Unmanned aerial vehicle cluster formation fault tolerance method based on protopigeon chaos adaptive sliding mode control

Abstract

The invention discloses an unmanned aerial vehicle cluster formation fault-tolerant method based on protopigeon chaos adaptive sliding mode control, and the method comprises the steps: 1, carrying out the kinematics modeling of an unmanned aerial vehicle, and determining the initial state of the unmanned aerial vehicle and a formation flight control system of wing aircrafts and lead aircrafts; 2, introducing a virtual reference unmanned aerial vehicle kinetic model, designing a tracking error, obtaining a dynamic tracking error equation, and ensuring the accuracy of a reference model; 3, designing a sliding mode surface function, and obtaining a reduced-order sliding mode kinematics equation by applying an adaptive sliding mode control technology; and the like. The method is easy to implement, the provided chaotic pigeon inspired mechanism can greatly optimize parameters in adaptive control and sliding mode control parameters, the control convergence speed is increased, and a robust solution is provided for solving the difficult problems that an unmanned aerial vehicle with communication faults cannot adapt to a complex environment and the like.

Description

Technical Field

[0001] The invention relates to a UAV cluster formation fault-tolerant method based on original pigeon chaos adaptive sliding mode control, belonging to the technical field of UAV cluster cooperative control. Background Art

[0002] In recent years, drone technology has been increasingly used in military and civilian fields, especially in reconnaissance, surveillance and search missions. The application advantages of drone formations are particularly prominent. Through the coordinated work of multiple drones, drone formations can expand the reconnaissance range, improve the coverage of missions, and enhance the reliability of missions. However, during the flight of drone formations, due to external interference, communication failures, sensor failures, and actuator failures, the formation may become unstable, thus affecting the successful execution of the entire mission.

[0003] In order to improve the reliability of UAV formation systems, fault-tolerant control technology has become one of the key research directions. The purpose of fault-tolerant control technology is that when a partial failure occurs in the aircraft, the system can still maintain system performance or achieve the predetermined task by adjusting the control strategy. Fault-tolerant control of UAV formations requires not only that a single UAV can self-adjust when a failure occurs, but also that the entire formation can continue to maintain the preset formation and effectively complete the task in a faulty environment.

[0004] In recent years, the sliding mode control method has become one of the widely used technologies in fault-tolerant control of UAV formations due to its good robustness and adaptability to system uncertainty. Sliding mode control designs a sliding surface and uses a sliding mode controller to keep the system state on the sliding surface after the system enters the sliding surface, so that the system has a strong ability to suppress uncertainty, external disturbances and system failures.

[0005] The present invention intends to introduce adaptive control on the basis of traditional sliding mode control to further enhance the adaptability of the system in complex environments, ensuring that the system can adjust the control law in real time according to the current system state after a fault occurs, thereby improving the fault tolerance of the system. Summary of the invention

[0006] The purpose of the present invention is to provide a UAV formation fault-tolerant control method based on original pigeon chaos adaptive sliding mode control, aiming to solve the formation instability problem caused by actuator failure, communication failure and external interference when multiple UAVs fly in coordinated formation in a complex environment. This method constructs a dynamic model of the UAV formation, introduces an adaptive sliding mode controller, and combines it with a fault detection and estimation module to achieve fault-tolerant control of the UAV formation in complex fault environments such as actuator performance degradation and communication interruption. In addition, the system designs a control mechanism based on a virtual reference model to guide the UAV to continue to perform formation tasks according to preset instructions when communication fails to ensure that the formation is maintained.

[0007] Aiming at the formation cooperative control problem of UAV clusters under mixed actuator and communication fault environments, the present invention invents a fault-tolerant control method for UAV formation based on original pigeon chaos adaptive sliding mode control. The algorithm implementation flow chart is as follows: Figure 1 As shown in the figure, it includes cluster state initialization, topology optimization and parameter optimization based on the original pigeon chaos mechanism, UAV fault estimation module, adaptive sliding mode controller combined with chaos series, etc. The specific implementation steps are as follows:

[0008] Step 1: UAV kinematic modeling and state information initialization.

[0009] Specifically: the kinematic modeling of the UAV is carried out, the flight dynamics system of the leader and the wingman is considered, and a rotating reference coordinate system fixed to the wingman is used. In the present invention, the focus is on the cluster formation control task of multiple wingmen and the leader, so the algorithm simulation verification scenario is simplified, the UAVs are set at the same altitude, and only two-dimensional plane coordinates are considered.

[0010] The kinematic equations for establishing the UAV formation flight control system are:

[0011]

[0012] In the formula, x and y represent the horizontal and vertical distances between the lead aircraft and the wingman on the coordinate axis, and v P , v Q represents the flight speed of the leader and wingman, φ P and φ Q Expressed as the heading angle of the lead and wingman, φ e represents the difference in heading angle between the leader and the wingman. In order to simplify the research content, the present invention ignores the aerodynamic coupling effect in the nonlinear equation of the formation flight control system. The formation flight control system of the wingman can be described by the following simplified equation:

[0013]

[0014] In the formula, represents the velocity time constant of the wingman, represents the wingman's azimuth time constant, Indicates the altitude time constant of the long aircraft, represents the altitude time constant of the wingman, and are the three control inputs of the wingman respectively. Combining formulas (1) and (2), we get the six-dimensional nonlinear control system:

[0015]

[0016] Where z is the vertical distance between the leader and the wingman, and η is the rate of change of z. In cluster distributed control systems, since the leader's attitude has a small rotation angle, its control input can be regarded as a disturbance signal. Therefore, the leader's control input interferes with the wingman, requiring the wingman to effectively suppress and compensate for these interference signals during the following process. By treating the leader's control input as interference, the design of the wingman's control strategy can be simplified, while helping to improve the robustness and stability of the system. In this framework, the interference signals are disturbances caused by different attitude changes, and further refinement includes yaw and other angular deviations φ introduced due to the leader's slight attitude adjustment. P , v P and Therefore, it can be linearized into the following perturbation equation:

[0017]

[0018] In the formula, d represents the straight-line distance between the leader and the wingman, and φ represents the angle between the leader and the wingman. To facilitate the study of controller design, the UAV formation flight system can be expressed as the following state space model to simplify the system analysis process and more intuitively describe the dynamic relationship between the state variables. Through this model, the attitude, speed and position change characteristics of the UAV in formation flight can be effectively captured, so that the controller design can clearly understand how the control input affects the evolution of the system state. This state space model not only provides a mathematical basis for analyzing the stability and response speed of the system, but also provides a parameter basis for optimizing the control law, thereby achieving accurate formation maintenance and path following:

[0019]

[0020]

[0021] Step 2: Introduce a virtual reference model, design the tracking error, and obtain the dynamic tracking error equation.

[0022] Specifically: when a communication failure occurs, the standard PI controller cannot maintain the geometric formation of multiple UAVs. Formula (5) in step 1 can be transformed into the following form:

[0023]

[0024] Where ω∈R 3 Represents uncertain fault variables, which may be caused by continuous or intermittent wireless communication failures. For the design of fault-tolerant controllers, the following reference model is introduced:

[0025]

[0026] Define the following tracking error and derive the dynamic tracking error equation:

[0027]

[0028] In order to ensure the accuracy of the reference model, some assumptions are needed to support the model establishment. There are some matrices M and N of suitable dimensions so that AA l =BM,B l =BN holds. The uncertain faults considered are continuous and bounded, and there exist positive constants ω1, ω2 such that ||ω||<ω1 and According to these assumptions, formula (8) can be transformed into:

[0029]

[0030] Step 3: Design the sliding surface function through adaptive sliding mode technology and obtain the reduced-order sliding mode kinematic equation.

[0031] Specifically, for the dynamic tracking error equation (9) established in step 2, the following sliding surface function is designed:

[0032] S=se=B T G -1 e (10)

[0033] In order to facilitate the design of sliding mode control law, the transformation matrix is ​​designed in It is B T Any basis in the null space. Let Then the transformation is:

[0034]

[0035] Where z1∈R 3 , z2∈R 3 The dynamic tracking error equation (9) established in step 2 can be transformed into:

[0036]

[0037] After the above transformation, the sliding surface becomes:

[0038] S=se=B T G -1 e=B T G -1 Bz2 (13)

[0039] When the sliding surface S = 0, the following reduced-order sliding kinematic equation can be obtained:

[0040]

[0041] Step 4: Introduce an H ∞ Performance index function, design an asymptotic stability criterion to ensure that the tracking error dynamics model can converge to the predetermined sliding surface. Under ideal conditions without communication failures and external interference, this criterion ensures that the tracking error always remains on the sliding surface, thereby achieving robust tracking performance of the system. At the same time, this design scheme ensures the asymptotic stability of the system, so that the control accuracy is effectively guaranteed under various disturbances, meeting the needs of high-precision tracking control.

[0042] Specifically: an asymptotic stability criterion is proposed to ensure the asymptotic stability of the sliding mode dynamic system in step 3 under a given disturbance suppression level μ1. Theorem 1: If there exists a symmetric positive definite matrix G such that the following linear matrix inequality holds

[0043]

[0044] Then the formula (14) in step 3 is that the reduced-order sliding mode dynamic system is asymptotically stable under the suppression level μ1. Here we introduce an H ∞ Performance indicator function: Let the Lyapunov function be Taking the derivative of V1, we can get:

[0045]

[0046] In the formula If Υ1<0, we can deduce Integrating this inequality yields:

[0047]

[0048] It is easy to show under zero initial conditions that the reduced-order sliding mode kinematic equations in step 3 are asymptotically stable under a given suppression level μ1.

[0049] Step 5: Design a virtual adaptive sliding mode controller, which includes the expected fault estimation law and neural network approximation weights to ensure asymptotic stability under a given suppression level μ2.

[0050] Specifically: When communication failures and external interference occur, relying solely on the sliding mode controller described in step 4 is not enough to maintain the stability and accuracy of the system, because at this time it is necessary to first obtain accurate estimation information of the communication failure in order to design a control law with a switching mechanism to eliminate the impact of the failure on the system. However, in the UAV flight control system, communication failure information is difficult to obtain accurately, and traditional methods have great limitations in real-time and practicality. To overcome this problem, a control strategy based on an adaptive neural network is proposed. By automatically adjusting the control parameters to deal with unknown faults, the system disturbances can be effectively suppressed, and the robustness and reliability of the system in complex environments can be enhanced.

[0051] In this method, an adaptive estimation law needs to be designed to estimate the fault value. First, a virtual adaptive sliding mode controller is designed, which contains the expected fault estimation law and the neural network weights. represents the estimated value of fault ω, so the estimation error is defined as: Theorem 2: Given a positive real scalar μ2>0, if there exists a positive real number a, b such that the following matrix Υ2:

[0052]

[0053] At the same time, the inequality holds:

[0054]

[0055] Then the tracking error model system can reach the sliding surface (13), and the motion system (9) can be kept on the sliding surface under the following virtual tracking controller when the suppression level μ2 is given. The controller is as follows:

[0056]

[0057] Design the following adaptive estimation law:

[0058]

[0059] Among them, a>0, b>0 are two positive constants. Construct Lyapunov function To derivate it, in order to make the fault-tolerant controller involved have a certain anti-interference ability, H is introduced ∞ Performance indicator function By verifying theorem 1 in step 4, we can get the following equation:

[0060]

[0061] In the formula According to formula (22), we can get Integrating both sides simultaneously gives the following inequality under zero initial conditions:

[0062]

[0063] Therefore, it can be seen that the virtual tracking controller and the adaptive estimation law are driven to the sliding surface, and it can be seen that the controller can achieve the desired effect.

[0064] Step 6: Integrate the adaptive sliding mode control parameters in steps 3 and 4 into the parameter vector P to be optimized, and introduce the original pigeon chaos mechanism to fully search for the optimal solution in the adaptation problem space. Through the global search and local fine-tuning capabilities of this mechanism, the efficiency and accuracy of parameter optimization are improved, thereby enhancing the response performance and robustness of the control system in a complex dynamic environment.

[0065] Specifically: When designing an adaptive sliding mode controller, three key parameters usually need to be optimized: a, b, and G. By introducing the original pigeon chaos mechanism, the optimal solution in the adaptation space can be effectively explored through the global search of the pigeon flock algorithm and the local fine search of the chaos search. First, a set of pigeon flock positions is randomly initialized to represent the initial parameter set of the controller. The position of each pigeon can be represented as a vector P containing three parameters to be optimized i =[a i b i G i ],Right now:

[0066] P i =[a i b i G i ],i=1,2,...,N (24)

[0067] In the formula, N is the number of pigeons. In order to evaluate the quality of each set of parameters, a fitness function is defined, and the system dynamic tracking error e(t) is selected, namely:

[0068]

[0069] In the formula, e(t) is the dynamic tracking error, and T is the simulation time. In order to prevent the pigeon swarm algorithm from falling into the local optimum, the chaotic search mechanism is combined to perform local optimization on the pigeon swarm. A chaotic mapping function (Logistic mapping) is used to generate a chaotic sequence, which is applied to the pigeon search process to increase the diversity of the population. The mapping is shown as follows:

[0070] x n+1 =gx n (1-x n ),g=4 (26)

[0071] Chaotic sequences can be used to disturb the position of the pigeon flock, making it jump out of the local optimum. Through chaotic search, the pigeon flock continues to search in the global scope, while improving the accuracy of local optimization. After the chaotic pigeon flock optimization is completed, the optimal parameters are obtained. It will be applied to the adaptive sliding mode controller to replace the original manually selected parameters. These optimized parameters will enable the controller to compensate for system uncertainties and external disturbances in a wider range, and improve dynamic performance and anti-disturbance while ensuring system stability.

[0072] Advantages and effects:

[0073] The present invention proposes a UAV cluster formation fault-tolerant method based on original pigeon chaos adaptive sliding mode control. A fixed geometric figure is formed by the mode of wingman following the leader. In order to accurately and quickly obtain the estimated value of the fault, a virtual reference model is introduced to obtain a dynamic tracking error equation. For this purpose, a virtual tracking controller and a fault estimation algorithm are designed. At the same time, the adaptive sliding mode control and the pigeon group optimization with a chaotic mapping mechanism are combined to design a formation fault-tolerant controller, which solves the formation stability problem of UAV formation cooperative flight in a fault interference environment.

[0074] The adaptive sliding mode control framework with the original pigeon chaos mechanism proposed in the present invention mainly has the following advantages: first, in the actual UAV flight process, the instability of the communication line and the acquisition of fault information are very difficult. The method uses an adaptive adjustment mechanism without relying on accurate fault estimation information, and directly achieves fault-tolerant control by adjusting the control parameters, which greatly improves the practicability of the system in complex environments; secondly, the adaptive sliding mode controller proposed in the present invention can automatically adjust the control gain according to environmental changes, thereby enhancing the system's adaptability to uncertainty and external disturbances, ensuring that the system can respond quickly when a fault or disturbance occurs, and controlling the steady-state error at an extremely low level, ensuring the accuracy and coordination of the UAV cluster in formation flight; in addition, by utilizing the original pigeon chaos mechanism, through the global search and local optimization capabilities of the chaotic sequence, the controller parameters can be automatically optimized, avoiding the risk of falling into local optimality, and ensuring that the control system reaches the optimal state on a global scale. When the UAV suffers from actuator failure and external interference, the present invention effectively solves the limitations of traditional sliding mode control methods in fault-tolerant control through the original pigeon chaos optimization mechanism and adaptive sliding mode control technology, and can still maintain the stability of the system under complex interference conditions, providing a feasible solution to the formation problem under complex environmental conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 This is the flow chart of fault-tolerant control of UAV swarm formation based on original pigeon chaos adaptive sliding mode control.

[0076] Figure 2 Plots of the three control inputs of the wingman versus time.

[0077] Figure 3 This is a curve diagram of the state variables and reference state variables of UAVs 1, 2, and 3 that simulate a fault at t = 3s.

[0078] Figure 4 This is a curve diagram of the state variables and reference state variables of UAV 4, 5 that simulate a fault at t = 3s.

[0079] Figure 5 This is the lateral distance, longitudinal distance and altitude trajectory diagram of the UAV cluster formation imitating the original pigeon chaos.

[0080] Figure 6 This is the trajectory diagram of the speed, heading angle and vertical distance of the UAV cluster formation that imitates the original pigeon chaos.

[0081] The numbers and symbols in the figure are explained as follows:

[0082] t——Simulation time

[0083] v Qu - Wingman speed control input;

[0084] φ Qu ——Wingman heading angle control input;

[0085] ——Wingman vertical range control input;

[0086] ——system total state variables;

[0087] ——State variables of drone 1;

[0088] ——state variables of the reference system of UAV 1;

[0089] ——State variables of drone 2;

[0090] ——State variables of the reference system of UAV 2;

[0091] ——State variables of drone 3;

[0092] ——state variables of the reference system of UAV 3;

[0093] ——State variables of drone 4;

[0094] - state variables of the reference system of UAV 4;

[0095] ——State variables of drone 5;

[0096] - state variables of the reference system of UAV 5;

[0097] x——lateral displacement of the leader and wingman on the coordinate axis;

[0098] y——longitudinal displacement of the leader and wingman on the coordinate axis;

[0099] z——vertical displacement of the leader and wingman on the coordinate axis;

[0100] v Q - The speed of the wingman;

[0101] φ Q ——the heading angle of the wingman;

[0102] z Q ——Changes in the vertical displacement of the wingman; DETAILED DESCRIPTION

[0103] The simulation process framework is shown in Figure 1 , the effectiveness of the UAV cluster formation fault-tolerant method based on original pigeon chaos adaptive sliding mode control proposed in the present invention is verified by using Matlab programming. The specific steps of the simulation verification process are as follows:

[0104] The mathematical simulation studies a formation of six drones, one leader and five wingmen. The values ​​of matrices A and B are as follows: Speed ​​time constant Heading time constant Attitude time constant λ zα =0.3s,λ zβ =3.85s. The parameter matrix of the reference model is given as follows:

[0105]

[0106] Knowable is the matrix B T A basis of the null space, let the interference suppression level μ1 = 0.4, and then the positive definite matrix G can be obtained by the linear matrix inequality in formula (15) in step 4:

[0107]

[0108] In the Matlab simulation, the leader's speed is 2m / s and the leader's heading angle is 2.1°. The initial state of the wingman is set to vQ0 =0.17m / s,φ Q0 =0.07°, z Q0 =0.3m, and the initial values ​​of the formation geometry are x0=0.17m, y0=0.09m, z0=0.03m. The above initial parameters and positive definite matrix are brought into the three control inputs of the wingman, and the curves of the three control inputs changing with time are obtained, as shown in Figure 2 As shown; the controller gain and adaptive coefficient are as follows: a = 0.3, b = 0.5; In order to verify the superior performance of the control method, it is assumed that the wireless communication fault shown in the command channel design at the 3rd second: ω = [cost + cos2tsint-sin2t cost-sin2t] T , the proposed fault-tolerant controller (20) can make the flight control system state and control input response have satisfactory dynamic performance in the event of a fault. According to the given wireless communication fault and the proposed fault handling controller, Figure 3 and Figure 4 , the change curves of the state variables and reference state variables of the five UAVs; the controller gain and adaptive coefficient obtained are the optimal parameters after traversing the chaotic pigeon swarm algorithm, generating Figure 5 and Figure 6 The lateral, longitudinal, altitude, formation speed, heading angle and vertical distance trajectory diagrams of the five drones and the lead aircraft.

Claims

1. A fault-tolerant method for UAV swarm formation based on original pigeon chaos adaptive sliding mode control, characterized by: The steps of this method are as follows: Step 1: UAV kinematic modeling and state information initialization; Among them, the flight dynamics system of the lead aircraft and the wingman is considered, and a rotating reference coordinate system fixed to the wingman is used. The control input of the lead aircraft is regarded as a disturbance signal to obtain a linearized disturbance equation; Step 2: introduce a virtual reference model, design the tracking error, and obtain the dynamic tracking error equation; Step 3: Design the sliding surface function through adaptive sliding mode technology to obtain the reduced-order sliding mode kinematic equation; Step 4: Introduce H ∞ Performance index function, design asymptotic stability criteria to ensure that the tracking error dynamics model reaches the sliding surface and can stay on the sliding surface when there is no communication failure and interference; Step 5: Design a virtual adaptive sliding mode controller, which includes the expected fault estimation law and the neural network approximation weights, to ensure asymptotic stability under a given suppression level μ2; Step 6: Introduce the original pigeon chaos mechanism, optimize the adaptive control parameters and sliding mode parameters through the global search of the pigeon swarm algorithm and the local fine search of the chaos search, and obtain the optimal controller parameter combination.

2. The method according to claim 1, characterized in that: The step 1 is as follows: kinematic modeling of the UAV is performed. The kinematic model of the UAV is established as: In the formula, x and y represent the horizontal and vertical distances between the lead aircraft and the wingman on the coordinate axis, and v P , v Q represents the flight speed of the leader and wingman, φ P and φ Q Expressed as the heading angle of the lead and wingman, φ e It represents the difference in heading angle between the leader and the wingman. The formation flight control system of the wingman is described by the following simplified equation: In the formula, represents the velocity time constant of the wingman, represents the wingman's azimuth time constant, Indicates the altitude time constant of the long aircraft, represents the altitude time constant of the wingman, and are the three control inputs of the wingman respectively; combining formulas (1) and (2), the six-dimensional nonlinear control system is obtained: Where z is the vertical distance between the leader and the wingman, and η is the rate of change of z. In cluster distributed control, due to the small attitude rotation angle, the control input of the leader is regarded as a disturbance signal, so the interference signals are φ P , v P and Therefore, it can be linearized into the following perturbation equation: Where d represents the straight-line distance between the leader and the wingman, φ represents the formation angle between the leader and the wingman, and the UAV formation flight system is represented by the following state space model: The corresponding coefficients and variables in the formula are as follows 3. The method according to claim 2, characterized in that: Step 2 is as follows: The state space model of the UAV formation flight system in step 1 is transformed into the following form: Where ω∈R 3 Represents uncertain fault variables. For the design of fault-tolerant controller, the following reference model is introduced: Define the following tracking error and derive the dynamic tracking error equation: The matrices M and N make AA l =BM,B l =BN holds; the uncertain faults considered are continuous and bounded, and there exist positive constants ω1, ω2 such that ||ω||<ω1 and Established; Formula (8) is transformed into:

4. The method according to claim 3, characterized in that: Step 3 is as follows: Based on the dynamic tracking error equation (9) established in step 2, the sliding surface function is designed as: S=se=B T G -1 e (10) Design transformation matrix in It is B T Any basis in the null space; let Then the transformation is: Where z1∈R 3 , z2∈R 3 The dynamic tracking error equation (9) established in step 2 is transformed into: After the above transformation, the sliding surface becomes: S=se=B T G -1 e=B T G -1 Bz2 (13) When the sliding surface S = 0, the following reduced-order sliding kinematic equation is obtained:

5. The method according to claim 4, characterized in that: Step 4 is as follows: If there exists a symmetric positive definite matrix G such that the following linear matrix inequality holds Then the formula (14) in step 3 is that the reduced-order sliding mode dynamic system is asymptotically stable under the suppression level μ1; introducing an H ∞ Performance indicator function: Let the Lyapunov function be Taking the derivative of V1, we get: In the formula, If Υ1<0, then Integrating this inequality yields: It is easy to show under zero initial conditions that the reduced-order sliding mode kinematic equations in step 3 are asymptotically stable under a given suppression level μ1.

6. The method according to claim 5, characterized in that: Step 5 proposes a design method for adaptive neural network; In this method, an adaptive estimation law needs to be designed to estimate the fault value. First, a virtual adaptive sliding mode controller is designed, which includes the expected fault estimation law and the neural network weights. represents the estimated value of fault ω, so the estimation error is defined as: If a positive real scalar μ2>0 exists, then there exists a positive real number a, b such that the following matrix Υ2: At the same time, the inequality holds: The tracking error model system reaches the sliding surface (13), and given the suppression level μ2, the motion system (9) remains on the sliding surface under the following virtual tracking controller; the controller is as follows: Design the following adaptive estimation law: Among them, a>0, b>0 are two normal numbers; construct Lyapunov function Taking its derivative, we introduce H ∞ Performance indicator function The following formula is established: In the formula, According to formula (22), we can get Integrating both sides simultaneously under zero initial conditions yields the following inequality:

7. The method according to claim 6, characterized in that: Step 6 is as follows: the adaptive sliding mode parameters in steps 3 and 4 are combined into a parameter vector P to be optimized, and the optimal solution in the adaptive problem space is explored by introducing the original pigeon chaos mechanism; When designing an adaptive sliding mode controller, three key parameters need to be optimized: a, b, and G; First, a set of pigeon positions is randomly initialized, which represents the initial parameter set of the controller; the position of each pigeon is represented by a vector P containing three parameters to be optimized i =[a i b i G i ],Right now: P i =[a i b i G i ],i=1,2,...,N (24) Where N is the number of pigeons; in order to evaluate the quality of each set of parameters, a fitness function is defined, and the system dynamic tracking error e(t) is selected, namely: In the formula, e(t) is the dynamic tracking error, and T is the simulation time. In order to prevent the pigeon swarm algorithm from falling into the local optimum, the chaotic search mechanism is combined to perform local optimization on the pigeon swarm. The chaotic mapping function is used to generate a chaotic sequence, which is applied to the pigeon search process to increase the diversity of the population. The mapping is shown as follows: x n+1 =gx n (1-x n ),g=4 (26)。

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