calculating the difference between the actual state vector and the desired trajectory state vector, and defining the difference as the trajectory tracking error; and differentiating the trajectory tracking error to obtain the difference between the first derivative of the actual state vector and the first derivative of the desired trajectory state vector, using this difference as the error derivative.

[0064] Computer devices can obtain the actual state vector of the controlled system. and the desired trajectory state vector Define trajectory tracking error for: Next, the derivative of the trajectory tracking error is obtained. : ;in, This represents the actual state vector of the controlled system. Represents the desired trajectory state vector. Let be the first derivative of the desired trajectory, and Both its derivative and its derivative are known and bounded.

[0065] Specifically, in this embodiment, the computer device can first collect real-time operating data of the controlled system through its sensors and integrate this data into an actual state vector. The actual state vector contains key state information required for the controlled system to achieve trajectory tracking, and it must completely describe the motion state of the controlled system. Furthermore, the collected data must be filtered to remove measurement noise. Simultaneously, the computer device can determine the desired trajectory state vector based on a preset path, task objective, etc. The desired trajectory state vector is the ideal state sequence that the controlled system needs to track, such as the position, heading angle, and corresponding velocity sequence corresponding to the desired navigation path of an unmanned surface vessel, or the joint state sequence corresponding to the desired motion trajectory of a robot's end effector. The desired trajectory state vector needs to be pre-generated using a path planning algorithm, and it and its first derivative must satisfy known and bounded conditions to ensure the effectiveness of subsequent calculations.

[0066] Step 204: Construct a predefined time observer for the system state and composite disturbances based on the controlled system, and define the observation error; estimate the state and composite disturbances of the controlled system that cannot be directly measured through the predefined time observer, and make the observation error converge within a pre-set time to obtain the state estimation result.

[0067] Computer equipment can introduce a predefined time mechanism to enable the state estimation error and trajectory tracking error of the controlled system to converge within a pre-set time range, thereby achieving precise constraints on the transient performance of the controlled system.

[0068] In one embodiment, a trajectory tracking control method based on a predefined time observer and a neural network may further include a process of constructing a predefined time observer. Specifically, this process includes: building a dual-channel observer framework containing a state estimation channel and a composite disturbance estimation channel; constructing a state estimation dynamic equation based on the known system dynamic equations and introducing a continuous nonlinear error feedback function related to predefined time parameters; constructing a composite disturbance estimation equation using the observation error as input; completing the construction of the predefined time observer; setting the convergence time of the observation error and designing the observer gain parameter; defining the observation error as the difference between the actual state of the controlled system, which cannot be directly measured, and the state estimate output by the observer, forming an error vector; constructing the Lyapunov function of the observation error and verifying the derivative of the Lyapunov function; and verifying that the observed error converges within a predefined time.

[0069] To address the issue that some state variables and composite disturbance terms in a controlled system cannot be directly measured, computer equipment can construct predefined time observers for the controlled system's state and composite disturbances. The structure of these observers is as follows: The observation error is defined as: ;in, Represents an estimate of the state of the controlled system. This represents the estimated value of the composite disturbance term of the controlled system. To control the input, and The nonlinear function is known or partially known to the controlled system. and To match the predefined time parameters The relevant continuous nonlinear error feedback function, This is the observer gain parameter.

[0070] In this embodiment, the computer device can distinguish between the known and unknown parts of the dynamic equations of the controlled system. The known parts may include known structural parameters, directly measurable state variables, and known nonlinear functions; the unknown parts may include non-directly measurable state variables, model parameter uncertainties, unmodeled dynamics, and external environmental disturbances. Next, the unknown parts can be integrated into a composite disturbance term; the observation targets are clearly defined as the non-directly measurable state variables and composite disturbance term of the controlled system.

[0071] Next, a dual-channel observer framework comprising a state estimation channel and a composite disturbance estimation channel can be constructed. The state estimation channel, based on the system's measurable state, known nonlinear functions, and control input, introduces a continuous nonlinear error feedback function related to predefined time parameters to construct the state estimation dynamic equation. The composite disturbance estimation channel, using the observation error as input, introduces a continuous nonlinear error feedback function related to predefined time parameters to construct the composite disturbance estimation equation, ensuring that the observer structure matches the dynamic model of the controlled system. The computer equipment can pre-set the convergence time of the observation error according to engineering control requirements, and by selecting a continuous nonlinear error feedback function with strong feedback when the error is large and smooth feedback when the error approaches zero, the observer gain parameters are designed, and a reasonable range of values ​​for the gain parameters is determined through Lyapunov stability analysis, thus completing the observer construction.

[0072] The computer equipment can define the observation error as the difference between the actual state of the controlled system that cannot be directly measured and the state estimate output by the observer; and construct the Lyapunov function of the observation error. By verifying that the derivative of the Lyapunov function satisfies the negative definite or semi-negative definite condition, it can ensure that the observation error converges to zero or a preset neighborhood within a predefined time.

[0073] In one embodiment, a trajectory tracking control method based on a predefined time observer and a neural network may further include a process of estimating the state and the composite disturbance. Specifically, this process includes: starting the predefined time observer and initializing the state estimate, the composite disturbance estimate, and various design parameters; after parameter initialization, the time observer takes the real-time measurement data of the controlled system and the control input as inputs, and dynamically adjusts the state estimate through the state estimation channel and tracks the dynamic changes of the composite disturbance in real time through the composite disturbance estimation channel, until a predefined time is reached; after the predefined time is reached, the observation error converges to zero or a preset neighborhood, the disturbance estimate is updated, and the state estimation result is obtained.

[0074] Computer equipment can adjust the observation error by appropriately selecting predefined time observers and various parameters in the observation error. It converges to zero or a preset neighborhood within a predefined time.

[0075] Specifically, when the controlled system initiates trajectory tracking control, the computer equipment can simultaneously start a predefined time observer to initialize the state estimate, composite disturbance estimate, and various design parameters. Through preset observation equations, the state estimate is dynamically adjusted via the state estimation channel to approximate the unmeasurable actual state, while the composite disturbance estimate is updated in real-time by tracking the dynamic changes of the composite disturbance via the composite disturbance estimation channel, thus obtaining the state estimation result. Next, the computer equipment can verify the accuracy of the state estimation result. If an anomaly occurs, it checks sensor measurement data or observer parameters and performs real-time corrections. After a predefined time has elapsed, it outputs a stable and accurate state estimation result and composite disturbance estimate.

[0076] Step 206: Construct non-singular fast terminal sliding mode variables using trajectory tracking error and error derivative.

[0077] In one embodiment, a trajectory tracking control method based on a predefined time observer and a neural network may further include a process of constructing a non-singular fast terminal sliding mode variable. The specific process includes: obtaining control parameters and terminal type exponential parameters, and selecting a sign function that characterizes the conformity of the variable; calculating the non-singular fast terminal sliding mode variable based on the trajectory tracking error, error derivative, control parameters, terminal type exponential parameters, and sign function.

[0078] That is, computer equipment can be based on trajectory tracking errors. and its derivative The non-singular fast terminal sliding mode variables are constructed as follows: ;in, For sliding mode variables, , For control parameters, , For terminal type index parameters, The sign function is represented. The sliding mode structure maintains continuity as the error approaches zero, thus avoiding singularities in terminal sliding mode control.

[0079] Step 208: Use a neural network to approximate the unknown nonlinearity and external disturbances in the controlled system online, and update the neural network weights in real time based on the sliding mode variables, and output the compensation term through the neural network.

[0080] Computer devices can utilize the universal approximation properties of neural networks to dynamically offset the effects of system uncertainties. Specifically, an appropriate neural network structure can be selected based on the characteristics and uncertainty complexity of the controlled system to ensure a balance between approximation capability and real-time performance.

[0081] In one embodiment, the trajectory tracking control method based on a predefined time observer and a neural network may further include an online approximation process using a neural network. The specific process includes: selecting an appropriate feedforward neural network and initializing the parameters in the neural network; real-time acquisition and preprocessing of system state data as input to the neural network to initiate online approximation; adjusting the neural network weights in real time through adaptive updates based on the sliding mode variable feedback after online approximation; and calculating and outputting a compensation term based on the adjusted neural network weights.

[0082] Computer equipment can use neural networks to perform online approximation of unknown nonlinearities and external disturbances in system dynamics, and its expression is as follows: ;in, For the ideal weight vector of the neural network, Given a smooth basis function vector, This represents the bounded approximation error. The neural network weights are adjusted according to an adaptive update law. The positive definite adaptive gain matrix is: .

[0083] Specifically, computer equipment can select a feedforward neural network as an approximator. Feedforward neural networks have a simple structure, low computational cost, are suitable for real-time online updates, and can approximate continuous nonlinear functions with arbitrary precision, meeting the approximation requirements of unknown nonlinearities and external disturbances in the system.

[0084] Computer equipment can collect input vector data of neural networks in real time, such as actual state vectors, trajectory tracking errors, and error derivatives. The collected input data is normalized, and outliers are filtered to avoid interfering with network training. Then, based on a preset adaptive update law, the adjustment amount of the weights is calculated in real time to ensure stable network operation. The network output is then calculated using the updated weights to achieve dynamic approximation of unknown nonlinearities and external disturbances. Finally, the approximation result of the neural network is converted into a compensation term that can be directly incorporated into the control law and output.

[0085] Step 210: Combine the state estimation results, sliding mode variables, and compensation terms to construct a trajectory tracking control law, and apply the trajectory tracking control law to the controlled system so that the trajectory tracking error converges to zero or a preset neighborhood within a preset time.

[0086] In one embodiment, a trajectory tracking control method based on a predefined time observer and a neural network may further include a process of constructing a trajectory tracking control law. The specific process includes: verifying the state estimation results, sliding mode variables, and compensation terms to ensure that the information dimensions of the state estimation results, sliding mode variables, and compensation terms are consistent, the timing is synchronized, and they are effective; and constructing a trajectory tracking control law based on the verified state estimation results, sliding mode variables, and compensation terms, combined with a positive definite control gain matrix.

[0087] The computer device can synthesize the estimation results of a predefined time observer, neural network compensation terms, and non-singular fast terminal sliding mode variables to construct the trajectory tracking control law as follows: ;in, It is a positive definite control gain matrix. This is the uncertainty compensation term for the output of the neural network.

[0088] Specifically, computer equipment can collect and verify state estimation results, sliding mode variables, and uncertainty compensation terms to ensure that information dimensions are unified, time-series synchronized, and effective; state tracking terms, sliding mode robust terms, and disturbance cancellation terms are designed separately and linearly superimposed and integrated with neural network compensation terms to construct a trajectory tracking control law that adapts to the input format of the controlled system; the closed-loop stability of the system is analyzed and verified through Lyapunov function analysis, the predefined time convergence characteristics of trajectory tracking error are verified by simulation, and control parameters are optimized as needed.

[0089] In one embodiment, a trajectory tracking control method based on a predefined time observer and a neural network may further include a closed-loop control and predefined time convergence process. The specific process includes: acquiring the control cycle and applying the trajectory tracking control law to the controlled system according to the control cycle; iteratively updating the neural network weights, trajectory tracking error, state estimation results, and trajectory tracking control law, and dynamically monitoring the trajectory tracking error convergence process, converging to zero or a preset neighborhood within a preset time.

[0090] Computer devices can control input The control law is applied to the controlled system to form a closed-loop control structure, enabling the system to maintain stable operation under conditions of model uncertainty and external disturbances. It also ensures that the trajectory tracking error converges to zero or a preset neighborhood within a pre-defined time range, thus achieving trajectory tracking control with predefined time performance constraints. Specifically, the computer equipment can apply the control law to the controlled system in real time according to the control cycle, synchronously iteratively updating the error, observation results, neural network weights, and control law, dynamically monitoring the error convergence process, and ensuring that it converges to zero or a preset neighborhood within a preset time.

[0091] This application provides a trajectory tracking control method based on a predefined time observer and a neural network. By introducing a predefined time observer, the system state and complex disturbances can be estimated quickly. By using a non-singular fast terminal sliding mode structure, the error convergence speed is accelerated and the terminal sliding mode singularity problem is avoided. Combined with the neural network for online compensation of unknown nonlinearities, the robustness of the control system and the trajectory tracking accuracy under uncertain environments are significantly improved.

[0092] In one embodiment, taking the trajectory tracking control system of an unmanned surface vessel (USV) as the research object, the non-singular fast terminal sliding mode trajectory tracking control method (NFTSMC) based on a predefined time observer (PTO) and a neural network (NN) proposed in this application is simulated and verified. The control framework for autonomous navigation trajectory tracking of an unmanned surface vessel (USV) is as follows: Figure 3 As shown, high-precision trajectory tracking in complex marine environments is achieved through multi-module collaboration. The functions and interaction logic of each module are as follows: System state and trajectory error acquisition module: It acquires the actual system state of the USV through sensors (observers) and calculates the trajectory error between the actual state and the desired trajectory, providing basic deviation information for subsequent control; Autonomous navigation platform, i.e., the controlled system, receives control commands and executes motion in conjunction with the autonomous navigation module; Uncertainty and disturbance set includes marine environmental disturbances and system modeling uncertainties, such as parameter drift and unmodeled dynamics, which are interference factors affecting USV trajectory tracking; Neural network predictor: It approximates the uncertainty and disturbance set online through a feedforward neural network and outputs compensation terms to offset the impact of disturbances on the system; Sliding mode controller: It receives information such as trajectory error and neural network compensation terms, and generates control commands through the sliding mode control system to guide the USV to track the desired trajectory.

[0093] like Figure 3 As shown, the observer collects the state and trajectory error of the USV and transmits it to the sliding mode controller; the disturbance information of the uncertainty and disturbance set is input into the neural network predictor to generate a compensation term and transmit it to the sliding mode controller; the sliding mode controller fuses the error and the compensation term and outputs control commands to the autonomous navigation platform (USV); the USV executes the control commands, and its motion state is collected by the observer again to form a closed-loop control.

[0094] The kinematics and dynamics model of the unmanned surface vessel (USV) is described in both the inertial coordinate system and the hull coordinate system. The USV coordinate system is illustrated as follows: Figure 4 As shown, the framework for trajectory tracking control of a non-singular fast terminal sliding mode unmanned surface vessel based on a predefined time observer and a neural network is as follows: Figure 5 As shown, its dynamic model is expressed as: , ;in, Here are the position and heading angle vectors. Let R be the velocity vector, M be the rotation matrix, C(υ) be the inertia matrix, D(υ) be the Coriolis force matrix, and g(η) be the damping matrix. Let τ be the external disturbance and τ be the control input. The reference trajectory model is set as an ideal unmanned surface vessel system whose dynamics do not contain uncertainties or external disturbances, and is used to generate the desired trajectory and desired velocity. For the desired trajectory, For the desired speed, As a reference control input, the position error and velocity error are defined as follows: Furthermore, the model uncertainty, external disturbances, and unmodeled dynamics in the system are uniformly grouped into unknown terms. A model of the error system with uncertainties is formed. The observed results of the velocity error are as follows: Figure 6 As shown.

[0095] For a velocity error system, a predefined time observer is introduced to estimate the system error state, with the following structure: , ;in, To be related to a predefined time The design parameters were determined. Lyapunov stability analysis proves that the designed observer can operate within a predetermined time. The internal error convergence is independent of initial conditions. To compensate for uncertainties and external disturbances in the system, a neural network is introduced to estimate the unknowns online. ,in The weight matrix, Let be the basis function vector. The neural network estimation results for uncertainties and perturbations are as follows: Figure 7 As shown, the network weights are updated in real time through an adaptive law, enabling accurate estimation of uncertainties and disturbances.

[0096] Next, the non-singular fast terminal sliding surface is constructed as follows: ;in, , 0, , Based on the constructed sliding surface, the control input is designed as follows:

[0097] Among them, the comparison of system trajectory tracking position error under different control methods is as follows: Figure 8 As shown, a comparison of the system trajectory tracking speed error under different control methods is presented. Figure 9 As shown. In this embodiment, the control law integrates a predefined time convergence term, a sliding mode term, and a neural network compensation term, effectively avoiding the singularity problem in traditional terminal sliding mode control.

[0098] The Cybership II unmanned surface vessel model and hydrodynamic parameters were used. The initial settings were as follows: The external disturbance is set as a periodically varying disturbance function. The predefined time parameter is set to... The remaining control parameters are selected according to stability conditions, and the total duration is 15 seconds. The system control input signal change process is as follows: Figure 10 As shown.

[0099] The results show that the predefined time observer is able to The proposed trajectory tracking control method, based on a predefined time observer and a neural network, accurately estimates the velocity error. The neural network effectively approximates system uncertainties and external disturbances. The controller, designed based on a predefined time observer and a neural network, achieves rapid convergence of position and velocity errors within a predefined time. Compared to traditional terminal sliding mode control methods, this method demonstrates superior performance in tracking accuracy, convergence speed, and control input smoothness.

[0100] It should be understood that although the steps in the flowchart above are shown sequentially as indicated by the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowchart above may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0101] In one embodiment, such as Figure 11 As shown, a trajectory tracking control system based on a predefined time observer and a neural network is provided, including: a trajectory tracking error construction module 1110, a time observer construction and state estimation module 1120, a sliding mode variable construction module 1130, an online approximation and compensation module 1140, and a trajectory tracking control module 1150, wherein:

[0102] The trajectory tracking error construction module 1110 is used to obtain the actual state vector and the desired trajectory state vector of the controlled system, define the trajectory tracking error based on the actual state vector and the desired trajectory state vector, and obtain the error derivative by taking the derivative of the trajectory tracking error.

[0103] The time observer construction and state estimation module 1120 is used to construct a predefined time observer for the system state and composite disturbances based on the controlled system, and to define the observation error; to estimate the state and composite disturbances of the controlled system that cannot be directly measured through the predefined time observer, and to make the observation error converge within a preset time to obtain the state estimation result;

[0104] The sliding mode variable construction module 1130 is used to construct non-singular fast terminal sliding mode variables using trajectory tracking error and error derivative;

[0105] The online approximation and compensation module 1140 is used to approximate the unknown nonlinearity and external disturbances in the controlled system online using a neural network, and to update the neural network weights in real time based on the sliding mode variables, and output the compensation term through the neural network.

[0106] The trajectory tracking control module 1150 is used to construct a trajectory tracking control law by combining the state estimation results, sliding mode variables, and compensation terms, and to apply the trajectory tracking control law to the controlled system so that the trajectory tracking error converges to zero or a preset neighborhood within a preset time.

[0107] In one embodiment, the trajectory tracking error construction module 1110 is further configured to acquire real-time operating data of the controlled system through the sensors of the controlled system, and preprocess the real-time operating data of the system to form an actual state vector containing the motion state of the system; obtain the desired trajectory state vector of the controlled system, wherein the desired trajectory state vector and its first derivative are known and bounded; calculate the difference between the actual state vector and the desired trajectory state vector, and define the difference as the trajectory tracking error; and take the derivative of the trajectory tracking error to obtain the difference between the first derivative of the actual state vector and the first derivative of the desired trajectory state vector, and use the difference as the error derivative.

[0108] In one embodiment, the time observer construction and state estimation module 1120 is further used to build a dual-channel observer framework including a state estimation channel and a composite disturbance estimation channel. The state estimation channel constructs the state estimation dynamic equation based on the known dynamic equation of the system and introduces a continuous nonlinear error feedback function related to the predefined time parameters. The composite disturbance estimation channel constructs the composite disturbance estimation equation with the observation error as input. The construction of the predefined time observer is completed. The convergence time of the observation error is set, and the observer gain parameter is designed. The observation error is defined as the difference between the actual state of the controlled system that cannot be directly measured and the state estimation value output by the observer, forming an error vector. The Lyapunov function of the observation error is constructed, and the derivative of the Lyapunov function is verified. The verified observation error converges within the predefined time.

[0109] In one embodiment, the time observer construction and state estimation module 1120 is further used to start a predefined time observer, initialize the state estimate, the composite disturbance estimate, and various design parameters; after initializing the parameters, the time observer takes the real-time measurement data of the controlled system and the control input as inputs, and dynamically adjusts the state estimate through the state estimation channel and tracks the dynamic changes of the composite disturbance in real time through the composite disturbance estimation channel until the predefined time is reached; after the predefined time is reached, the observation error converges to zero or a preset neighborhood, the disturbance estimate is updated, and the state estimation result is obtained.

[0110] In one embodiment, the sliding mode variable construction module 1130 is further configured to obtain control parameters, terminal type exponent parameters, and select a sign function that characterizes the variable conformity characteristics; and calculate non-singular fast terminal sliding mode variables based on trajectory tracking error, error derivative, control parameters, terminal type exponent parameters, and sign function.

[0111] In one embodiment, the online approximation and compensation module 1140 is further configured to select an appropriate feedforward neural network and initialize the parameters in the neural network; collect and preprocess system state data in real time as input to the neural network and start online approximation; based on the sliding mode variable feedback after online approximation, adjust the neural network weights in real time through adaptive updates; and calculate and output the compensation term based on the adjusted neural network weights.

[0112] In one embodiment, the trajectory tracking control module 1150 is also used to verify the state estimation results, sliding mode variables, and compensation terms to ensure that the information dimensions of the state estimation results, sliding mode variables, and compensation terms are consistent, the timing is synchronized, and they are effective; based on the verified state estimation results, sliding mode variables, and compensation terms, combined with the positive definite control gain matrix, a trajectory tracking control law is constructed.

[0113] In one embodiment, the trajectory tracking control module 1150 is further configured to acquire the control cycle and apply the trajectory tracking control law to the controlled system according to the control cycle; iteratively update the neural network weights, trajectory tracking error, state estimation results, and trajectory tracking control law; and dynamically monitor the trajectory tracking error convergence process, converging to zero or a preset neighborhood within a preset time.

[0114] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 12As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When the computer program is executed by the processor, it implements a trajectory tracking control method based on a predefined time observer and a neural network. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0115] Those skilled in the art will understand that Figure 12 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0116] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of a trajectory tracking control method based on a predefined time observer and a neural network.

[0117] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program being executed by a processor to implement the steps of a trajectory tracking control method based on a predefined time observer and a neural network.

[0118] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0119] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0120] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A trajectory tracking control method based on a predefined time observer and a neural network, characterized in that, The method includes: Obtain the actual state vector and the desired trajectory state vector of the controlled system, define the trajectory tracking error based on the actual state vector and the desired trajectory state vector, and obtain the error derivative by taking the derivative of the trajectory tracking error; Based on the controlled system, a predefined time observer is constructed for the system state and composite disturbance, and the observation error is defined; the state and composite disturbance of the controlled system that cannot be directly measured are estimated through the predefined time observer, and the observation error is made to converge within a preset time to obtain the state estimation result; Using the trajectory tracking error and error derivative, a non-singular fast terminal sliding mode variable is constructed; A neural network is used to approximate the unknown nonlinearity and external disturbances in the controlled system online, and the weights of the neural network are updated in real time based on the sliding mode variables. The compensation term is output through the neural network. The trajectory tracking control law is constructed by combining the state estimation results, sliding mode variables, and compensation terms, and then applied to the controlled system so that the trajectory tracking error converges to zero or a preset neighborhood within a preset time.

2. The trajectory tracking control method based on a predefined time observer and a neural network according to claim 1, characterized in that, Obtain the actual state vector and the desired trajectory state vector of the controlled system, define the trajectory tracking error based on the actual state vector and the desired trajectory state vector, and obtain the error derivative by differentiating the trajectory tracking error, including: The system's real-time operating data is collected by the sensors of the controlled system, and the real-time operating data is preprocessed to form an actual state vector containing the system's motion state; the desired trajectory state vector of the controlled system is obtained, and the desired trajectory state vector and its first derivative are known and bounded. Calculate the difference between the actual state vector and the desired trajectory state vector, and define the difference as the trajectory tracking error; The difference between the first derivative of the actual state vector and the first derivative of the desired trajectory state vector is obtained by taking the derivative of the trajectory tracking error, and the difference is used as the error derivative.

3. The trajectory tracking control method based on a predefined time observer and a neural network according to claim 1, characterized in that, Based on the controlled system, a predefined time observer is constructed for the system state and composite disturbances, and the observation error is defined, including: A dual-channel observer framework comprising a state estimation channel and a composite perturbation estimation channel is constructed. The state estimation channel constructs the state estimation dynamic equation based on the known dynamic equations of the system and introduces a continuous nonlinear error feedback function related to predefined time parameters. The composite perturbation estimation channel constructs the composite perturbation estimation equation using the observation error as input. The construction of the predefined time observer is then completed. Set the convergence time of the observation error and design the observer gain parameters; The observation error is defined as the difference between the actual state of the controlled system, which cannot be directly measured, and the state estimate output by the observer, forming an error vector. Construct a Lyapunov function for the observation error and verify the derivative of the Lyapunov function. Observation errors that pass the verification converge within a predefined time.

4. The trajectory tracking control method based on a predefined time observer and a neural network according to claim 3, characterized in that, The state and composite disturbances of the controlled system that cannot be directly measured are estimated using the predefined time observer, and the observation error is made to converge within a pre-set time to obtain the state estimation result, including: Start the predefined time observer and initialize the state estimate, composite disturbance estimate and various design parameters; After initializing the parameters, the time observer takes the real-time measurement data and control input of the controlled system as inputs, and dynamically adjusts the state estimation value through the state estimation channel and tracks the dynamic changes of the composite disturbance in real time through the composite disturbance estimation channel until a predefined time is reached. After a predefined time is reached, the observation error converges to zero or a preset neighborhood, the disturbance estimate is updated, and the state estimation result is obtained.

5. The trajectory tracking control method based on a predefined time observer and a neural network according to claim 1, characterized in that, Using the trajectory tracking error and its derivative, non-singular fast terminal sliding mode variables are constructed, including: Obtain control parameters and terminal index parameters, and select a sign function that represents the conformity of the variables; Calculate the non-singular fast terminal sliding mode variable based on the trajectory tracking error, error derivative, control parameters, terminal type exponential parameter, and sign function.

6. The trajectory tracking control method based on a predefined time observer and a neural network according to claim 1, characterized in that, A neural network is used to approximate the unknown nonlinearity and external disturbances in the controlled system online, and the weights of the neural network are updated in real time based on the sliding mode variables. The compensation term is output through the neural network, including: Select a suitable feedforward neural network and initialize the parameters in the neural network; The system status data is collected and preprocessed in real time and used as the input to the neural network to initiate online approximation; Based on the sliding mode variable feedback after online approximation, the neural network weights are adjusted in real time through adaptive updates; the neural network calculates and outputs the compensation term based on the adjusted neural network weights.

7. The trajectory tracking control method based on a predefined time observer and a neural network according to claim 1, characterized in that, The trajectory tracking control law is constructed by combining the state estimation results, sliding mode variables, and compensation terms, including: The state estimation results, sliding mode variables, and compensation terms are verified to ensure that the information dimensions of the state estimation results, sliding mode variables, and compensation terms are consistent, the timing is synchronized, and they are effective. Based on the verified state estimation results, sliding mode variables, compensation terms, and positive definite control gain matrix, a trajectory tracking control law is constructed.

8. The trajectory tracking control method based on a predefined time observer and a neural network according to claim 1, characterized in that, Applying the trajectory tracking control law to the controlled system, causing the trajectory tracking error to converge to zero or a preset neighborhood within a preset time, includes: The control cycle is acquired, and the trajectory tracking control law is applied to the controlled system according to the control cycle; The neural network weights, trajectory tracking error, state estimation results, and trajectory tracking control law are iteratively updated, and the trajectory tracking error convergence process is dynamically monitored, converging to zero or a preset neighborhood within a preset time.

9. A trajectory tracking control system based on a predefined time observer and a neural network, characterized in that, The system includes: The trajectory tracking error construction module is used to obtain the actual state vector and the desired trajectory state vector of the controlled system, define the trajectory tracking error based on the actual state vector and the desired trajectory state vector, and obtain the error derivative by taking the derivative of the trajectory tracking error. The time observer construction and state estimation module is used to construct a predefined time observer of the system state and composite disturbance based on the controlled system, and define the observation error; estimate the state and composite disturbance of the controlled system that cannot be directly measured through the predefined time observer, and make the observation error converge within a preset time to obtain the state estimation result; The sliding mode variable construction module is used to construct non-singular fast terminal sliding mode variables using the trajectory tracking error and error derivative; The online approximation and compensation module is used to approximate the unknown nonlinearity and external disturbances in the controlled system online using a neural network, and to update the neural network weights in real time based on the sliding mode variables, and output compensation terms through the neural network. The trajectory tracking control module is used to construct a trajectory tracking control law by combining the state estimation results, sliding mode variables, and compensation terms, and to apply the trajectory tracking control law to the controlled system so that the trajectory tracking error converges to zero or a preset neighborhood within a preset time.

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