An unmanned aerial vehicle cluster formation fault-tolerant method based on original pigeon chaotic adaptive sliding mode control

Abstract

The application discloses a kind of unmanned aerial vehicle cluster formation fault-tolerant method based on original pigeon chaotic adaptive sliding mode control, including the following steps: step one: the kinematics of unmanned aerial vehicle is modeled, the initial state of unmanned aerial vehicle is determined and the formation flight control system of wingman and long machine;Step two: introduce the virtual reference unmanned aerial vehicle dynamics model, design tracking error, obtain dynamic tracking error equation, ensure the accuracy of reference model;Step three: design sliding mode surface function, obtain reduced order sliding mode kinematics equation by using adaptive sliding mode control technology;Six steps such as.The method of the application is simple, the proposed chaotic pigeon group mechanism can greatly optimize the parameters in adaptive control and sliding mode control parameters, increase the control convergence speed, and give a robust solution to the difficult problems such as unmanned aerial vehicle unable to adapt to complex environment due to communication failure.

Description

TECHNICAL FIELD

[0001] The application relates to a UAV cluster formation fault-tolerant method based on original pigeon chaotic adaptive sliding mode control and belongs to the technical field of UAV cluster cooperative control. BACKGROUND

[0002] In recent years, the application of UAV technology in military and civilian fields is increasingly widespread, especially when performing reconnaissance, surveillance and search tasks, the application advantage of UAV formation is particularly prominent. UAV formation can expand the reconnaissance range, improve the coverage rate of the task, and enhance the reliability of the task through the cooperative work of multiple UAVs. However, during the flight of the UAV formation, due to external interference, communication failure, sensor failure and actuator failure and other factors, the formation may be unstable, thereby affecting the successful execution of the entire task.

[0003] In order to improve the reliability of the UAV formation system, 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 through the adjustment of the control strategy. UAV formation fault-tolerant control not only requires a single UAV to adjust itself when a fault occurs, but also requires the entire formation to continue to maintain the preset formation and effectively complete the task under the fault environment.

[0004] In recent years, the sliding mode control method has become one of the widely used technologies in UAV formation fault-tolerant control due to its good robustness and adaptability to system uncertainties. Sliding mode control designs a sliding mode surface, and after the system enters the sliding mode surface, the system state is kept on the sliding mode surface through the sliding mode controller, so that the system can have strong inhibition ability to uncertainties, external disturbances and system failures.

[0005] The application intends to introduce adaptive control on the basis of traditional sliding mode control to further enhance the adaptability of the system in complex environments and ensure 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-tolerant ability of the system. SUMMARY

[0006] The purpose of the present application is to provide a kind of unmanned aerial vehicle formation fault-tolerant control method based on original pigeon chaotic adaptive sliding mode control, to solve the problem of formation instability caused by actuator failure, communication failure and external disturbance when multiple unmanned aerial vehicles cooperate in complex environment.The method realizes the unmanned aerial vehicle formation fault-tolerant control under the complex fault environment such as actuator performance decline and communication interruption by constructing the dynamic model of unmanned aerial vehicle formation, introducing adaptive sliding mode controller and combining fault detection and estimation module.In addition, the system designs a control mechanism based on virtual reference model to guide the unmanned aerial vehicle to continue to perform formation task according to preset instruction when communication failure occurs, and ensures the formation to be kept.

[0007] The present application aims at the formation cooperative control problem of unmanned aerial vehicle cluster under the environment of actuator and communication mixed fault, and invents a kind of unmanned aerial vehicle formation fault-tolerant control method based on original pigeon chaotic adaptive sliding mode control, and the algorithm implementation flow chart is as shown in Figure 1 The specific implementation steps are as follows:

[0008] Step one: kinematics modeling of unmanned aerial vehicle and state information initialization.

[0009] Specifically: kinematics modeling of unmanned aerial vehicle, considering the flight dynamics system of lead aircraft and wingman, using the rotating reference coordinate system fixed on wingman, focusing on the cluster formation control task of multiple wingmen and lead aircraft in the present application, so the algorithm simulation verification scene is simplified, and the unmanned aerial vehicle is set at the same height, only two-dimensional plane coordinates are considered.

[0010] The kinematics equation of unmanned aerial vehicle formation flight control system is established as follows:

[0011]

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

[0013]

[0014] In the formula, represents the speed time constant of wingman, This represents the wingman's position time constant. This represents the altitude time constant of the lead aircraft. The altitude time constant of the wingman. and These are the three control inputs for the wingman. Combining formulas (1) and (2), a six-dimensional nonlinear programming control system is obtained:

[0015]

[0016] In the formula, z is the vertical distance between the lead aircraft and the wingman, and η is the rate of change of z. In a cluster distributed control system, since the lead aircraft's rotation angle is small, its control input can be considered as a disturbance signal. Therefore, the lead aircraft's control input interferes with the wingman, requiring the wingman to effectively suppress and compensate for these disturbance signals during the following process. By treating the lead aircraft's control input as a disturbance, the design of the wingman's control strategy can be simplified, while also improving the system's robustness and stability. In this framework, the disturbance signals are the disturbances caused by different attitude changes, and further refined, they include angular deviations such as yaw introduced by the lead aircraft's small attitude adjustments. 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 lead aircraft and the wingman, and φ represents the formation angle between the lead aircraft and the wingman. To facilitate controller design research, the UAV formation flight system can be represented by the following state-space model, which simplifies the system analysis process and more intuitively describes the dynamic relationships between various state variables. This model effectively captures the attitude, speed, and position change characteristics of UAVs during formation flight, enabling controller design to clearly define how control inputs affect system state evolution. This state-space model not only provides the mathematical basis for analyzing system stability and response speed but also provides parameter basis for optimizing control laws, thereby achieving precise 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. For example, formula (5) in step one can be transformed into the following form:

[0023]

[0024] where ω ∈ R 3 The fault variable ω represents the uncertain fault, which can be caused by continuous or discontinuous wireless communication failure. To design the fault-tolerant controller, the following reference model is introduced:

[0025]

[0026] The tracking error is defined as follows, and the dynamic tracking error equation is obtained by derivation:

[0027]

[0028] To ensure the accuracy of the reference model, some assumptions are needed to support the model establishment. There are some suitable dimension matrices M and N such that A-A l = BM, B l = BN. The considered fault uncertainty is continuous bounded, and there are positive constants ω1, ω2 such that ||ω|| < ω1 and hold. According to these assumptions, formula (8) can be transformed as:

[0029]

[0030] Step three: By adaptive sliding mode technology, a sliding mode surface function is designed to obtain the reduced order sliding mode kinematic equation.

[0031] Specifically: for the dynamic tracking error equation (9) established in step two, a sliding mode surface function is designed as follows:

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

[0033] In order to facilitate the design of sliding mode control law, a transformation matrix is designed, where is an arbitrary basis in the null space of B T . Let Then the transformation is obtained:

[0034]

[0035] where z1 ∈ R 3 , z2 ∈ R 3 . The dynamic tracking error equation (9) established in step two can be transformed as:

[0036]

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

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

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

[0040]

[0041] Step four: 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. The criterion ensures that the tracking error always remains on the sliding surface under ideal conditions without communication failure and external disturbance, thereby achieving robust tracking performance of the system. At the same time, the design scheme ensures the asymptotic stability of the system, so that the control accuracy is effectively guaranteed under various disturbances, meeting the demand for high-precision tracking control.

[0042] Specifically: a criterion for asymptotic stability is proposed to ensure the asymptotic stability of the sliding mode dynamic system in step three 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 formula (14) in step three is asymptotically stable for the reduced-order sliding mode dynamic system under the suppression level μ1. Here, an H ∞ performance index function is introduced: Let the Lyapunov function be Take the derivative of V1, and after transformation, we can get:

[0045]

[0046] In the formula If Υ1 < 0, it can be deduced that Integrating this inequality, we get:

[0047]

[0048] Under zero initial conditions, it is easy to conclude that the reduced-order sliding mode kinematic equation in step three is asymptotically stable under the given suppression level μ1.

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

[0050] Specifically: in the presence of communication failure and external disturbance, only relying on the sliding mode controller described in step four is not enough to maintain the stability and accuracy of the system, because at this time the accurate estimation information of the communication failure needs to be obtained first to design the control law with switching mechanism to eliminate the influence of the failure on the system. However, in the flight control system of unmanned aerial vehicles, it is difficult to accurately obtain the communication failure information, and the traditional method has great limitations in real-time performance and practicality. To overcome this difficulty, a control strategy based on adaptive neural network is proposed, which automatically adjusts the control parameters to deal with unknown failures, effectively suppresses the disturbance of the system, and enhances the robustness and reliability of the system in complex environments.

[0051] In this method, the fault value needs to be estimated by designing an adaptive estimation law. First, a virtual adaptive sliding mode controller is designed, which includes the expected fault estimation law and neural network weights. Let represent the estimated value of the 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, make the inequality hold:

[0054]

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

[0056]

[0057] The adaptive estimation law is designed as follows:

[0058]

[0059] Where a>0, b>0 are two normal numbers. Construct the Lyapunov function Take the derivative, in order to make the fault-tolerant controller have a certain anti-interference ability, introduce H ∞ Performance index function By the establishment of theorem 1 in step four, the following formula can be obtained:

[0060]

[0061] In the formula From formula (22), we can get Integrating both sides can get the following inequality under the zero initial condition:

[0062]

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

[0064] Step Six: Integrate the adaptive sliding mode control parameters from Steps Three and Four into a parameter vector P to be optimized, and introduce a primitive pigeon chaos mechanism to fully search for the optimal solution in the 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 complex dynamic environments.

[0065] Specifically, when designing an adaptive sliding mode controller, it is typically necessary to optimize three key parameters: a, b, and G. By introducing a primitive pigeon chaos mechanism, and through the global search of the pigeon flock algorithm and the local fine-grained search of the chaotic search, the optimal solution in the adaptation space can be effectively explored. First, a set of pigeon flock positions is randomly initialized, representing the initial parameter set of the controller. The position of each pigeon can be represented as a vector P containing the 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. To evaluate the quality of each set of parameters, a fitness function is defined, and the system dynamic tracking error e(t) is selected as:

[0068]

[0069] In the formula, e(t) represents the dynamic tracking error, and T represents the simulation time. To avoid the pigeon flock algorithm getting trapped in local optima, a chaotic search mechanism is used to optimize the pigeon flock locally. A chaotic mapping function (Logistic mapping) is used to generate a chaotic sequence, which is then applied to the pigeon search process to increase the diversity of the population. The mapping formula is as follows:

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

[0071] The chaotic sequence can be used to disturb the position of the pigeon group, so that it jumps out of the local optimum. Through the chaotic search, the pigeon group continues to search in the global range, while improving the accuracy of local optimization. After the end of the chaotic pigeon group optimization, the optimal parameters The application will be applied to the adaptive sliding mode controller, instead of the original artificial selection parameters. The optimized parameters will enable the controller to compensate for system uncertainties and external disturbances in a larger range, and improve the dynamic performance and disturbance rejection while ensuring system stability.

[0072] Advantages and effects:

[0073] The present application provides a kind of unmanned aerial vehicle cluster formation fault-tolerant method based on original pigeon chaotic adaptive sliding mode control, by the mode of wingman following long plane constitutes a fixed geometric figure, in order to accurately and quickly obtain the estimated value of fault, a virtual reference model is introduced, a dynamic tracking error equation is obtained, for this, a virtual tracking controller and fault estimation algorithm are designed, adaptive sliding mode control and pigeon optimization with chaotic mapping mechanism are combined, a formation fault-tolerant controller is designed, and the problem of formation stability of unmanned aerial vehicle formation cooperative flight in fault interference environment is solved.

[0074] The adaptive sliding mode control framework with original pigeon chaotic mechanism provided by the present application mainly has the following advantages: first, in the actual unmanned aerial vehicle flight process, the instability of communication line and the acquisition of fault information are very difficult, the present application directly realizes fault-tolerant control by adjusting control parameters through adaptive adjustment mechanism without relying on accurate fault estimation information, which greatly improves the practicability of the system in complex environment;Second, the adaptive sliding mode controller proposed by the present application can automatically adjust the control gain according to the change of environment, thereby enhancing the adaptability of the system to uncertainty and external disturbance, ensuring that the system can quickly respond when fault or disturbance occurs, and controlling the steady-state error at a very low level, ensuring the accuracy and coordination of unmanned aerial vehicle cluster in formation flight;In addition, by using original pigeon chaotic mechanism, through the global search and local optimization ability of chaotic sequence, the controller parameters can be automatically optimized, avoiding the risk of falling into local optimum, and ensuring that the control system reaches the optimal state in the global range. The present application effectively solves the limitations of traditional sliding mode control method in fault-tolerant control under the condition of actuator failure and external disturbance of unmanned aerial vehicle, and still maintains the stability of the system under complex interference conditions, which provides a feasible solution for formation problem under complex environmental conditions. DETAILED DESCRIPTION

[0075] Figure 1 The flow chart of unmanned aerial vehicle cluster formation fault-tolerant control based on original pigeon chaotic adaptive sliding mode control.

[0076] Figure 2 Plot of the three control inputs of the wingman as a function of time.

[0077] Figure 3 Plot of the state variables and reference state variables of the faulty UAVs 1, 2, 3 as a function of time for the simulation at t = 3 s.

[0078] Figure 4 Plot of the state variables and reference state variables of the faulty UAVs 4, 5 as a function of time for the simulation at t = 3 s.

[0079] Figure 5 Trajectory plot of the lateral distance, longitudinal distance and altitude of the flock of UAVs simulating the pigeon chaos.

[0080] Figure 6 Trajectory plot of the speed, heading angle and vertical distance of the flock of UAVs simulating the pigeon chaos.

[0081] Legend and symbols in the figures are as follows:

[0082] t - simulation time

[0083] v Qu - wingman speed control input;

[0084] φ Qu - wingman heading angle control input;

[0085] - wingman vertical distance control input;

[0086] - total state variable of the system;

[0087] - state variable of UAV 1;

[0088] - state variable of the reference system of UAV 1;

[0089] - state variable of UAV 2;

[0090] - state variable of the reference system of UAV 2;

[0091] - state variable of UAV 3;

[0092] - state variable of the reference system of UAV 3;

[0093] - state variable of UAV 4;

[0094] - state variable of the reference system of the drone 4;

[0095] - state variable of the drone 5;

[0096] - state variable of the reference system of the drone 5;

[0097] x - lateral displacement of the lead and the wingman on the coordinate axis;

[0098] y - longitudinal displacement of the lead and the wingman on the coordinate axis;

[0099] z - vertical displacement of the lead and the wingman on the coordinate axis;

[0100] v Q - speed of the wingman;

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

[0102] z Q - displacement change of the wingman in the vertical direction; DETAILED DESCRIPTION

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

[0104] The mathematical simulation researches a formation composed of six UAVs, one lead and five wingmen. The matrix A and B are assigned as shown below: speed time constant heading time constant attitude time constant λ zα = 0.3 s, λ zβ = 3.85 s. The parameter matrix of the reference model is given as follows:

[0105]

[0106] It can be known that is a basis of the null space of the matrix B T , let the disturbance suppression level μ1 = 0.4, and then the positive definite matrix G can be obtained from the linear matrix inequality in formula (15) in step four:

[0107]

[0108] In the Matlab simulation, the speed of the lead is 2 m / s, and the heading angle of the lead is 2.1°. The initial state of the wingman is set to vQ0 =0.17m / s, φ Q0 =0.07°, z Q0 =0.3m, the initial values ​​of the formation geometry are set as x0 = 0.17m, y0 = 0.09m, z0 = 0.03m. Substituting these initial parameters and the positive definite matrix into the three control inputs of the wingman, the curves of the three control inputs changing over time are obtained, as shown below. Figure 2 As shown; the controller gain and adaptive coefficients are as follows: a = 0.3, b = 0.5; to verify the superior performance of the control method, assume a wireless communication fault occurs in the command channel design at the 3rd second: ω = [cost + cos²t sinint - sin²t cost - sin²t] T The proposed fault-tolerant controller (20) can achieve satisfactory dynamic performance of the flight control system state and control input response under fault conditions. Based on the given wireless communication fault and the proposed fault handling controller, the following is obtained: Figure 3 and Figure 4 The graphs show the changes in the state variables of the five UAVs and the reference state variable; the obtained controller gain and adaptive coefficients are optimized parameters after traversing the chaotic pigeon swarm algorithm, generating... Figure 5 and Figure 6 The trajectories of the five drones and the lead aircraft in terms of lateral, longitudinal, altitude, formation speed, heading angle, and vertical distance.

Claims

1. A UAV cluster formation fault-tolerant method based on original pigeon chaos adaptive sliding mode control, characterized in that: The method steps are as follows: Step one, unmanned aerial vehicle kinematics modeling and state information initialization; wherein, considering the flight dynamics system of the long machine and the wingman, using the rotating reference frame fixed on the wingman, the control input of the long machine is regarded as a disturbance signal, and a linearized disturbance equation is obtained; Step two, a virtual reference model is introduced, a tracking error is designed, and a dynamic tracking error equation is obtained; Step three, through adaptive sliding mode technology, a sliding mode surface function is designed, and a reduced order sliding mode kinematics equation is obtained; Step four, introducing H ∞ The performance index function is designed to ensure that the tracking error dynamics model reaches the sliding surface and remains on the sliding surface when there is no communication failure and disturbance. Step five, a virtual adaptive sliding mode controller is designed, including an expected fault estimation law and a neural network approximation weight, to ensure asymptotic stability under a given suppression level μ2; Step six, the original pigeon chaos mechanism is introduced, and the adaptive control parameters and the sliding mode parameters are optimized through global search of the pigeon algorithm and local fine search of the chaos search to obtain the optimal controller parameter combination; In step five, a virtual adaptive sliding mode controller is designed, which contains the expected fault estimation law and the neural network weights; let represents the estimation of the fault ω, so the estimation error is defined as: If a positive real scalar μ2>0 is given, if there is a positive real number a, b, so that the following matrix Υ2: In the formula, B and κ represent matrices in the linearized state space model; G represents a symmetric positive definite matrix in the sliding mode surface function; At the same time, the inequality is established: In the formula, ω1 and ω2 represent normal numbers; S represents the sliding mode surface function; ζ represents the disturbance signal; Then the tracking error model system reaches the sliding mode surface, and the motion system remains on the sliding mode surface under the following virtual tracking controller when the given suppression level μ2 is reached; the controller is as follows: In the formula, M and N are matrices selected to ensure the accuracy of the reference model; The adaptive estimation law is designed as follows: where a > 0, b > 0 are two normal numbers; construct Lyapunov function Derivation, introduce H ∞ Performance index function The following equation is obtained: where From the validity of equation (22) we obtain Integrating both sides simultaneously under the zero initial condition we obtain the following inequality:

2. The method of claim 1, wherein: The step one is specifically as follows: the unmanned aerial vehicle is kinematically modeled, The unmanned aerial vehicle kinematics model is established as follows: where x, y represent the lateral and longitudinal distances of the leader and the wingman from the coordinate axis, v P , v Q represent the flight speeds of the leader and the wingman, φ P and φ Q represent the heading angles of the leader and the wingman, and φ e represents the difference between the heading angles of the leader and the wingman; the formation flight control system of the wingman is described by the following simplified equation: where represents the velocity time constant of the wingman, represents the azimuth time constant of the wingman, represents the altitude time constant of the lead aircraft, represents the altitude time constant of the wingman, and are the three control inputs of the wingman, respectively; combining equations (1) and (2) gives a six-dimensional nonlinear pilot-vehicle control system: In the formula, z is the distance between the leader and the wingman in the vertical direction, and η is the change rate of z; in the cluster distributed control, the control input of the leader is regarded as a disturbance signal because the attitude rotation angle is small, so the disturbance signals are φ P , P and Therefore, it can be linearized into the following disturbance equation: In the formula, d represents the linear distance between the long machine and the wingman, φ represents the formation angle between the long machine and the wingman, and the unmanned aerial vehicle formation flight system is represented as a state space model as follows: where the corresponding coefficients and variables are as follows 3. The method of claim 2, wherein: The step two is specifically as follows: The state space model of the unmanned aerial vehicle formation flight system in step one is transformed into the following form: where ω ∈ R 3 To design the fault-tolerant controller, the following reference model is introduced: In the formula, A l , B l denotes a parameter matrix of the reference model; denotes a state quantity of the reference model; The tracking error is defined as follows, and the dynamic tracking error equation is obtained by derivation: The matrices M and N are such that A - A l = BM, B l = BN holds; the considered uncertainty is continuously bounded and there exist positive constants ω1, ω2 such that ||ω|| < ω1 and holds; formula (8) is transformed into:

4. The method of claim 3, wherein: The step three is specifically as follows: for the dynamic tracking error equation (9) established in step two, the sliding mode surface function is designed as follows: S = se = B T G -1 e (10) Design transformation matrix where is B T an arbitrary basis in the null space; let Then the transformation yields: where z1∈R 3 , z2∈R 3 ; the dynamic tracking error equation (9) established in step two is transformed into: After the above transformation, the sliding mode surface becomes: S = se = B T G -1 e = B T G -1 Bz2 (13) When the sliding mode surface S=0, the following reduced order sliding mode kinematics equation is obtained:

5. The method of claim 4, wherein: The step four is specifically as follows: If there is a symmetric positive definite matrix G that makes the following linear matrix inequality Then, the formula (14) in step three is asymptotically stable for the reduced order sliding mode dynamic system at the suppression level μ1; introduce a H ∞ Performance index function: Let Lyapunov function be Derivate V1, get through transformation: where If Y1< 0, it follows that Integrating this inequality gives: Under the zero initial condition, it is easy to obtain that the reduced order sliding mode kinematics equation in step three is asymptotically stable under a given suppression level μ1.

6. The method of claim 1, wherein: The step six is specifically as follows: the adaptive sliding mode parameters in steps three and four 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 the adaptive sliding mode controller, three key parameters a, b, and G need to be optimized; First, a set of pigeon positions is randomly initialized, representing the initial parameter set of the controller; the position of each pigeon is represented as a vector P containing three parameters to be optimized i = [a i b i G i ], that is: P i = [a i b i G i ], i = 1, 2,..., N (24) In the formula, N is the number of pigeons; in order to evaluate the advantages and disadvantages of each group of parameters, a fitness function is defined, and the system dynamic tracking error e(t) is selected as follows: In the formula, e(t) is the dynamic tracking error, and T is the simulation time; in order to avoid the pigeon algorithm falling into local optimization, the pigeon is locally optimized by combining the chaos search mechanism; the chaos sequence is generated by using the chaos mapping function and applied to the pigeon search process to increase the diversity of the population; the mapping public is as follows: x n+1 = gx n (1 - x n ), g = 4 (26).

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