A fuzzy optimization formation control method and system for multiple unmanned systems

Abstract

This application discloses a fuzzy optimization formation control method and system for multiple unmanned systems, belonging to the field of unmanned control technology. The method includes: after confirming the positions of the target system and neighboring systems, calculating the position errors of the target system and neighboring systems; inputting the position data and position errors of the target system into a fuzzy identifier to obtain dynamic data; designing an adaptive backstepping controller based on the target system's position data, position errors, and dynamic data to obtain the adaptive backstepping control input; obtaining the optimal control input based on the new error dynamic system, and applying smooth saturation constraints to the adaptive backstepping control input and the optimal control input to obtain the control signal. This application utilizes the universal approximation characteristic of fuzzy logic systems to establish a fuzzy identifier that approximates the dynamic data of the target system and a formation optimization controller with a single evaluation structure, solving the technical problem of control performance degradation caused by input saturation in unmanned formations.

Description

Technical Field

[0001] This application belongs to the field of unmanned control technology, specifically relating to a fuzzy optimization formation control method and system for multiple unmanned systems. Background Technology

[0002] Unmanned systems are systems that rely on their own perception, decision-making, and execution capabilities to independently complete various tasks, encompassing a variety of types such as unmanned vehicles, unmanned ships, unmanned underwater vehicles, and drones. With the rapid advancement of artificial intelligence, information technology, and robotics, these systems are now widely used in fields such as intelligent transportation, search and rescue operations, environmental monitoring, marine resource exploration, industrial automation, and military operations, demonstrating their enormous potential in improving efficiency and safety.

[0003] As the scope, intensity, and complexity of operational tasks expand, relying solely on a single unmanned system (UHV) is no longer sufficient to meet current operational demands. Therefore, collaborative operations involving multiple UHV systems have become particularly important. Against this backdrop, formation control, as a key technology for achieving collaborative operations among multiple UHV systems, is gradually becoming a research focus and hot topic, attracting considerable attention from researchers. In reality, each UHV system, in addition to facing external environmental disturbances, has a limited force or torque provided by its own actuators, i.e., the input saturation problem. Ignoring this problem in the design of control schemes may lead to a decline in formation control performance or instability of the formation control system. Therefore, the input saturation problem is crucial for the formation control of multiple UHV systems. Due to factors such as parameter perturbations, unmodeled dynamic characteristics, and external disturbances in the dynamic models of UHV systems, traditional formation control methods often struggle to achieve ideal performance. Summary of the Invention

[0004] Purpose of the invention: This application develops a fuzzy optimization formation control method and system for multi-unmanned systems, aiming to solve the technical problem of degraded unmanned formation control performance in the prior art.

[0005] Technical Solution: In a first aspect, embodiments of this application provide a fuzzy optimization formation control method for multiple unmanned systems, applied to an unmanned formation system, wherein the unmanned formation system includes multiple unmanned systems, and the fuzzy optimization formation control method includes:

[0006] The target system and neighboring systems are identified among the multiple unmanned systems, and the location information of the target system and neighboring systems is obtained;

[0007] The location error is obtained based on the location information of the target system and the neighboring system;

[0008] The position data and position error of the target system are input into a preset fuzzy identifier to obtain the dynamic data of the target system;

[0009] An adaptive backstepping controller is designed based on the position data, position error, and dynamic data of the target system, and the adaptive backstepping control input is obtained.

[0010] Obtain the cooperative tracking error dynamic system of the target system, and obtain the optimal control input based on the error dynamic system;

[0011] Smooth saturation constraints are applied to the adaptive backstepping control input and the optimal control input to obtain the control signal;

[0012] The target system is controlled based on the control signals to achieve formation control.

[0013] In some embodiments, the step of presetting the fuzzy detector includes:

[0014] Based on the location data of the target system, an Eulerian-Lagrange physical model of the target system is constructed, and a model transformation is performed to obtain a dynamic model, which includes unknown dynamic parameters; the characterization formula of the dynamic model includes:

[0015]

[0016] in, For x 1,i The first derivative, x 1,i The position of the target system i; x 2,i τ is the velocity of the target system i. Δ,i =μ i -τ i μ i For control input with input saturation, For adaptive backstepping control input vector, To optimize the control input vector; σ i For environmental disturbance; f 2,i (x 1,i ,x 2,i ) and b i (x 2,i ) represents an unknown dynamic parameter;

[0017] Based on the approximation principle of fuzzy logic systems, unknown dynamic parameters are solved to obtain a model identifier; the characterization formula of the fuzzy identifier includes:

[0018]

[0019] in, for The first derivative, For x 2,i The estimate, x 2,i The velocity of the target system i; and They are respectively and The estimate, and The ideal fuzzy parameter matrix is ​​represented by T, which is the transpose operation. It is a vector composed of fuzzy basis functions; It is a matrix composed of fuzzy basis functions;

[0020] The formulas for characterizing dynamic parameters include:

[0021]

[0022] Among them, A x,i for The converged matrix; for The converged matrix;

[0023] In some embodiments, the step of designing an adaptive backstepping controller based on the position data, position error, and dynamic data of the target system, and obtaining the adaptive backstepping control input includes:

[0024] The backstep virtual control input is obtained based on the position error;

[0025] Confirm the speed data of the target system and the neighboring system, and obtain the speed error between the target system and the neighboring system;

[0026] The adaptive law of the target system is obtained based on the backstepping virtual control input and the velocity error;

[0027] The adaptive backstepping control input is obtained based on the backstepping virtual control input and the adaptive law.

[0028] In some embodiments, the step of obtaining the backstepping virtual control input based on the position error includes:

[0029] Based on the location data of the target system and the neighboring systems, and the location error, a location error vector is obtained;

[0030] Construct a Lyapunov function based on the position error vector;

[0031] The adaptive backstepping virtual control input is obtained based on the position error vector and the Lyapunov function.

[0032] In some embodiments, the step of obtaining the cooperative tracking error dynamic system of the target system and obtaining the optimal control input based on the error dynamic system includes:

[0033] Obtain the dynamic system of the cooperative tracking error of the target system with an affine nonlinear form, and the characterization formula of the dynamic system of the cooperative tracking error includes:

[0034]

[0035] in, For the cooperative tracking error dynamic system of the target system i, E i This is a combination of position and velocity errors in the new error dynamic system; Let n be the drift dynamics matrix of the new error dynamic system, where n is the system dimension and h is the dynamics matrix. E,i This refers to the mechanical error caused by drift. Let N be the gain matrix of the new error dynamic system, and N be the number of unmanned systems in the formation. i,j Let b be the time-varying relative position vector between target system i and neighboring system j; i This is the original dynamic gain matrix;

[0036] A local cost function is constructed based on the aforementioned cooperative tracking error dynamic system. The characterization formula of the local cost function includes:

[0037]

[0038] Among them, V i Let be the local cost function of target system i; t be time; e be a constant; γ be the local cost function of target system i. i γ is the discount factor for target system i. i >0; s is the integration variable; and It is a symmetric positive definite weighted matrix. Let U be the set of all neighboring nodes of the target system i. i U is the optimal control input to be designed for target system i. j For the control input of neighbor system j;

[0039] The Hamiltonian function is obtained based on the cooperative tracking error dynamic system and the local cost function. The characterization formula of the Hamiltonian function includes:

[0040]

[0041] Among them, H i The Hamiltonian function is mentioned above. For V i (Ei (relative to E) i The gradient of F; i For the new error dynamic system drift mechanics matrix; G i The gain matrix of the new error dynamic system;

[0042] Solve the Hamiltonian function to obtain the result of the optimal control input:

[0043] By solving The optimal control input is obtained as follows:

[0044]

[0045] in, This is the optimal control input; for Relative to E i gradient, This is the optimal cost function.

[0046] In some embodiments, the step of solving the Hamiltonian function to obtain the optimal control input further includes:

[0047] The Hamilton-Jacobi-Bellman equation is obtained based on the Hamiltonian function and the optimal control input. The characterization formula of the Hamilton-Jacobi-Bellman equation includes:

[0048]

[0049] in, For matrix G i and R i,i The matrix of the new combination; For matrix G j R i,j and R j,j The matrix of the new combination; The optimal cost function for the neighbor system Relative to E j The gradient; This is its own optimal cost function;

[0050] The optimal cost function is obtained based on a fuzzy logic system, and the optimal cost function is obtained relative to the combination E of position error and velocity error. i The gradient;

[0051] The ideal optimal control input is obtained based on the gradient, and its characterization formula includes:

[0052]

[0053] in, For ideal optimal control input; for; for; for Relative to E i gradient, for; For ε c,i (E i (relative to E) i The gradient, ε c,i (E i ) represents the approximate error.

[0054] In some embodiments, the step of solving the Hamiltonian function to obtain the optimal control input further includes:

[0055] The Hamiltonian function is updated based on the optimal cost function, the gradient, and the ideal optimal control input, and its characterization formula includes:

[0056]

[0057] To obtain an approximate value of the ideal optimal control input, the approximate formula for the optimal control input includes:

[0058]

[0059] in, This is the approximate optimal control input; for Relative to E i gradient, Let l be a vector composed of fuzzy basis functions. c,i The number of fuzzy basis functions; For the ideal weight vector The estimate.

[0060] In some embodiments, the ideal weight vector Estimate The characterization formulas include:

[0061]

[0062]

[0063] in, for The update law; k wa,i >0 and k wb,i >0 represents a design parameter. For parameters greater than 0, For the new combination matrix, To approximate the Hamiltonian function value, Lyapunov function with additional terms, Regarding E i The gradient.

[0064] In some embodiments, the step of applying smooth saturation constraints to the adaptive backstepping control input and the optimal control input to obtain the control signal includes:

[0065] A preliminary signal is obtained based on the adaptive backstepping control input and the optimal control input. The characterization formula of the preliminary signal includes:

[0066]

[0067] Where, τ i This is a preliminary control signal; This serves as the adaptive backstepping control input for the target system i; This is the optimal control input for the target system i;

[0068] The initial signal is subjected to smooth saturation constraint to obtain a control signal, the characterization formula of which includes:

[0069]

[0070] Where, τ= l,i For τ i The constituent elements (l = 1, 2, ..., n) in the middle The maximum value after the switch, a l,i >0 is a design parameter, S i (·) represents the sigmoid function, with the following expression:

[0071]

[0072] Secondly, embodiments of this application also provide a fuzzy optimization formation control system for multiple unmanned systems, applied to an unmanned formation system, wherein the unmanned formation system includes multiple unmanned systems, and the fuzzy optimization formation control system includes:

[0073] A location acquisition module is used to identify the target system and neighboring systems among multiple unmanned systems and acquire the location information of the target system and neighboring systems;

[0074] An error acquisition module is used to acquire a position error based on the position information of the target system and the neighboring system.

[0075] A dynamic data acquisition module is used to input the position data and position error of the target system into a preset fuzzy identifier to acquire the dynamic data of the target system.

[0076] A backstepping control input acquisition module is used to design an adaptive backstepping controller based on the position data, position error, and dynamic data of the target system, and to acquire the adaptive backstepping control input.

[0077] A control output acquisition module is used to acquire the cooperative tracking error dynamic system of the target system and acquire the optimal control input based on the error dynamic system.

[0078] The control output optimization module is used to apply smooth saturation constraints to the adaptive backstepping control input and the optimal control input, obtain a control signal, and control the target system based on the control signal to achieve formation control.

[0079] Beneficial Effects: Compared with the prior art, the fuzzy optimization formation control method for multiple unmanned systems provided in this application calculates the position errors of the target system and neighboring systems after confirming their positions. The position data and position errors of the target system are input into a fuzzy identifier to obtain the dynamic data of the target system. An adaptive backstepping controller is designed based on the position data, position errors, and dynamic data of the target system to obtain the adaptive backstepping control input. An optimal control input is designed using the adaptive backstepping control input, and smooth saturation constraints are applied to the adaptive backstepping control input and the optimal control input to obtain the control signal, which is then used for unmanned formation control. This application utilizes the universal approximation characteristic of fuzzy logic systems to establish a formation optimization controller based on the approximation and prediction of the target system's dynamic data using a fuzzy identifier and a single evaluation structure. The universal approximation characteristic of fuzzy logic systems solves the technical problem of control performance degradation caused by input saturation in unmanned formations. Furthermore, the optimal control input is obtained through backstepping, and finally, smooth saturation constraints are applied. The optimal control input is obtained through optimal control theory, thus optimizing and reducing the control energy consumption of unmanned formations. Attached Figure Description

[0080] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0081] Figure 1 A flowchart illustrating the steps of a fuzzy optimization formation control method for a multi-unmanned system provided in this application embodiment;

[0082] Figure 2A flowchart illustrating the steps of setting up a fuzzy identifier in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment;

[0083] Figure 3 A flowchart illustrating the steps for obtaining adaptive backstepping control input in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment;

[0084] Figure 4 A flowchart illustrating the steps for obtaining backstepping virtual control input in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment;

[0085] Figure 5 A flowchart illustrating the steps for calculating the optimal control input in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment;

[0086] Figure 6 A flowchart illustrating the steps involved in designing the ideal optimal control input in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment;

[0087] Figure 7 A flowchart illustrating the steps of approximating the optimal control input in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment;

[0088] Figure 8 A flowchart illustrating the steps of smooth saturation constraint in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment;

[0089] Figure 9 A module connection diagram of a fuzzy optimization formation control system for a multi-unmanned system provided in an embodiment of this application;

[0090] Figure 10 A structural block diagram of the fuzzy optimization formation control method;

[0091] Figure 11 The flowchart for the formation control method;

[0092] Reference numerals: 10, Position acquisition module; 20, Error acquisition module; 30, Power data acquisition module; 40, Backstepping control input acquisition module; 50, Control output acquisition module; 60, Control output optimization module; 70, Output control module. Detailed Implementation

[0093] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0094] Unmanned systems are systems that rely on their own perception, decision-making, and execution capabilities to independently complete various tasks, encompassing a variety of types such as unmanned vehicles, unmanned ships, unmanned underwater vehicles, and drones. With the rapid advancement of artificial intelligence, information technology, and robotics, these systems are now widely used in fields such as intelligent transportation, search and rescue operations, environmental monitoring, marine resource exploration, industrial automation, and military operations, demonstrating their enormous potential in improving efficiency and safety.

[0095] As the scope, intensity, and complexity of operational tasks expand, relying solely on a single unmanned system (UAV) is no longer sufficient to meet current operational demands. Therefore, collaborative operation of multiple UAVs has become particularly important. Against this backdrop, formation control, as a key technology for achieving collaborative operation of multiple UAVs, is gradually becoming a research focus and hot topic, attracting considerable attention from researchers. In reality, each UAV faces not only external environmental disturbances but also a limited force or torque provided by its own actuators, i.e., the input saturation problem. Ignoring this problem in the design of control schemes may lead to a decline in formation control performance or instability of the formation control system. Therefore, the input saturation problem is crucial for the formation control of multiple UAVs. Due to factors such as parameter perturbations, unmodeled dynamic characteristics, and external disturbances in the dynamic models of UAVs, traditional formation control methods often struggle to achieve ideal performance. However, fuzzy logic systems, with their universal approximation properties, provide an effective approach to solving the modeling and control problems of such UAVs. It is worth noting that most multiple UAVs are powered by rechargeable batteries. To achieve longer endurance, the energy consumption of multi-UAV formation control is an important factor to consider. Optimal control theory provides an important approach to optimizing energy consumption in the formation control of multi-unmanned systems. Currently, there is a lack of algorithms for fuzzy optimization control of multi-unmanned systems considering input saturation. Therefore, the fuzzy optimization formation control method for multi-unmanned systems proposed in this invention has significant application value and practical significance.

[0096] This invention presents a formation control method for multi-unmanned systems with unknown dynamics and input saturation, enabling energy optimization. The method utilizes a smooth saturation model to constrain the control input. While modeling the unknown dynamics of the unmanned system using a fuzzy logic system, it establishes a single evaluation structure to approximate the solution of the Hamilton-Jacobi-Bellman equations to obtain the optimal control input. Furthermore, an adaptive law is designed to reduce the impact of input saturation on the system.

[0097] In view of this, embodiments of this application provide a fuzzy optimization formation control method for multiple unmanned systems. After confirming the positions of the target system and neighboring systems, the position errors of the target system and neighboring systems are calculated. The position data and position errors of the target system are input into a fuzzy identifier to obtain the dynamic data of the target system. An adaptive backstepping controller is designed based on the position data, position errors, and dynamic data of the target system to obtain the adaptive backstepping control input. The optimal control input is designed through the adaptive backstepping control input, and smooth saturation constraints are applied to the adaptive backstepping control input and the optimal control input to obtain the control signal, which is then used for unmanned formation control. This application utilizes the universal approximation characteristic of fuzzy logic systems to establish a formation optimization controller with a single evaluation structure based on the approximation and prediction of the target system's dynamic data q by a fuzzy identifier. By leveraging the universal approximation characteristic of fuzzy logic systems, the technical problem of control performance degradation caused by input saturation in unmanned formation is solved. Furthermore, the optimal control input is obtained through backstepping, and finally, smooth saturation constraints are applied. The optimal control input is obtained through optimal control theory, thus optimizing and reducing the control energy consumption of unmanned formation.

[0098] In some embodiments, please refer to 1. Figure 1 This is a flowchart illustrating the steps of a fuzzy optimization formation control method for multiple unmanned systems provided in this application. The fuzzy optimization formation control method for multiple unmanned systems provided in this application is applied to an unmanned formation system, which includes multiple unmanned systems. Specifically, it is implemented through steps 100 to 700:

[0099] Step 100: Identify the target system and neighboring systems among multiple unmanned systems, and obtain the location information of the target system and neighboring systems.

[0100] Step 200: Obtain the location error based on the location information of the target system and neighboring systems;

[0101] Step 300: Input the position data and position error of the target system into the preset fuzzy identifier to obtain the dynamic data of the target system.

[0102] In some embodiments, please refer to Figure 2 , Figure 2This is a flowchart illustrating the steps of setting up a fuzzy identifier in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment. The method of setting up a fuzzy identifier in this application is specifically implemented through steps 310 to 320:

[0103] Step 310: Construct an Eulerian-Lagrange physical model of the target system based on the location data of the target system, and perform model transformation to obtain a dynamic model, which includes unknown dynamic parameters.

[0104] In some embodiments, the characterization formula of the dynamic model includes:

[0105]

[0106] in, For x 1,i The first derivative, x 1,i The position of target system i; x 2,i τ represents the velocity of the target system i. Δ,i =μ i -τ i μ i For control input with input saturation, For adaptive backstepping control input vector, To optimize the control input vector; σ i For environmental disturbance; f 2,i (x 1,i ,x 2,i ) and b i (x 2,i ) represents an unknown dynamic parameter.

[0107] Step 320: Based on the approximation principle of fuzzy logic systems, solve for the unknown dynamic parameters and obtain the model identifier.

[0108] In some embodiments, the representation formula of the fuzzy identifier includes:

[0109]

[0110] in, for The first derivative, For x 2,i The estimate, x 2,i Let i be the velocity of the target system i; and They are respectively and The estimate, and The ideal fuzzy parameter matrix is ​​represented by T, which is the transpose operation. It is a vector composed of fuzzy basis functions; It is a matrix composed of fuzzy basis functions;

[0111] The formulas for characterizing dynamic parameters include:

[0112]

[0113] Among them, A x,i for The converged matrix; for The converged matrix;

[0114] Step 400: Design an adaptive backstepping controller based on the position data, position error, and dynamic data of the target system, and obtain the adaptive backstepping control input.

[0115] In some embodiments, please refer to Figure 3 , Figure 3 The flowchart illustrates the steps for obtaining adaptive backstepping control input in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment. Specifically, the method for obtaining adaptive backstepping control input in this application is implemented through steps 410 to 440:

[0116] Step 410: Obtain the backstepping virtual control input based on the position error.

[0117] In some embodiments, please refer to Figure 4 , Figure 4 The flowchart illustrates the steps for obtaining backstepping virtual control input in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment. Specifically, the method for obtaining backstepping virtual control input in this application is implemented through steps 411 to 413:

[0118] Step 411: Based on the location data of the target system and neighboring systems, and the location error, obtain the location error vector.

[0119] Step 412: Construct the Lyapunov function based on the position error vector.

[0120] Step 413: Obtain the adaptive backstepping virtual control input based on the position error vector and Lyapunov function.

[0121] Step 420: Confirm the speed data of the target system and neighboring systems, and obtain the speed error between the target system and neighboring systems.

[0122] Step 430: Obtain the adaptive law of the target system based on the backstepping virtual control input and velocity error.

[0123] Step 440: Obtain adaptive backstepping control input based on backstepping virtual control input and adaptive law.

[0124] Step 500: Obtain the cooperative tracking error dynamic system of the target system, and obtain the optimal control input based on the error dynamic system.

[0125] In some embodiments, please refer to Figure 5 , Figure 5 This is a flowchart illustrating the steps of predicting the optimal control input in the fuzzy optimization formation control method for multi-unmanned systems provided in this application. The method for designing the optimal control input in this application is specifically implemented through steps 510 to 540:

[0126] Step 510: Obtain the dynamic system of the cooperative tracking error of the target system in affine nonlinear form.

[0127] In some embodiments, the characterization formula for the cooperative tracking error dynamic system includes:

[0128]

[0129] in, For the cooperative tracking error dynamic system of target system i, E i This is a combination of position and velocity errors in the new error dynamic system; Let n be the drift dynamics matrix of the new error dynamic system, where n is the system dimension and h is the dynamics matrix. E,i This refers to the mechanical error caused by drift. Let N be the gain matrix of the new error dynamic system, and N be the number of unmanned systems in the formation. i,j Let b be the time-varying relative position vector between target system i and neighboring system j; i This is the original dynamic gain matrix;

[0130] Step 520: Construct a local cost function based on the collaborative tracking error dynamic system.

[0131] In some embodiments, the characterization formula for the local cost function includes:

[0132]

[0133] Among them, V i Let be the local cost function of target system i; t be time; e be a constant; γ be the local cost function of target system i. i γ is the discount factor for target system i. i >0; s is the integration variable; and It is a symmetric positive definite weighted matrix. Let U be the set of all neighboring nodes of the target system i. i U is the optimal control input to be designed for target system i. j For the control input of neighbor system j;

[0134] Step 530: Obtain the Hamiltonian function based on the collaborative tracking error dynamic system and the local cost function.

[0135] In some embodiments, the characterization formula for the Hamiltonian function includes:

[0136]

[0137] Among them, H i It is the Hamiltonian function; For V i (E i (relative to E) i The gradient of F; i For the new error dynamic system drift mechanics matrix; G i The gain matrix of the new error dynamic system;

[0138] Step 540: Solve for the Hamiltonian function to obtain the optimal control input.

[0139] In some embodiments, by solving The optimal control input is obtained as follows:

[0140]

[0141] in, This is the optimal control input; for Relative to E i gradient, This is the optimal cost function.

[0142] In some embodiments, please refer to Figure 6 , Figure 6 The flowchart of the steps for designing the ideal optimal control input in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment is shown. In this application, the method for designing the ideal optimal control input is specifically implemented through steps 550 to 570:

[0143] Step 550: Obtain the Hamilton-Jacobi-Bellman equations based on the Hamiltonian function and optimal control input.

[0144] In some embodiments, the characterization formulas for the Hamilton-Jacobi-Bellman equations include:

[0145]

[0146] in, For matrix G i and R i,i The matrix of the new combination; For matrix G jR i,j and R j,j The matrix of the new combination; The optimal cost function for the neighbor system Relative to E j The gradient; This is its own optimal cost function;

[0147] Step 560: Obtain the optimal cost function based on the fuzzy logic system, and obtain the optimal cost function relative to the combination E of position error and velocity error. i The gradient;

[0148] Step 570: Design the optimal control input based on gradient.

[0149] In some embodiments, the characterization formula for designing the ideal optimal control input includes:

[0150]

[0151] in, For ideal optimal control input; For R i,i The inverse matrix; For G i Transpose of; for Relative to E i gradient, for; For ε c,i (E i (relative to E) i The gradient, ε c,i (E i ) represents the approximate error.

[0152] In some embodiments, please refer to Figure 7 , Figure 7 The flowchart illustrates the steps for approximating the optimal control input in the fuzzy optimization formation control method for multi-unmanned systems provided in this application embodiment. Specifically, the method for approximating the optimal control input is implemented through steps 580 to 590:

[0153] Step 580: Update the Hamiltonian function based on the optimal cost function, gradient, and ideal optimal control input.

[0154] In some embodiments, the formula for updating the Hamiltonian function includes:

[0155]

[0156] Step 590: Obtain an approximate value of the ideal optimal control input.

[0157] In some embodiments, the formula for representing the approximate optimal control input includes:

[0158]

[0159] in, This is the approximate optimal control input; for Relative to E i gradient, Let l be a vector composed of fuzzy basis functions. c,i The number of fuzzy basis functions; For the ideal weight vector The estimate.

[0160] In some embodiments, the ideal weight vector Estimate The characterization formulas include:

[0161]

[0162]

[0163] in, for The update law; k wa,i >0 and k wb,i >0 represents a design parameter. For parameters greater than 0, For the new combination matrix, To approximate the Hamiltonian function value, Lyapunov function with additional terms, For L w,i (E i Regarding E i The gradient.

[0164] Step 600: Apply smooth saturation constraints to the adaptive backstepping control input and the optimal control input to obtain the control signal.

[0165] In some embodiments, please refer to Figure 8 , Figure 8 This is a flowchart illustrating the steps of smooth saturation constraint in the fuzzy optimization formation control method for multi-unmanned systems provided in this application. The method for obtaining the control signal by applying smooth saturation constraint to the adaptive backstepping control input and the optimal control input in this application is specifically implemented through steps 610 to 620:

[0166] Step 610: Obtain the preliminary signal based on the adaptive backstepping control input and the optimal control input.

[0167] In some embodiments, the formula for representing the initial signal includes:

[0168]

[0169] Where, τ i This is a preliminary control signal; The adaptive backstepping control input is for the target system i; This is the optimal control input for the target system i.

[0170] Step 620: Apply smooth saturation constraints to the initial signal to obtain the control signal.

[0171] In some embodiments, applying a smooth saturation constraint to the initial signal to obtain a formula representing the control signal includes:

[0172]

[0173] Where, τ l,i For τ i The constituent elements (l = 1, 2, ..., n) in the middle The maximum value after the switch, a l,i >0 is a design parameter, S i (·) represents the sigmoid function, with the following expression:

[0174]

[0175] Step 700: Control the target system based on control signals to achieve formation control.

[0176] Understandably, embodiments of this application provide a fuzzy optimization formation control method for multiple unmanned systems. After confirming the positions of the target system and neighboring systems, the position errors of the target system and neighboring systems are calculated. The position data and position errors of the target system are input into a fuzzy identifier to obtain the dynamic data of the target system. An adaptive backstepping controller is designed based on the position data, position errors, and dynamic data of the target system to obtain the adaptive backstepping control input. The optimal control input is designed through the adaptive backstepping control input, and smooth saturation constraints are applied to the adaptive backstepping control input and the optimal control input to obtain the control signal, which is then used for unmanned formation control. This application utilizes the universal approximation characteristic of fuzzy logic systems to establish a formation optimization controller based on the approximation and prediction of the target system's dynamic data and a single evaluation structure using a fuzzy identifier. By leveraging the universal approximation characteristic of fuzzy logic systems, the technical problem of control performance degradation caused by input saturation in unmanned formation is solved. Furthermore, the optimal control input is obtained through backstepping, and finally, smooth saturation constraints are applied. The optimal control input is obtained through optimal control theory, thus optimizing and reducing the control energy consumption of unmanned formation.

[0177] For example, please refer to Figure 10 and Figure 11 , Figure 10 The structural block diagram of the fuzzy optimization formation control method is shown. Figure 11 The flowchart of the formation control method is shown below. An example of the modeling steps of the fuzzy optimization formation control method for multi-unmanned systems provided in the embodiments of this application is as follows:

[0178] 1. Establish a mathematical model for the unmanned system.

[0179] Consider a formation system consisting of N unmanned systems and a virtual navigator. The i-th unmanned system can be described by the following Eulerian-Lagrange system (i = 1, 2, ..., N):

[0180]

[0181] In the formula, and Let represent the inertial matrix, Coriolis force-centrifugal force matrix, and gravity vector of unmanned system i, respectively. as well as It is unknown. and These represent the position, velocity, and acceleration vectors of the unmanned system, respectively. Indicates environmental disturbance. For control inputs with input saturation, i.e.:

[0182]

[0183] In the formula, l = 1, 2, ..., n, and sign(·) is the sign function. To control input τ l,i The maximum value.

[0184] To facilitate design control, let x 1,i =q i , and τ Δ,i =μ i -τ i Therefore, (1) is reformulated as

[0185]

[0186] In the formula, For x 1,i The first derivative, x 1,i The position of target system i; x 2,i τ represents the velocity of the target system i. Δ,i =μ i -τ i μ iFor control input with input saturation, τ i For initial control signals, For the adaptive backstepping control input of the target system i, σ is the optimal control input for target system i; i For environmental disturbance; f 2,i (x 1,i ,x 2,i ) and b i (x 2,i ) represents an unknown dynamic parameter, f 2,i (x 1,i ,x 2,i )=-M i (x 2,i ) -1 (C i (x 1,i ,x 2,i )x 2,i +g i (x 2,i )) and b i (x 2,i ) = M i (x 2,i ) -1 These are unknown dynamic parameters.

[0187] 2. Design a smooth saturated input model

[0188] Since (2) is a non-smooth saturated function, it is necessary to design the following smooth saturated model to replace it:

[0189]

[0190] In the formula, τ l,i For τ i The constituent elements (l = 1, 2, ..., n) in the middle The maximum value after the switch, a l,i >0 is a design parameter, S i (·) represents the sigmoid function, with the following expression:

[0191]

[0192] 3. Design a fuzzy recognition device

[0193] Because f 2,i (x 1,i ,x 2,i ) and b i (x 2,i Since (4) is unknown, a fuzzy logic system design will be used to reconstruct the unknown dynamic model of the system. Therefore, (4) is re-expressed as

[0194]

[0195] In the formula For an ideal fuzzy parameter matrix, Let be a vector composed of fuzzy basis functions, and let its input vector be... It is a matrix composed of fuzzy basis functions. This is the approximate error vector.

[0196] Due to the ideal fuzzy parameter matrix and Since it is unknown, a fuzzy approximation-based identifier is designed according to (7). as follows:

[0197]

[0198] In the formula, for The first derivative of is used to characterize the identifier. For x 2,i The estimate, x 2,i Let i be the velocity of the target system i; and They are respectively and The estimate, and The ideal fuzzy parameter matrix is ​​represented by T, which is the transpose operation. It is a vector composed of fuzzy basis functions; It is a matrix composed of fuzzy basis functions;

[0199]

[0200] and The update law is designed as follows:

[0201]

[0202] In the formula, for The renewal law; for The renewal law; for The law of renewal; Ξ a,i Ξ b,i and Ξ c,i Positive design parameters; For x 2,i The estimate; This is for estimating the error.

[0203] and It can converge to a constant matrix and a vector A respectively. x,i θ f,i , and χ i (8) It can be rebuilt as follows:

[0204]

[0205] In the formula, A x,i for The converged matrix; for The converged matrix;

[0206] 4. Design a fuzzy optimization formation controller

[0207] Based on equation (10), the controller will be designed using backstepping and adaptive dynamic programming, while an adaptive law will be designed to reduce the impact of input saturation. Define x 1,0 The position vector of the unmanned system.

[0208] Define the formation position error vector E of the i-th unmanned system. 1,i and velocity error vector E 2,i as follows:

[0209]

[0210] E 2,i =x 2,i -α i (12)

[0211] In the formula, a i,j The time-varying relative position vector between the i-th unmanned system and the j-th unmanned system, where i is the target system and j is the neighboring system; x Δi,j Let be the positional deviation between the i-th unmanned system and the j-th unmanned system. For adaptive backstepping virtual control input vector, To optimize the virtual control input vector;

[0212] Step 1: According to (12) and (3), the time derivative of (11) is

[0213]

[0214] in, The position error vector E 1,i The first derivative of ; j is the neighbor system, and N is the number of neighbor systems; For x1,i The first derivative; For x 1,j The first derivative; For x Δi,j The first derivative.

[0215] Define the Lyapunov function L 1,i as follows:

[0216]

[0217] Combining the time derivatives of (13) and (14) The derivation is as follows:

[0218]

[0219] An adaptive backstepping virtual control law can be designed as follows:

[0220]

[0221] In the formula, It is a positive definite design matrix.

[0222] Then, substituting (16) into (15) yields...

[0223]

[0224] Step 2: According to (23), we can obtain E in (12). 2,i time derivative for:

[0225]

[0226] In the formula, and For adaptive backstepping control input vector, To optimize the control input vector; For α i The first derivative.

[0227] In the design process below, an adaptive law is designed to reduce the impact of input saturation. Definition For τ Δi The vector formed by the upper bounds of the median components, i.e. Therefore, let for The estimated vector, To estimate the error vector.

[0228] Choose the Lyapunov function L b,i for

[0229] L b,i =L1,i +L 2,i +L ξ,i (19)

[0230] In the formula, It is a positive definite design matrix.

[0231] According to (17) and (18), L in (19) b,i time derivative It can be deduced as follows:

[0232]

[0233] in, K 1,i The design matrix is ​​positive definite. for The first derivative.

[0234] Then, define the design of the adaptive backstepping control law. and corresponding adaptive laws as follows:

[0235]

[0236] In the formula, The design matrix is ​​positive definite; k ξ,i >0, k ξ,i For design parameters; E 2,i,1 E 2,i,2 ,…,E 2,i,n For E 2,i The components in, k E,i >0, k E,i For design parameters; h E,i =f 2,i (x 1,i ,x 2,i )-f 2,i (x 1,i ,α i ),

[0237] Then, substitute equations (21) and (22) into (20). According to the Cauchy-Schwarz and Young's inequalities, Simplified as follows:

[0238]

[0239] In the formula, This is the sum of the position error and the velocity error; λ represents the optimal virtual control input and the combination of optimal control inputs to be designed. min (·) represents the eigenvalue function that minimizes the eigenvalue; kt =0.2785.

[0240] Step 2: According to (23), consider the following cooperative tracking error dynamic system with affine nonlinear form.

[0241]

[0242] In the formula, For E i The first derivative is used to characterize the dynamic system of cooperative tracking error with affine nonlinear form, E i This is a combination of position and velocity errors in the new error dynamic system; Let n be the system dimension and h be the drift dynamics matrix of the new error dynamic system. E,i This refers to the mechanical error caused by drift. Let N be the gain matrix of the new error dynamic system, and N be the number of unmanned systems in the formation. i,j Let b be the time-varying relative position vector between target system i and neighboring system j; i This is the original dynamic gain matrix.

[0243] For (24), let a local cost function V i (E i (t) is:

[0244]

[0245] In the formula, V i Let be the local cost function of target system i; t be time; e be a constant; γ be the local cost function of target system i. i γ is the discount factor for target system i. i >0; s is the integration variable; and It is a symmetric positive definite weighted matrix. Let U be the set of all neighboring nodes of the target system i. i U is the optimal control input to be designed for target system i. j This is the control input for the neighbor system j.

[0246] To solve for the optimal control law, the Hamiltonian function H is defined. i (E i U i U j )as follows:

[0247]

[0248] In the formula, H i It is the Hamiltonian function; For V i (E i (relative to E) i The gradient of F; i For the new error dynamic system drift mechanics matrix; G i This is the gain matrix of the new error dynamic system.

[0249] Then, by solving The optimal control law can be obtained. for

[0250]

[0251] In the formula, This is the optimal control input; for Relative to E i gradient, This is the optimal cost function.

[0252] Substituting (27) into (26) yields the following Hamilton-Jacobi-Bellman equation:

[0253]

[0254] In the formula, For matrix G i and R i,i The matrix of the new combination; For matrix G j R i,j and R j,j The matrix of the new combination; The optimal cost function for the neighbor system Relative to E j The gradient; This is its own optimal cost function.

[0255] The following will employ an approximate optimal cost function for a fuzzy logic system. Right now

[0256]

[0257] In the formula, For the ideal parameter vector, Let l be a vector composed of fuzzy basis functions. c,i ε represents the number of fuzzy basis functions. c,i (E i ) represents the approximation error.

[0258] Then, we can obtain Relative to E i gradient as follows

[0259]

[0260] In the formula, and They are respectively and ε c,i (E i (relative to E) i The gradient.

[0261] Substituting (30) into (27), the optimal control law is... It is deduced as:

[0262]

[0263] in, For ideal optimal control input; For R i,i The inverse matrix; For G i transpose; for Relative to E i gradient, for; For ε c,i (E i (relative to E) i The gradient, ε c,i (E i ) represents the approximate error.

[0264] Substituting (29), (30), and (31) into (28), we obtain the Hamiltonian function. as follows:

[0265]

[0266] In the formula, for and R a,i,i The matrix formed and R b,i,j The matrix formed.

[0267]

[0268] Indicates residual error. This is the ideal error equation under optimal control.

[0269] definition For the ideal weight vector The estimate. approximate values ​​and Regarding E i The gradient is as follows:

[0270]

[0271] Therefore, according to (34), an approximate optimal control law can be obtained. The calculation is as follows:

[0272]

[0273] This is an approximation of the ideal optimal control input; for Relative to E i gradient, Let l be a vector composed of fuzzy basis functions. c,i The number of fuzzy basis functions; For the ideal weight vector The estimate.

[0274] Substituting (33) and (34) into (28), the following approximate Hamiltonian function is derived.

[0275]

[0276] Next, a fuzzy parameter update law is designed. as follows:

[0277]

[0278]

[0279] in, for The update law; k wa,i >0 and k wb,i >0 represents a design parameter. For parameters greater than 0, For the new combination matrix, To approximate the Hamiltonian function value, Lyapunov function with additional terms, For L w,i (E i Regarding E i The gradient.

[0280] Accordingly, embodiments of this application also provide a fuzzy optimization formation control system for multi-unmanned systems. Please refer to [link / reference]. Figure 9 , Figure 9 This is a module connection diagram of the fuzzy optimization formation control system for a multi-unmanned system provided in this application embodiment. The fuzzy optimization formation control system for a multi-unmanned system provided in this application embodiment includes:

[0281] Location acquisition module 10 is used to identify the target system and neighboring systems among multiple unmanned systems and to acquire the location information of the target system and neighboring systems.

[0282] Error acquisition module 20 is used to acquire position error based on the position information of the target system and neighboring systems;

[0283] The dynamic data acquisition module 30 is used to input the position data and position error of the target system into a preset fuzzy identifier to acquire the dynamic data of the target system.

[0284] The backstepping control input acquisition module 40 is used to design an adaptive backstepping controller based on the position data, position error and dynamic data of the target system, and to acquire the adaptive backstepping control input.

[0285] The control output acquisition module 50 is used to predict the optimal control input based on the adaptive backstepping control input.

[0286] The control output optimization module 60 is used to apply smooth saturation constraints to the adaptive backstepping control input and the optimal control input to obtain the control signal.

[0287] Output control module 70 is used to control the target system based on control signals to achieve formation control.

[0288] In some embodiments, the power data acquisition module is specifically used for:

[0289] Based on the location data of the target system, an Eulerian-Lagrange physical model of the target system is constructed, and model transformation is performed to obtain a dynamic model, which includes unknown dynamic parameters; the characterization formulas of the dynamic model include:

[0290]

[0291] in, For x 1,i The first derivative, x 1,i The position of target system i; x 2,i τ represents the velocity of the target system i. Δ,i =μ i -π i μ i For control input with input saturation, For adaptive backstepping control input vector, To optimize the control input vector; σ i For environmental disturbance; f 2,i (x 1,i,x 2,i ) and b i (x 2,i ) represents an unknown dynamic parameter;

[0292] Based on the approximation principle of fuzzy logic systems, unknown dynamic parameters are solved to obtain a model identifier; the characterization formula of the fuzzy identifier includes:

[0293]

[0294] in, for The first derivative, For x 2,i The estimate, x 2,i Let i be the velocity of the target system i; and They are respectively and The estimate, and The ideal fuzzy parameter matrix is ​​represented by T, which is the transpose operation. It is a vector composed of fuzzy basis functions; It is a matrix composed of fuzzy basis functions;

[0295] The formulas for characterizing dynamic parameters include:

[0296]

[0297] Among them, A x,i for The converged matrix; for The converged matrix;

[0298] In some embodiments, the backstepping control input acquisition module is specifically used for:

[0299] Obtain the backstepping virtual control input based on the position error;

[0300] Confirm the speed data of the target system and neighboring systems, and obtain the speed error between the target system and neighboring systems;

[0301] The adaptive law of the target system is obtained based on the backstepping virtual control input and velocity error;

[0302] Adaptive backstepping control input is obtained based on backstepping virtual control input and adaptive law.

[0303] In some embodiments, the backstepping control input acquisition module is specifically used for:

[0304] Based on the location data of the target system and neighboring systems, as well as the location error, obtain the location error vector;

[0305] Constructing a Lyapunov function based on the position error vector;

[0306] The adaptive backstepping virtual control input is obtained based on the position error vector and the Lyapunov function.

[0307] In some embodiments, the control output acquisition module is specifically used for:

[0308] The dynamic system of the cooperative tracking error of the target system with affine nonlinear form is obtained. The characterization formula of the dynamic system of the cooperative tracking error includes:

[0309]

[0310] in, For the cooperative tracking error dynamic system of target system i, E i This is a combination of position and velocity errors in the new error dynamic system; For the new error dynamic system drift mechanics, where n is the system dimension and h E,i This refers to the mechanical error caused by drift. Let N be the gain matrix of the new error dynamic system, and N be the number of unmanned systems in the formation. i,j Let b be the time-varying relative position vector between target system i and neighboring system j; i This is the original dynamic gain matrix;

[0311] A local cost function is constructed based on the collaborative tracking error dynamic system. The representation formula of the local cost function includes:

[0312]

[0313] Among them, V i Let be the local cost function of target system i; t be time; e be a constant; γ be the local cost function of target system i. i γ is the discount factor for target system i. i >0; s is the integration variable; and It is a symmetric positive definite weighted matrix. Let U be the set of all neighboring nodes of the target system i. i U is the optimal control input to be designed for target system i. j For the control input of neighbor system j;

[0314] The Hamiltonian function is obtained based on the collaborative tracking error dynamic system and the local cost function. The characterization formula of the Hamiltonian function includes:

[0315]

[0316] Among them, H i It is the Hamiltonian function; For V i (E i (relative to E) i The gradient of F; i For the new error dynamic system drift mechanics matrix; G i The gain matrix of the new error dynamic system;

[0317] Solve for the Hamiltonian function to obtain the optimal control input:

[0318] By solving The optimal control input is obtained as follows:

[0319]

[0320] in, This is the optimal control input; for Relative to E i gradient, This is its own optimal cost function.

[0321] In some embodiments, the control output acquisition module is specifically used for:

[0322] The Hamilton-Jacobi-Bellmann equations are derived based on the Hamiltonian function and optimal control input. The characterization formulas for the Hamilton-Jacobi-Bellmann equations include:

[0323]

[0324] in, For matrix G i and R i,i The matrix of the new combination; For matrix G j R i,j and R j,j The matrix of the new combination; The gradient of the optimal cost function for the neighbor system; This is its own optimal cost function;

[0325] The optimal cost function is obtained based on a fuzzy logic system, and the optimal cost function is obtained relative to the combination E of position error and velocity error. i The gradient;

[0326] The ideal optimal control input is obtained based on the gradient, and its characterization formula includes:

[0327]

[0328] in, For ideal optimal control input; for; for; for Relative to E i gradient, It is a vector composed of fuzzy basis functions; For ε c,i (E i (relative to E) i The gradient, ε c,i (E i ) represents the approximate error.

[0329] In some embodiments, the control output acquisition module is specifically used for:

[0330] The Hamiltonian function is updated based on the optimal cost function, gradient, and ideal optimal control input. Its characterization formula includes:

[0331]

[0332] To obtain an approximate optimal control input, the formulas representing the approximate optimal control input include:

[0333]

[0334] in, This is the approximate optimal control input; for Relative to E i gradient, Let l be a vector composed of fuzzy basis functions. c,i The number of fuzzy basis functions; For the ideal weight vector The estimate.

[0335] This application has provided a detailed description of a fuzzy optimization formation control method and system for a multi-unmanned system, as provided in the embodiments of this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and its core ideas. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A fuzzy optimization formation control method for a multi-unmanned system, characterized in that, The fuzzy optimization formation control method is applied to an unmanned formation system, which includes multiple unmanned systems, and includes: The target system and neighboring systems are identified among the multiple unmanned systems, and the location information of the target system and neighboring systems is obtained; The location error is obtained based on the location information of the target system and the neighboring system; The position data and position error of the target system are input into a preset fuzzy identifier to obtain the dynamic data of the target system; the step of presetting the fuzzy identifier includes: Based on the location data of the target system, an Eulerian-Lagrange physical model of the target system is constructed, and a model transformation is performed to obtain a dynamic model, which includes unknown dynamic parameters; the characterization formula of the dynamic model includes: in, For x 1,i The first derivative, x 1,i The position of the target system i; x 2,i τ is the velocity of the target system i. Δ,i =μ i -τ i μ i For control input with input saturation, For adaptive backstepping control input vector, To optimize the control input vector; σ i For environmental disturbance; f 2,i (x 1,i ,x 2,i ) and b i (x 2,i () represents an unknown dynamic parameter; Based on the approximation principle of fuzzy logic systems, unknown dynamic parameters are solved to obtain a fuzzy identifier; the characterization formula of the fuzzy identifier includes: in, for The first derivative, For x 2,i The estimate, x 2,i The velocity of the target system i; and They are respectively and The estimate, and The ideal fuzzy parameter matrix is ​​represented by T, which is the transpose operation. It is a vector composed of fuzzy basis functions; It is a matrix composed of fuzzy basis functions; The formulas for characterizing dynamic parameters include: Among them, A x,i for The converged matrix; for The converged matrix; An adaptive backstepping controller is designed based on the position data, position error, and dynamic data of the target system, and the adaptive backstepping control input is obtained. Obtain the cooperative tracking error dynamic system of the target system, and obtain the optimal control input based on the error dynamic system; Smooth saturation constraints are applied to the adaptive backstepping control input and the optimal control input to obtain the control signal; The target system is controlled based on the control signals to achieve formation control.

2. The fuzzy optimization formation control method for multi-unmanned systems according to claim 1, characterized in that, The step of designing an adaptive backstepping controller based on the position data, position error, and dynamic data of the target system, and obtaining the adaptive backstepping control input, includes: The backstep virtual control input is obtained based on the position error; Confirm the speed data of the target system and the neighboring system, and obtain the speed error between the target system and the neighboring system; The adaptive law of the target system is obtained based on the backstepping virtual control input and the velocity error; The adaptive backstepping control input is obtained based on the backstepping virtual control input and the adaptive law.

3. The fuzzy optimization formation control method for multi-unmanned systems according to claim 2, characterized in that, The step of obtaining the backstep virtual control input based on the position error includes: Based on the location data of the target system and the neighboring systems, and the location error, a location error vector is obtained; Construct a Lyapunov function based on the position error vector; The adaptive backstepping virtual control input is obtained based on the position error vector and the Lyapunov function.

4. The fuzzy optimization formation control method for multi-unmanned systems according to claim 1, characterized in that, The steps of obtaining the cooperative tracking error dynamic system of the target system and obtaining the optimal control input based on the error dynamic system include: Obtain the dynamic system of the cooperative tracking error of the target system with an affine nonlinear form, and the characterization formula of the dynamic system of the cooperative tracking error includes: in, For the cooperative tracking error dynamic system of the target system i, E i This is a combination of position and velocity errors in the new error dynamic system; Let n be the drift dynamics matrix of the new error dynamic system, where n is the system dimension and h is the dynamics matrix. E,i This refers to the mechanical error caused by drift. Let N be the gain matrix of the new error dynamic system, and N be the number of unmanned systems in the formation. i,j Let b be the time-varying relative position vector between target system i and neighboring system j; i This is the original dynamic gain matrix; A local cost function is constructed based on the aforementioned cooperative tracking error dynamic system. The characterization formula of the local cost function includes: Among them, V i Let be the local cost function of target system i; t be time; e be a constant; γ be the local cost function of target system i. i γ is the discount factor for target system i. i >0; s is the integration variable; and It is a symmetric positive definite weighted matrix. Let U be the set of all neighboring nodes of the target system i. i U is the optimal control input to be designed for target system i. j For the control input of neighbor system j; The Hamiltonian function is obtained based on the cooperative tracking error dynamic system and the local cost function. The characterization formula of the Hamiltonian function includes: Among them, H i The Hamiltonian function is mentioned above. For V i (E i (relative to E) i The gradient of F; i For the new error dynamic system drift mechanics matrix; G i The gain matrix of the new error dynamic system; Solve the Hamiltonian function to obtain the optimal control input: By solving The optimal control input is obtained as follows: in, This is the optimal control input; For V i * (E i (relative to E) i The gradient of V i * This is the optimal cost function.

5. The fuzzy optimization formation control method for multi-unmanned systems according to claim 4, characterized in that, The step of solving the Hamiltonian function to obtain the calculation result of the optimal control input further includes: The Hamilton-Jacobi-Bellman equation is obtained based on the Hamiltonian function and the optimal control input. The characterization formula of the Hamilton-Jacobi-Bellman equation includes: in, For matrix G i and R i,i The matrix of the new combination; For matrix G j R i,j and R j,j The matrix of the new combination; The optimal cost function V for the neighbor system j * (E j (relative to E) j gradient; V i * (E i () is its own optimal cost function; The optimal cost function is obtained based on a fuzzy logic system, and the optimal cost function is obtained relative to the combination E of position error and velocity error. i The gradient; The ideal optimal control input is obtained based on the gradient, and its characterization formula includes: in, For ideal optimal control input; For R i,i The inverse matrix; For G i Transpose of; for Relative to E i gradient, for; For ε c,i (E i (relative to E) i The gradient, ε c,i (E i ) represents the approximate error.

6. The fuzzy optimization formation control method for multi-unmanned systems according to claim 5, characterized in that, The step of solving the Hamiltonian function to obtain the optimal control input result further includes: The Hamiltonian function is updated based on the optimal cost function, the gradient, and the ideal optimal control input, and its characterization formula includes: To obtain an approximate value of the ideal optimal control input, the approximate formula representing the optimal control input includes: in, This is an approximation of the ideal optimal control input; for Relative to E i gradient, Let l be a vector composed of fuzzy basis functions. c,i The number of fuzzy basis functions; For the ideal weight vector The estimate.

7. The fuzzy optimization formation control method for multi-unmanned systems according to claim 6, characterized in that, The ideal weight vector Estimate The characterization formulas for the update law include: in, for The update law; k wa,i >0 and k wb,i >0 represents a design parameter. For parameters greater than 0, For the new combination matrix, To approximate the Hamiltonian function value, Lyapunov function with additional terms, For L w,i (E i Regarding E i The gradient.

8. The fuzzy optimization formation control method for multi-unmanned systems according to claim 1, characterized in that, The step of applying smooth saturation constraints to the adaptive backstepping control input and the optimal control input to obtain the control signal includes: A preliminary signal is obtained based on the adaptive backstepping control input and the optimal control input. The characterization formula of the preliminary signal includes: Where, τ i This is a preliminary control signal; This serves as the adaptive backstepping control input for the target system i; This is the optimal control input for the target system i; The initial signal is subjected to smooth saturation constraint to obtain a control signal, the characterization formula of which includes: in, For τ i The constituent elements This is the maximum value after the switch. For design parameters, S i (·) represents the sigmoid function, with the following expression:

9. A fuzzy optimization formation control system for a multi-unmanned system, characterized in that, The fuzzy optimization formation control system is applied to an unmanned formation system, which includes multiple unmanned systems. Location acquisition module (10), the location acquisition module (10) is used to identify the target system and the neighboring system in the multiple unmanned systems, and acquire the location information of the target system and the neighboring system; Error acquisition module (20), the error acquisition module (20) is used to acquire position error based on the position information of the target system and the neighboring system; The dynamic data acquisition module (30) is used to input the position data and position error of the target system into a preset fuzzy identifier to acquire the dynamic data of the target system; the step of presetting the fuzzy identifier includes: Based on the location data of the target system, an Eulerian-Lagrange physical model of the target system is constructed, and a model transformation is performed to obtain a dynamic model, which includes unknown dynamic parameters; the characterization formula of the dynamic model includes: in, For x 1,i The first derivative, x 1,i The position of the target system i; x 2,i τ is the velocity of the target system i. Δ,i =μ i -τ i μ i For control input with input saturation, For adaptive backstepping control input vector, To optimize the control input vector; σ i For environmental disturbance; f 2,i (x 1,i ,x 2,i ) and b i (x 2,i () represents an unknown dynamic parameter; Based on the approximation principle of fuzzy logic systems, unknown dynamic parameters are solved to obtain a fuzzy identifier; the characterization formula of the fuzzy identifier includes: in, for The first derivative, For x 2,i The estimate, x 2,i The velocity of the target system i; and They are respectively and The estimate, and The ideal fuzzy parameter matrix is ​​represented by T, which is the transpose operation. It is a vector composed of fuzzy basis functions; It is a matrix composed of fuzzy basis functions; The formulas for characterizing dynamic parameters include: Among them, A x,i for The converged matrix; for The converged matrix; The backstepping control input acquisition module (40) is used to design an adaptive backstepping controller for the position data, position error and dynamic data of the target system, and to acquire the adaptive backstepping control input; A control output acquisition module (50) is used to acquire the cooperative tracking error dynamic system of the target system and acquire the optimal control input based on the error dynamic system; The control output optimization module (60) is used to apply smooth saturation constraints to the adaptive backstepping control input and the optimal control input to obtain a control signal; Output control module (70) is used to control the target system based on the control signal to realize formation control.

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