Finite-time cross-domain aircraft cluster formation control method based on neural network

Abstract

The application provides a limited time cross-domain aircraft cluster formation control method based on a neural network, relates to the field of aircraft control, and specifically comprises the following steps: a unified nonlinear non-strict feedback system is established according to the dynamic characteristics of cross-domain aircraft in different domains; real-time flight states and position information of a plurality of followers are collected; an improved Tan-type nonlinear mapping function is designed, the initial output constraint type of the system is identified, and new variables without constraints are obtained; a double neural network combining a shared network and a dedicated network is constructed, a backstepping method combined with a switching function and a non-singular fast limited time control strategy are designed, and the output of the double neural network structure is controlled; and a switching threshold event triggering mechanism is designed, so that the UAV cluster has different responses in different environments. The technical scheme of the application overcomes the problem that the formation control method in the prior art does not consider mode switching, dynamic coupling and collaborative consistency in cross-domain cooperation.

Description

Technical Field

[0001] This invention relates to the field of aircraft control, and more specifically to a finite-time cross-domain aircraft swarm formation control method based on neural networks. Background Technology

[0002] With the widespread application of unmanned systems such as drones, unmanned surface vessels, and unmanned vehicles in various fields, cross-domain collaborative operations have become an important direction for the development of future intelligent unmanned systems. Cross-domain aircraft swarms possess the ability to operate across media, both in the air and on the water, and can perform complex tasks such as wide-area monitoring, collaborative search and rescue, and distributed detection. However, the formation control of cross-domain aircraft swarms faces severe challenges due to multiple factors, including dynamic switching of operational domains, strongly nonlinear coupled dynamics, limited multi-agent communication, and external environmental disturbances.

[0003] At the technical level, the dynamics models of cross-domain aircraft are highly nonlinear and time-varying. Cross-domain aircraft are governed by aerodynamics in the air domain and influenced by hydrodynamics in the water domain, with fundamental differences in fluid drag, propulsion efficiency, and stability. During cross-domain transitions, the aircraft's dynamic parameters (such as mass distribution, inertia, and damping coefficients) change drastically, making traditional control methods based on precise models (such as PID control and sliding mode control) difficult to adapt, leading to decreased control performance or even instability. Furthermore, existing formation control methods are mostly based on asymptotic stability theory, which cannot guarantee rapid system convergence within a finite time, affecting mission execution efficiency. In the presence of external disturbances such as wind, waves, and currents, traditional control methods lack effective online compensation mechanisms, easily leading to formation disruption or increased tracking errors. In terms of communication, most methods assume a fixed topology, making it difficult to adapt to dynamic topology changes (such as node failures or link interruptions), limiting the system's flexibility and reliability.

[0004] Current research both domestically and internationally indicates that some studies have attempted to introduce neural networks to enhance the adaptive capabilities of systems. For example, adaptive control methods for rotorcraft UAVs based on switching systems handle dynamic changes within a single domain through mode switching, but do not address cross-domain cooperation issues. While multimodal smooth switching control methods for boom-mounted UAVs improve adaptability, they lack systematic guarantees for finite-time convergence performance. Furthermore, existing technologies primarily focus on formation control within a single domain, neglecting issues such as mode switching, dynamic coupling, and cooperative consistency in cross-domain cooperation.

[0005] Therefore, there is a need for a finite-time cross-domain aircraft swarm formation control method based on neural networks that can adapt to cross-domain dynamic characteristics, has strong robustness and fast convergence capability. Summary of the Invention

[0006] The main objective of this invention is to provide a finite-time cross-domain aircraft swarm formation control method based on neural networks, in order to solve the problems of mode switching, dynamic coupling and cooperative consistency in existing formation control methods that do not consider cross-domain cooperation.

[0007] To achieve the above objectives, this invention provides a finite-time cross-domain aircraft swarm formation control method based on neural networks, specifically including the following steps:

[0008] S1 establishes a unified nonlinear non-strict feedback system to address the dynamic characteristics of cross-domain aircraft in different domains.

[0009] S2 collects the real-time flight status and location information of multiple followers, sends the leader's status to multiple followers, and enables communication between multiple followers.

[0010] S3. Design an improved Tan-type nonlinear mapping function, analyze the original state received by the sensor, identify the type of initial output constraint of the system, and obtain new unconstrained variables.

[0011] S4 constructs a dual neural network that combines a shared network and a dedicated network. The shared network learns the general dynamic characteristics of cross-domain aircraft, using the same network structure and initial weights, and combines local gradients and distributed consistency terms to learn cross-domain commonalities. The dedicated network compensates for the individual differences of aircraft in each domain, updates independently based on individual tracking errors, and designs personalized network structures according to domain type.

[0012] S5 proposes a backstepping method combined with a switching function and a non-singular fast finite-time control strategy to control the output of a dual neural network structure.

[0013] S6 is designed with a threshold event triggering mechanism that combines fixed and relative thresholds as triggering conditions. Based on the dual judgment of weight change rate and time interval, the drone swarm can respond differently in different environments.

[0014] Furthermore, step S1 specifically includes the following steps:

[0015] S1.1 establishes a heterogeneous cross-domain aircraft cluster consisting of 1 leader and N followers, where the dynamics model of each follower is described by a nonlinear, non-strict feedback system:

[0016] ;

[0017] The trajectory of a leader :

[0018] Given a bounded smooth function;

[0019] in, For the first The state variables of the follower aircraft For unknown smooth nonlinear functions, including: aerodynamic, hydrodynamic, and environmental disturbance factors. For the first The system order of a follower aircraft For the first The control input for a follower aircraft For the first The highest order of the state vectors of the follower aircraft state, For the first The output of a follower aircraft.

[0020] S1.2, constrains the leader's trajectory and the followers' outputs:

[0021] and derivative It is known and bounded;

[0022] System output Subject to constraints, i.e. or ,in, , ; for constant constraints, for Time-varying constraints, It is a constant. It is a time-varying function.

[0023] Furthermore, step S3 specifically includes the following steps:

[0024] S3.1, When the output constraint type is constant output, the mapping function for:

[0025] ;

[0026] in, For the constrained original output variables, It is the tangent function.

[0027] S3.2, When the output constraint type is time-varying output, the mapping function for:

[0028] .

[0029] S3.3, let This ensures that the system will not experience a singularity.

[0030] Furthermore, step S4 specifically includes the following steps:

[0031] S4.1, Dedicated Network Compensation The unique dynamic characteristics of the follower aircraft, as output by the dedicated network, are as follows:

[0032] ;

[0033] in, It is the first The status of a follower aircraft It is the transpose of the real-time estimated weights of a dedicated neural network. These are dedicated network RBF basis functions. It is the state vector of the dedicated network system. It is an unknown dynamic estimate of each individual in the dedicated network.

[0034] S4.2, the shared network learns the common dynamic characteristics shared by all follower aircraft, and the output of the shared network is:

[0035] ;

[0036] in, It is the transpose of the network weights of a shared neural network. These are shared network RBF basis functions. It is an unknown dynamic estimate of each individual in the shared network. This is for the shared network system state vector.

[0037] S4.3, Section The total unknown nonlinear approximation for a single follower aircraft is:

[0038] ;

[0039] in, and These are the real-time weight estimates for shared and private networks, respectively.

[0040] S4.4, determine network performance based on error magnitude. If the shared network error is less than the dedicated network error, then... This indicates that the shared network performs better; conversely: This indicates that the dedicated network is more suitable for the current situation, and therefore the fusion weights are dynamically adjusted. The output of the dual neural network structure for:

[0041] .

[0042] Furthermore, the weight estimation of the dedicated neural network in step S4.1 specifically includes the following steps:

[0043] S4.1.1, For a real, unknown dynamic function, there exists an ideal optimal weight. Make:

[0044] ;

[0045] in, It is a nonlinear function. For optimal weights, for transpose, For basis vector functions, To approximate the residual;

[0046] Estimated output of dedicated neural network for:

[0047] ;

[0048] in, To estimate the weights.

[0049] S4.1.2 defines the approximation error between the network estimate and the true value. for:

[0050] ;

[0051] Define weight error The difference between the actual weights and the estimated weights:

[0052] ;

[0053] Substituting and expanding, we obtain the approximation error equation:

[0054] .

[0055] In section S4.1.3, to ensure the stability of the subsequent closed-loop system, based on the Lyapunov stability analysis of the overall system, the weight update law for the continuous form of the dedicated network is derived. for:

[0056] ;

[0057] in, The learning rate matrix, This refers to the system tracking error defined in the subsequent backstepping method. For the attenuation coefficient of the dedicated network, and .

[0058] By discretizing the continuous update law of the exclusive network weights, we can directly obtain the final discrete update process of the exclusive network weights in practical engineering applications:

[0059] ;

[0060] in, and These are the dedicated network weight estimates for the next discrete time step and the current time step, respectively. The learning rate matrix for the dedicated network; It is the first The follower aircraft was in The backstepping tracking error of the step.

[0061] Furthermore, the weight estimation of the shared neural network in step S4.2 is specifically as follows:

[0062] ;

[0063] in, It is the first The follower aircraft was in In step-backstep control, the shared network weights are estimated at the next discrete time step. It is an estimate of the shared network weights at the current discrete time. It is the learning rate matrix of the shared network; These are the RBF basis function vectors of the shared network; It is the first The follower aircraft was in The backstepping tracking error of the step; It is the first Estimation of the shared network weights of each follower aircraft at the current moment; These are elements of the communication topology adjacency matrix; It is the first A set of neighbors for a follower aircraft; Let be the attenuation coefficient of the shared network, and .

[0064] Furthermore, step S5 specifically includes the following steps:

[0065] S5.1, the impact of the residual is approximated by using the backstepping tracking error, and the residual compensation term is designed accordingly:

[0066] ;

[0067] in, To compensate for the gain; For the first The follower aircraft at the highest level The system tracking error of the step.

[0068] S5.2 employs an adaptive backstepping method to progressively design virtual control laws for each follower aircraft, define coordinate transformations, and define the first error variable. :

[0069] ;

[0070] in, It is the leader connectivity coefficient. For mapping functions;

[0071] Redefining the first Error variables :

[0072] ;

[0073] in, It is the first The virtual control law is designed step by step.

[0074] Furthermore, step S5 also includes the following steps:

[0075] S5.3, combining the approximation error of the dual neural network, performs the design of the backstepping virtual control law and the overall Lyapunov stability, targeting the first... Error dynamics of the step, combined with the system model The unknown nonlinear function is replaced with a dual neural network approximation form. The error dynamics equation is obtained as follows:

[0076]

[0077] in, for The derivative, for transpose, No. The follower aircraft was in The difference between the actual weights and the estimated weights of each step. It is the first The follower aircraft was in Step-shared network RBF basis functions, No. The follower aircraft was in Approaching the residual step for The derivative of .

[0078] S5.4, to ensure the stability of the closed-loop system, the design of the first... Lyapunov function of step The system tracking error and the neural network weight estimation error are both incorporated into the energy function:

[0079] ;

[0080] in, The learning rate matrix is ​​such that, since the optimal weights are constants, ... ,right Taking the derivative and substituting it into the error dynamics equation, we get:

[0081] ;

[0082] in, for The derivative of .

[0083] S5.5, in order to eliminate unknown weight cross terms ,make The theoretical continuous update law for estimating weights using the dedicated network in step S4 is derived as follows:

[0084] ;

[0085] At the same time, in order to make Satisfying the negative definite condition, i.e. ,make The ideal tracking target is a virtual control law Based on this, the first design The virtual control law for the step is:

[0086] ;

[0087] in, It is the first The linear gain of the step; For the first The dynamic estimate of the output of the dual neural network is used in the step-by-step and back-step derivation; The first-order time derivative of the previous virtual control law is used as a feedforward term to eliminate the coupled dynamics in the backstep recursion process; For the first The residual compensation gain of the step.

[0088] Furthermore, step S5 also includes the following steps:

[0089] S5.6, Designing non-singular switching functions to avoid singularity:

[0090] ;

[0091] in, Error variables in backstep design ; The switching threshold; , where is the exponential parameter; , It is a positive odd number, and .

[0092] S5.7, the final control law Integrating backstepping basic control, nonsingular fast finite-time control, and dual neural network compensation, the complete design is as follows:

[0093] ;

[0094] in, To track errors, To control the gain, For the first The derivative of the virtual control law. This is an estimate of the output of the dual neural network structure.

[0095] Furthermore, step S6 specifically includes the following steps:

[0096] S6.1, defining the first A follower aircraft Time measurement error for:

[0097] ;

[0098] in, The ideal control input that the system expects to execute at the current moment; For the first The moment when a follower aircraft last successfully triggered an event and updated its state; The control commands that the actuator is currently actually executing.

[0099] S6.2, Design the dual-mode switching threshold trigger condition, when ,in, As a preset control input boundary constant, a relative threshold strategy is adopted, and the next event trigger time is... The determination criteria are:

[0100] ;

[0101] in, Represents the minimum time lower bound that satisfies the condition; This is the relative threshold coefficient; It is a very small positive number;

[0102] when The trigger condition has been changed to:

[0103] ;

[0104] in, This is a fixed safety threshold that is set.

[0105] S6.3, When the system state satisfies any of the triggering conditions in step S6.2, the current time is marked as... At this time, the first Each follower aircraft will broadcast the latest status information to its neighbors, and the latest... The update is handed over to the actuator; if the conditions are not met, the instructions from the previous moment are maintained. .

[0106] The present invention has the following beneficial effects:

[0107] This invention first establishes a unified dynamic model for a cross-domain aircraft swarm, considering non-strict feedback structures and output constraints. An improved Tan-type nonlinear mapping function transforms constrained outputs into unconstrained variables, fundamentally avoiding constraint violations. Second, an output controller based on a dual neural network (shared network and dedicated network) is designed to estimate and compensate for system uncertainties and external disturbances in real time. The shared network learns the general dynamic characteristics of the cross-domain aircraft and promotes swarm knowledge sharing through a distributed consensus protocol; the dedicated network compensates for individual differences, updating independently based on local tracking errors to achieve personalized adaptation. Furthermore, an adaptive finite-time formation controller is constructed, combining graph theory to describe the communication topology between aircraft and designing a distributed cooperative control law. By introducing a non-singular fast finite-time convergence mechanism, the formation error is ensured to converge to zero within a finite time, significantly improving response speed. In addition, a switching threshold event triggering strategy is adopted to dynamically adjust the communication topology and controller updates, effectively reducing communication burden, avoiding the Zeno phenomenon, and enhancing system robustness.

[0108] This invention achieves real-time compensation for cross-domain dynamic characteristics and environmental disturbances through adaptive updates of dual neural networks and real-time updates of neural network weights. A finite-time control mechanism ensures rapid formation convergence, making it suitable for urgent mission scenarios. An event-triggered communication strategy reduces resource consumption and improves system flexibility. This method can be widely applied to scenarios such as air-to-surface cross-domain collaborative reconnaissance, distributed sensing, and multi-task collaborative execution, significantly improving the formation convergence speed, anti-interference capability, and collaborative control accuracy of cross-domain aircraft swarms in complex environments. Attached Figure Description

[0109] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific 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. In the drawings:

[0110] Figure 1 A flowchart of a finite-time cross-domain aircraft swarm formation control method based on neural networks according to the present invention is shown.

[0111] Figure 2 The tracking position curves of the leader and the follower are shown.

[0112] Figure 3 The tracking error curve of the follower is shown. Detailed Implementation

[0113] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0114] like Figure 1 The method for finite-time cross-domain aircraft swarm formation control based on neural networks, as shown, specifically includes the following steps:

[0115] S1 establishes a unified nonlinear, non-strict feedback system for the dynamic characteristics of cross-domain aircraft in different domains. The system state derivatives, final state derivatives, and outputs constrained within the set are given.

[0116] S2 collects real-time flight status and position information from multiple followers, sends the leader's status to the followers, and enables communication between the followers. Considering aircraft characteristics, environmental disturbances, and physical constraints, it collects swarm status data and leader reference information. Through sensors mounted on the aircraft and the swarm communication network, it gathers its own status and trajectory commands issued by the leader. The sensors include an inertial measurement unit (IMU), a global positioning system (GPS) receiver, and a depth sensor; the IMU collects the aircraft's angular velocity and linear acceleration, while the GPS receiver provides absolute position and velocity information in the air or on the water surface.

[0117] S3 designs an improved Tan-type nonlinear mapping function to analyze the original state received by the sensor and identify the type of initial output constraint of the system. It can be divided into two types: constant output constraint and time-varying output constraint, thereby obtaining new unconstrained variables, fundamentally avoiding constraint violations, and realizing dynamic adaptation of constraint boundaries.

[0118] S4. The domain type of the aircraft is determined, and domain features are extracted accordingly. A subset of effective features is selected based on the domain type determination, and airspace and water domain features are embedded into a unified feature vector space to construct a unified-dimensional input vector. This ensures the consistency of the shared network structure and the feasibility of distributed consistency learning, while also providing domain-specific activation features for the dedicated network. Based on this, a high-precision approximation dual neural network control system based on RBF neural networks and distributed neural networks is implemented to realize unknown nonlinear functions.

[0119] A dual neural network combining a shared network and a dedicated network is constructed. The shared network learns the general dynamic characteristics of cross-domain aircraft, using the same network structure and initial weights, and combining local gradients and distributed consistency terms to learn cross-domain commonalities. The dedicated network compensates for the individual differences of aircraft in each domain, updates independently based on individual tracking errors, and designs personalized network structures according to domain type.

[0120] S5. A backstepping method combined with a switching function and a nonsingular fast finite-time control strategy is designed to control the output of a dual neural network structure. A virtual control law based on the backstepping method is designed. The virtual control signal is constructed step by step using the backstepping method to handle the control problem of a high-order nonlinear system and ensure the stability of each subsystem. Subsequent steps involve developing a nonsingular fast finite-time control strategy and designing a nonsingular finite-time control law based on a switching function.

[0121] Error judgment is initiated. For large errors, nonlinear feedback is used to accelerate convergence, while for small errors, linear feedback is used to avoid singularities, thereby ensuring that the system state converges to the equilibrium point within a finite time.

[0122] S6 is designed with a threshold event triggering mechanism that combines fixed and relative thresholds as triggering conditions. Based on the dual judgment of weight change rate and time interval, the drone swarm can respond differently in different environments, effectively reducing the communication burden.

[0123] Specifically, step S1 includes the following steps:

[0124] S1.1 establishes a heterogeneous cross-domain aircraft cluster consisting of 1 leader and N followers, where the dynamics model of each follower is described by a nonlinear, non-strict feedback system:

[0125] ;

[0126] The trajectory of a leader :

[0127] Given a bounded smooth function;

[0128] in, For the first The state variables of the follower aircraft For unknown smooth nonlinear functions, including: aerodynamic, hydrodynamic, and environmental disturbance factors. For the first The system order of a follower aircraft For the first The control input for a follower aircraft For the first The highest order of the state vectors of the follower aircraft state, For the first The output of a follower aircraft (i.e., the quantities that need to be controlled, such as position, altitude, etc.).

[0129] S1.2, constrains the leader's trajectory and the followers' outputs:

[0130] Assumption 1: and derivative It is known and bounded;

[0131] Assumption 2: System output Subject to constraints, i.e. or ,in, , ; for constant constraints, for Time-varying constraints, It is a constant. It is a time-varying function.

[0132] Although airborne and waterborne aircraft have different physical characteristics, they both follow the basic laws of Newtonian mechanics. This model can uniformly describe the dynamic behavior of both types of aircraft, with a state recursion structure. This is used to simulate the cascade relationship of state variables in actual aircraft, providing a mathematical basis for subsequent backstepping control design, involving unknown smooth nonlinear functions. It encompasses complex nonlinear factors such as aerodynamics, hydrodynamics, and environmental disturbances; The first one is described The dynamic change law of the highest-order state in the state vector of a follower aircraft is analyzed. A direct bridge is established between the control input and the system dynamics, which is the final execution point of the entire control model; output definition. The formation control problem is transformed into an output tracking problem, along with the leader trajectory. Establish clear tracking objectives.

[0133] The leader's trajectory status The staff sends trajectory commands in real time through the ground control station, which are then converted into smooth reference signals by the leader.

[0134] The above model construction not only ensures the rigor of the theory, but also provides a feasible framework for practical engineering applications. It is the theoretical cornerstone for realizing adaptive finite-time cross-domain formation control.

[0135] In step S2, data is collected using a data acquisition system, which consists of two parts: sensors that sense their own state and communication equipment that receives cluster information.

[0136] First, there are the self-awareness sensors. Each follower aircraft is equipped with a multi-sensor fusion system to accurately acquire its real-time status. This includes an Inertial Measurement Unit (IMU): containing a three-axis gyroscope and a three-axis accelerometer, directly measuring the aircraft's angular velocity and linear acceleration. It provides high-frequency, continuous dynamic information, which is the basis for estimating attitude and position changes. A Global Positioning System (GPS) receiver: providing absolute position (latitude and longitude) and velocity when operating in the air or on the water. It is crucial for correcting accumulated IMU errors. Finally, there are depth sensors: providing diving depth information by measuring water pressure during the underwater phase, and providing precise position information as the aircraft approaches the surface.

[0137] Secondly, there is the cluster information receiving and communication equipment. For airspace communication, high-speed wireless data transmission modules (such as Wi-Fi, 4G / 5G) are used to achieve low-latency, high-bandwidth data transmission for exchanging large amounts of state information and neural network weights. For waterborne communication, an underwater acoustic communication modem is used to encode digital data into sound waves for transmission. This is the only effective long-distance communication method underwater, but it has low bandwidth and high latency. Therefore, integrating these two communication modules into a cross-domain aircraft enables full-domain connectivity.

[0138] Strict protocols are followed during data transmission to ensure reliability and efficiency; the leader transmits their status. This information is packaged according to a preset communication protocol and its trajectory information is transmitted via broadcast. In this process, followers not only receive information from the leader, but also exchange data (especially the weights of the shared network) with neighboring nodes within the communication range to achieve distributed consistency.

[0139] After receiving this information, the follower's communication module analyzes, verifies, and filters it. The filtering function aims to eliminate sensor noise, compensate for errors, and fuse multi-source data to obtain the optimal state estimate. The core algorithm involved is the Kalman filter algorithm.

[0140] The high-frequency angular velocity and acceleration from the IMU are used as predicted values, while the low-frequency position / velocity from GPS and the depth from the depth sensor are used as observed values. A Kalman filter algorithm is used for data fusion to optimally estimate the complete state vector required in the system model. .For example, It's about location. These are speeds, derived from the filtered output, not from a single, noisy sensor reading. This process provides reliable state feedback, offering high-precision, low-latency, and noise-free system state for finite-time controllers and neural networks. This is the foundation of all control decisions.

[0141] Specifically, in cross-domain aircraft formation control, constraint processing is a necessary requirement for both physical realities and safety. Firstly, there are physical limit constraints: in airspace control, there are upper limits to the aircraft's airspeed, angle of attack, and roll angle; exceeding these limits may lead to stall or structural damage. In water control, the diving depth must be within a certain range to avoid bottoming out or surfacing and exposure. In addition, there are mission safety constraints; aircraft must maintain a minimum safe distance to prevent collisions. If there are further requirements, such as maintaining the formation shape within a certain geometric range, all of these controls require constraint processing. Without output constraint processing, tracking errors may exceed the controller's stable region, causing system divergence.

[0142] Traditional constraint handling methods (such as obstacle Lyapunov functions) are usually quite complex. This invention employs a novel nonlinear mapping method, introducing an improved Tan-type nonlinear mapping function to map the constrained output to an unconstrained space.

[0143] Step S3 specifically includes the following steps:

[0144] S3.1, When the output constraint type is constant output, the mapping function for:

[0145] ;

[0146] in, For the constrained original output variable, i.e. , It is the tangent function.

[0147] S3.2, When the output constraint type is time-varying output, the mapping function for:

[0148] .

[0149] This function is strictly monotonic, and the mapping function... It is strictly increasing within its domain, guaranteeing the invertibility of the mapping. Secondly, there are its boundary properties:

[0150] ,

[0151] This means that as long as the mapped variables Maintain boundedness, original output It will never violate the constraint boundary. and Meanwhile, time-varying constraints They have the same characteristics.

[0152] S3.3, let This ensures that the system will not experience a singularity.

[0153] In the initial steps of specific controller design, the output of each aircraft is... and the leader's output The above mapping function is used to convert the variables into unconstrained variables. and This mapping transformation inherently guarantees that the state variables will never violate physical constraints. When the state approaches the constraint boundary, the mapping function generates a large control force to push it back to the safe region, improving control performance. This allows subsequent dual neural networks and finite-time controllers to be designed in an unconstrained space, greatly simplifying the complexity of the control law.

[0154] Specifically, after completing feature extraction and data reception for the cross-domain aircraft, a dual neural network is constructed. To handle the unknown nonlinear functions in the system, this invention designs a dual neural network structure based on radial basis functions (RBF). The design process mainly considers the following factors: First, the heterogeneity of the cross-domain nature; the dynamic characteristics of airspace and water-based aircraft differ significantly, requiring consideration of both common knowledge and individual characteristics; second, compensation for unknown nonlinearities: the unknown functions in the system model... Online approximation is required; the dual neural network output fusion function is used to approximate the unknown nonlinear function in the system dynamics model online, thereby realizing real-time compensation for the complex dynamics and external disturbances of cross-domain aircraft; in addition, individuals in the cluster need to share learning results, so the network weight update law is used to improve the overall learning efficiency.

[0155] Step S4 specifically includes the following steps:

[0156] S4.1, Dedicated Network Compensation Each aircraft possesses unique dynamic characteristics (such as aerodynamic / hydrodynamic variations and actuator differences across different domains). This is equivalent to a personalized compensator for aspects not covered by the shared model. Its core functions are: firstly, receiving the aircraft's state and domain characteristics to calculate personalized nonlinear compensation outputs; secondly, adjusting its own weights online based on the aircraft's tracking error; and finally, combining with the shared network through weighted fusion to form the final uncertainty estimate. The dedicated network structure and parameters can be customized for different domains.

[0157] The input contains domain-specific states or characteristics.

[0158] Exclusive network compensation The unique dynamic characteristics of the follower aircraft, as output by the dedicated network, are as follows:

[0159] ;

[0160] in, It is the first The status of a follower aircraft It is the transpose of the real-time estimated weights of a dedicated neural network. These are dedicated network RBF basis functions. It is the state vector of the dedicated network system. It is an unknown dynamic estimate of each individual in the dedicated network.

[0161] S4.2, the shared network learns the common dynamic characteristics shared by all follower aircraft, and the output of the shared network is:

[0162] ;

[0163] in, It is the transpose of the network weights of a shared neural network. These are shared network RBF basis functions. It is an unknown dynamic estimate of each individual in the shared network. This is for the shared network system state vector.

[0164] S4.3, Section The total unknown nonlinear approximation for a single follower aircraft is:

[0165] ;

[0166] in, and These are the real-time weight estimates for shared and private networks, respectively.

[0167] S4.4, determine network performance based on error magnitude. If the shared network error is less than the dedicated network error, then... This indicates that the shared network performs better; conversely: This indicates that the dedicated network is more suitable for the current situation, and therefore the fusion weights are dynamically adjusted. The output of the dual neural network structure for:

[0168] .

[0169] The outputs of the dedicated network and the shared network are weighted and fused to form the final control approximation function; the fusion weights are dynamically adjusted based on real-time performance evaluation results, and the weight of the shared network is increased if the performance of the shared network is better. ↑), otherwise increase the weight of the dedicated network ( (↓); At the same time, through the distributed consensus algorithm, the shared network parameters are updated using the weight information of neighboring nodes, realizing knowledge sharing and weight collaborative optimization of cluster collaboration. Finally, the control accuracy is improved through residual compensation processing, and the accurate allocation of real-time control output is completed.

[0170] Specifically, the weight estimation of the dedicated neural network in step S4.1 includes the following steps:

[0171] S4.1.1, For a real, unknown dynamic function, there exists an ideal optimal weight. Make:

[0172] ;

[0173] in, It is a nonlinear function. For optimal weights, for transpose, For basis vector functions, To approximate the residual.

[0174] Estimated output of dedicated neural network for:

[0175] ;

[0176] in, To estimate the weights.

[0177] S4.1.2 defines the approximation error between the network estimate and the true value. for:

[0178] ;

[0179] Define weight error The difference between the actual weights and the estimated weights:

[0180] ;

[0181] Substituting and expanding, we obtain the approximation error equation:

[0182] .

[0183] S4.1.3, Define tracking error using the backstepping method Differentiating the error yields the error dynamics equation:

[0184] ;

[0185] in, For the control input of the design, The rate of change of the transformed error. for The derivative is then substituted into the neural network for approximation:

[0186] .

[0187] Specifically, the weight estimation of the shared neural network in step S4.2 is as follows:

[0188] ;

[0189] in, It is the first The follower aircraft was in In step-backstep control, the shared network weights are estimated at the next discrete time step. It is an estimate of the shared network weights at the current discrete time. It is the learning rate matrix of the shared network; These are the RBF basis function vectors of the shared network; It is the first The follower aircraft was in The backstepping tracking error of the step; It is the first Estimation of the shared network weights of each follower aircraft at the current moment; These are elements of the communication topology adjacency matrix, representing nodes. With nodes Inter-communication weights; It is the first A follower aircraft (i.e., a node) The set of neighbors of ) Let be the attenuation coefficient of the shared network, and .

[0190] Consistency items:

[0191] ;

[0192] in, This refers to the weights of neighboring nodes. Its purpose is to drive the system to gradually equalize the weights of two nodes when they differ.

[0193] The mathematical meaning is, This enables cluster collaborative learning, allowing all aircraft to share learning experiences and improve approximation efficiency.

[0194] Specifically, step S5 includes the following steps:

[0195] S5.1, the first step is residual compensation processing. In step S4, since the dual neural network inevitably produces approximation residuals when approximating unknown nonlinear functions... This leads to the real nonlinear function With network estimates There is an estimation error, i.e. If this error is not addressed, it will affect the final control accuracy.

[0196] To suppress the approximation error of the neural network, this invention introduces a residual compensation term in the control law design. Due to the actual approximation error Difficult to obtain directly, this invention utilizes backstepping tracking error. To approximate the impact of the residuals, the residual compensation term is designed as follows:

[0197] ;

[0198] in, To compensate for the gain; For the first The follower aircraft at the highest level The system tracking error is calculated step by step. This residual compensation term is ultimately integrated into the final control law. This effectively suppresses residual disturbances and improves the robustness and formation accuracy of the closed-loop system.

[0199] In a dual neural network structure, in order to dynamically adjust the fusion weights It is necessary to analyze the performance contributions of the shared network and the dedicated network. Since the true nonlinear function is unknown, this invention utilizes the system's tracking error. Approximately evaluate network performance. Calculate the shared network error separately. With dedicated network error (in and These are the local tracking errors generated when using only a single network. Network performance is judged based on the magnitude of the error: if... This indicates that the shared network performs better, and the current dynamics are dominated by commonalities, so the weights of the shared network need to be increased. Conversely, if This indicates that the dedicated network is more suitable for the current situation, and the weight of the dedicated network needs to be increased. This enables adaptive behavior of constraint boundaries and dynamic characteristics.

[0200] S5.2 employs an adaptive backstepping method to progressively design virtual control laws for each follower aircraft, define coordinate transformations, and define the first error variable. (Based on the mapped variables):

[0201] ;

[0202] in, It is the leader connectivity coefficient. This is the mapping function. The error measures the consistency among neighbors.

[0203] Redefining the first One error variable:

[0204] ;

[0205] in, It is the first The virtual control law is designed step by step.

[0206] Specifically, step S5 also includes the following steps:

[0207] S5.3, combining the approximation error of the dual neural network, performs the design of the backstepping virtual control law and the overall Lyapunov stability, targeting the first... Error dynamics of the step, combined with the system model The unknown nonlinear function is replaced with a dual neural network approximation form. The error dynamics equation is obtained as follows:

[0208] ;

[0209] in, for The derivative, for transpose, No. The follower aircraft was in The difference between the actual weights and the estimated weights of each step. It is the first The follower aircraft was in Step-shared network RBF basis functions, No. The follower aircraft was in Approaching the residual step for The derivative;

[0210] S5.4, to ensure the stability of the closed-loop system, the design of the first... Lyapunov function of step The system tracking error and the neural network weight estimation error are both incorporated into the energy function:

[0211] ;

[0212] in, The learning rate matrix is ​​such that, since the optimal weights are constants, ... ,right Taking the derivative and substituting it into the error dynamics equation, we get:

[0213] ;

[0214] in, for The derivative of .

[0215] S5.5, in order to eliminate unknown weight cross terms ,make The theoretical continuous update law for estimating weights using the dedicated network in step S4 is derived as follows:

[0216] ;

[0217] At the same time, in order to make Satisfying the negative definite condition (i.e.) ),make The ideal tracking target is a virtual control law Based on this, the first design The virtual control law for the step is:

[0218] ;

[0219] in, It is the first The linear gain of the step; For the first The dynamic estimate of the output of the dual neural network is used in the step-by-step and back-step derivation; The first-order time derivative of the previous virtual control law is used as a feedforward term to eliminate the coupled dynamics in the backstep recursion process; For the first The residual compensation gain of the step.

[0220] Specifically, step S5 also includes the following steps:

[0221] S5.6, the nonlinear feedback term is mainly applied to nonsingular fast finite-time control strategies. Nonsingular fast finite-time control is a tool for solving performance problems. It ensures rapid convergence within a finite time in formation control systems, which is a core performance advantage compared to traditional asymptotic convergence controllers. Accordingly, to improve convergence performance, we introduce a fast finite-time stability term into the virtual control law.

[0222] First, we analyze the problems of traditional finite-time methods, specifically the use of traditional terminal sliding mode. ( ) item, but Time-varying derivatives can introduce singularities. Therefore, non-singular switching functions are designed to avoid singularities.

[0223] ;

[0224] in, Error variables in backstep design ; The switching threshold; , where is the exponential parameter; , It is a positive odd number, and This guarantees .

[0225] when When the error is large, the system is in The nonlinear feedback mode provides fast finite-time convergence. The convergence time is bounded above and is independent of the initial state. This mode exhibits fast finite-time convergence, enabling rapid reduction of large errors.

[0226] when When the error is extremely small and close to zero (which is the dangerous region where singularities are likely to occur), the system switches to linear feedback mode. and a higher-order term This design ensures that in Place The derivative is bounded, thus completely avoiding singularity.

[0227] S5.7, after completing the design of the virtual control laws for the error variables of each order mentioned above, for the first... The highest rank of the follower aircraft (i.e., the...) For the (order) subsystem, derive and generate the final continuous ideal control law. Due to the influence of unknown nonlinear dynamics and external disturbances on the cross-domain flight system, the final control law... Integrating backstepping basic control, nonsingular fast finite-time control, and dual neural network compensation, the complete design is as follows:

[0228] ;

[0229] in, To track errors, To control the gain, For the first The derivative of the virtual control law. This is an estimate of the output of the dual neural network structure.

[0230] It is based on the backstepping recursive control term. Utilizing the derivative of the previous-order virtual control law and the current-order error, it provides basic linear exponential stability.

[0231] This is a non-singular switching function term. By introducing this term, the system is provided with non-singular, fast, and finite-time stability, ensuring tracking error accuracy. It can quickly converge to zero within a finite time and completely avoids the singularity problem that occurs when the error approaches zero in traditional terminal sliding mode.

[0232] Used to counteract unknown nonlinear dynamics of cross-domain aircraft online.

[0233] For residual compensation items, where To compensate for the gain, tracking error is used. Approximate estimation of the residuals is used to suppress the approximation error of the neural network and further improve the robustness of the system.

[0234] Specifically, step S6 includes the following steps:

[0235] In traditional control systems, the controller sends control signals to the actuators at fixed time intervals (e.g., every 0.01 seconds). However, in cross-domain aircraft swarms, frequent communication consumes a significant amount of valuable bandwidth resources.

[0236] To conserve valuable communication resources, we designed a Switching Threshold Event Triggered Control (ETC) strategy for each follower.

[0237] The following is a brief description of the event-triggered mechanism: Controller updates are no longer driven by fixed time intervals, but rather by a preset event trigger condition. Only when the condition is met does the aircraft broadcast its status information to its neighbors and update the controller. Understanding the advantages of fixed thresholds and relative thresholds, we combine the advantages of both methods to design a switching threshold. The specific steps are as follows:

[0238] S6.1 defines control measurement error. The controller update is no longer driven by fixed time intervals, but by the real-time measured deviation of the control signal. Define the... A follower aircraft Time measurement error for:

[0239] ;

[0240] in, The ideal control input that the system expects to execute at the current moment; For the first The moment when a follower aircraft last successfully triggered an event and updated its state; This refers to the control commands that the actuator is currently actually executing. This error... It measures the deviation between ideal control requirements and actual performance.

[0241] S6.2, Design the dual-mode switching threshold trigger condition. To balance control accuracy and communication flexibility, based on the current ideal control input... The system dynamically switches between the following two threshold strategies to determine the magnitude of the amplitude:

[0242] Modal 1 (relative threshold strategy): when ,in, When the preset control input boundary constant is used, i.e., when the system control input is small and in a relatively stable tracking state, a relative threshold strategy is adopted, and the next event trigger time is... The determination criteria are:

[0243] ;

[0244] in, Represents the minimum time lower bound that satisfies the condition; It is a relative threshold coefficient, which allows the tolerance error to be dynamically adjusted with the control input; This is a very small positive constant, used to avoid triggering communication infinitely frequently when the control input approaches zero (i.e., avoiding the Zeno phenomenon). This mode can save communication resources to the greatest extent when the error is small.

[0245] Modality 2 (Fixed Threshold Strategy): When When the control input is large, and the system is undergoing drastic cross-domain adjustments or encountering strong disturbances, a fixed threshold strategy is adopted, and the trigger condition is switched to:

[0246] ;

[0247] in, This is a fixed safety threshold. It's to ensure safety at the switching boundary. To ensure a smooth transition of the triggering conditions, this invention imposes strict boundary continuity constraints on the system parameters: This constraint completely eliminates the problem of frequent false triggers (Zeno phenomenon) or missed triggers caused by threshold discontinuities, ensuring the stability and safety of mode switching.

[0248] S6.3, Perform control update. When the system state meets any of the triggering conditions in step S6.2, the current time is marked as... At this time, the first Each follower aircraft will broadcast the latest status information to its neighbors, and the latest... The update is handed over to the actuator for control; if the conditions are not met, the instructions from the previous moment are maintained. .

[0249] The following simulation experiment verifies the beneficial effects of the present invention:

[0250] like Figure 2 and Figure 3 As shown, controlling a group of three followers and one leader can first avoid the Zeno phenomenon. Theoretical analysis can prove that the time interval between any two triggering events has a strictly positive lower bound. ,Right now This ensures that an infinite number of triggers will not occur within a finite time interval, and that the strategy is physically realizable. Secondly, there is a stability guarantee: within the event trigger interval, the system's Lyapunov function remains negative definite or semi-negative definite, thus guaranteeing the eventual uniform bounded stability of the closed-loop system.

[0251] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A finite-time cross-domain aircraft swarm formation control method based on neural networks, characterized in that, Specifically, the steps include the following: S1, to establish a unified nonlinear non-strict feedback system for the dynamic characteristics of cross-domain aircraft in different domains; S2 collects the real-time flight status and location information of multiple followers, sends the leader's status to multiple followers, and enables communication between multiple followers; S3. Design an improved Tan-type nonlinear mapping function, analyze the original state received by the sensor, identify the type of initial output constraint of the system, and obtain new unconstrained variables; S4. Construct a dual neural network that combines a shared network and a dedicated network. The shared network is used to learn the general dynamic characteristics of cross-domain aircraft. It adopts the same network structure and initial weights, and combines local gradients and distributed consistency terms to learn cross-domain commonalities. A dedicated network is used to compensate for individual differences among aircraft in different domains. The network is updated independently based on individual tracking errors, and a personalized network structure is designed according to the domain type. S5. A backstepping method combined with a switching function and a non-singular fast finite-time control strategy is designed to control the output of the dual neural network structure. S6, designed a switching threshold event triggering mechanism, which combines fixed threshold and relative threshold triggering conditions, and makes dual judgments based on weight change rate and time interval, so that the drone swarm can have different responses in different environments; Step S5 also includes the following steps: S5.3, combining the approximation error of the dual neural network, performs the design of the backstepping virtual control law and the overall Lyapunov stability, targeting the first... Error dynamics of the step, combined with the system model The unknown nonlinear function is replaced with a dual neural network approximation form. The error dynamics equation is obtained as follows: ； in, for The derivative, for transpose, No. The follower aircraft was in The difference between the actual weights and the estimated weights of each step. It is the first The follower aircraft was in Step-shared network RBF basis functions, No. The follower aircraft was in Approaching the residual step for The derivative; S5.4, to ensure the stability of the closed-loop system, the design of the first... Lyapunov function of step The system tracking error and the neural network weight estimation error are both incorporated into the energy function: ； in, The learning rate matrix is ​​such that, since the optimal weights are constants, therefore... ,right Taking the derivative and substituting it into the error dynamics equation, we get: ； in, for The derivative; S5.5, in order to eliminate unknown weight cross terms ,make The theoretical continuous update law for estimating weights using the dedicated network in step S4 is derived as follows: ； At the same time, in order to make Satisfying the negative definite condition, i.e. ,make The ideal tracking target is a virtual control law Based on this, the first design The virtual control law for the step is: ； in, It is the first The linear gain of the step; For the first The dynamic estimate of the output of the dual neural network is used in the step-by-step and back-step derivation; The first-order time derivative of the previous virtual control law is used as a feedforward term to eliminate the coupling dynamics in the backstep recursion process; For the first The residual compensation gain of the step.

2. The finite-time cross-domain aircraft swarm formation control method based on neural networks according to claim 1, characterized in that, Step S1 specifically includes the following steps: S1.1 establishes a heterogeneous cross-domain aircraft cluster consisting of 1 leader and N followers, where the dynamics model of each follower is described by a nonlinear, non-strict feedback system: ； The trajectory of a leader : Given a bounded smooth function; in, For the first The state variables of the follower aircraft For unknown smooth nonlinear functions, including: aerodynamic, hydrodynamic, and environmental disturbance factors. For the first The system order of a follower aircraft For the first The control input for a follower aircraft For the first The highest order of the state vectors of the follower aircraft state, For the first The output of a follower aircraft; S1.2, constrains the leader's trajectory and the followers' outputs: and derivative It is known and bounded; System output Subject to constraints, i.e. or ,in, , ; for Constant constraints, for Time-varying constraints, It is a constant. It is a time-varying function.

3. The finite-time cross-domain aircraft swarm formation control method based on neural networks according to claim 1, characterized in that, Step S3 specifically includes the following steps: S3.1, When the output constraint type is constant output, the mapping function for: ； in, For the constrained original output variables, It is the tangent function; S3.2, When the output constraint type is time-varying output, the mapping function for: ； S3.3, let This ensures that the system will not experience a singularity.

4. The finite-time cross-domain aircraft swarm formation control method based on neural networks according to claim 1, characterized in that, Step S4 specifically includes the following steps: S4.1, Dedicated Network Compensation The unique dynamic characteristics of the follower aircraft, as output by the dedicated network, are as follows: ； in, It is the first The status of a follower aircraft It is the transpose of the real-time estimated weights of a dedicated neural network. These are dedicated network RBF basis functions. It is the state vector of the dedicated network system. It is an unknown dynamic estimate of each individual in the dedicated network; S4.2, the shared network learns the common dynamic characteristics shared by all follower aircraft, and the output of the shared network is: ； in, It is the transpose of the network weights of a shared neural network. These are shared network RBF basis functions. It is an unknown dynamic estimate of each individual in the shared network. For the shared network system state vector; S4.3, Section The total unknown nonlinear approximation for a single follower aircraft is: ； in, and These are the real-time weight estimates for shared and private networks, respectively; S4.4, determine network performance based on error magnitude. If the shared network error is less than the dedicated network error, then... This indicates that the shared network performs better; conversely: This indicates that the dedicated network is more suitable for the current situation, and therefore the fusion weights are dynamically adjusted. The output of the dual neural network structure for: 。 5. The finite-time cross-domain aircraft swarm formation control method based on neural networks according to claim 4, characterized in that, Step S4.1, the weight estimation of the dedicated neural network, specifically includes the following steps: S4.1.1, For a real, unknown dynamic function, there exists an ideal optimal weight. Make: ； in, It is a nonlinear function. For optimal weights, for transpose, For basis vector functions, To approximate the residual; Estimated output of dedicated neural network for: ； in, To estimate the weights; S4.1.2 defines the approximation error between the network estimate and the true value. for: ； Define weight error The difference between the actual weights and the estimated weights: ； Substituting and expanding, we obtain the approximation error equation: ； In section S4.1.3, to ensure the stability of the subsequent closed-loop system, based on the Lyapunov stability analysis of the overall system, the weight update law for the continuous form of the dedicated network is derived. for: ； in, The learning rate matrix, This refers to the system tracking error defined in the subsequent backstepping method. For the attenuation coefficient of the dedicated network, and ; By discretizing the continuous update law of the exclusive network weights, we can directly obtain the final discrete update process of the exclusive network weights in practical engineering applications: ； in, and These are the dedicated network weight estimates for the next discrete time step and the current time step, respectively. The learning rate matrix for the dedicated network; It is the first The follower aircraft was in The backstepping tracking error of the step.

6. The finite-time cross-domain aircraft swarm formation control method based on neural networks according to claim 4, characterized in that, The weight estimation of the shared neural network in step S4.2 is specifically as follows: ； in, It is the first The follower aircraft was in In step-backstep control, the shared network weights are estimated at the next discrete time step. It is an estimate of the shared network weights at the current discrete time. It is the learning rate matrix of the shared network; These are the RBF basis function vectors of the shared network; It is the first The follower aircraft was in The backstepping tracking error of the step; It is the first Estimation of the shared network weights of each follower aircraft at the current moment; These are elements of the communication topology adjacency matrix; It is the first A set of neighbors for a follower aircraft; Let be the attenuation coefficient of the shared network, and .

7. The finite-time cross-domain aircraft swarm formation control method based on neural networks according to claim 1, characterized in that, Step S5 specifically includes the following steps: S5.1, the impact of the residual is approximated by using the backstepping tracking error, and the residual compensation term is designed accordingly: ； in, To compensate for the gain; For the first The follower aircraft at the highest level The system tracking error of the step; S5.2 employs an adaptive backstepping method to progressively design virtual control laws for each follower aircraft, defining coordinate transformations and the first error variable. : ； in, It is the leader connectivity coefficient. For mapping functions; Redefining the first Error variables : ； in, It is the first The virtual control law is designed step by step.

8. The finite-time cross-domain aircraft swarm formation control method based on neural networks according to claim 1, characterized in that, Step S5 also includes the following steps: S5.6, Designing non-singular switching functions to avoid singularity: ； in, Error variables in backstep design ; The switching threshold; , where is the exponential parameter; , It is a positive odd number, and ; S5.7, the final control law Integrating backstepping basic control, nonsingular fast finite-time control, and dual neural network compensation, the complete design is as follows: ； in, To track errors, To control the gain, For the first The derivative of the virtual control law. This is an estimate of the output of the dual neural network structure.

9. A finite-time cross-domain aircraft swarm formation control method based on neural networks according to claim 1, characterized in that, Step S6 specifically includes the following steps: S6.1, defining the first A follower aircraft Time measurement error for: ； in, The ideal control input that the system expects to execute at the current moment; For the first The moment when a follower aircraft last successfully triggered an event and updated its state; The control commands that the actuator is currently actually executing; S6.2, Design the dual-mode switching threshold trigger condition, when ,in, As a preset control input boundary constant, a relative threshold strategy is adopted, and the next event trigger time is... The determination criteria are: ； in, Represents the minimum time lower bound that satisfies the condition; This is the relative threshold coefficient; It is a very small positive number; when The trigger condition has been changed to: ； in, A fixed safety threshold is set. S6.3, When the system state satisfies any of the triggering conditions in step S6.2, the current time is marked as... At this time, the first Each follower aircraft will broadcast the latest status information to its neighbors, and the latest... The update is handed over to the actuator for control; if the conditions are not met, the instructions from the previous moment are maintained. .

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