Self-adjusting predetermined performance consistency control method of multi-agent system

Abstract

The invention discloses a self-adjusting predetermined performance consistency control method for a multi-agent system, and the method comprises the steps: building a mathematical model of the multi-agent system, and defining a synchronization error of a follower agent; describing an information interaction relationship among the agents in the multi-agent system based on a graph theory; defining a performance constraint of a synchronization error and a self-adjusting performance boundary function, and introducing a boundary adjusting mechanism with a safety interval detection function to dynamically adapt to disturbance; mapping the synchronization error constrained by the predetermined performance boundary into an unconstrained variable through error conversion and a barrier function; and on the basis of a backstepping method, designing a virtual controller of each order, a final actual controller and an adaptive rate, and realizing cooperative tracking control of the multi-agent system. According to the method, the problems of initial condition feasibility, fixed performance boundary rigid constraint and symmetric performance limitation can be solved, burst interference can be dealt with through a self-regulation mechanism while overshoot, convergence time and steady-state precision are ensured, and the robustness of the system is remarkably improved.

Description

Technical Field

[0001] This invention relates to the technical field of multi-agent system control, and more particularly to a self-regulating predetermined performance consistency control method for multi-agent systems. Background Technology

[0002] Multi-Agent Systems (MAS) have demonstrated broad application prospects in many key areas, such as smart grid scheduling, unmanned aerial vehicle (UAV) formation control, satellite constellation collaboration, and distributed sensor networks, due to their core advantages of high cost-effectiveness, strong scalability, and good fault tolerance. In these application scenarios, consistency control is one of the fundamental and core technologies for achieving collaborative operation in MAS, aiming to synchronize and coordinate the states or outputs of multiple agents.

[0003] In recent years, based on the recursive design framework of backstepping, various control schemes have been proposed to solve the consistency control problem of multi-agent systems. However, in many practical engineering systems, fast and accurate reference tracking is a key prerequisite for ensuring the safe and reliable operation of the system. To this end, high-performance control methods such as Prescribed Performance Control (PPC) and Funnel Control have been developed in related fields. These methods allow designers to quantitatively predefine the transient and steady-state performance indicators of synchronization errors, including key parameters such as convergence time, overshoot, and steady-state accuracy.

[0004] The existing technology has the following main drawbacks:

[0005] First, there is the issue of initial condition feasibility. Most existing high-performance control methods have strict requirements for feasible initial conditions, meaning the initial value of the synchronization error must be within the performance envelope. This implies that when the system restarts, the reference value changes abruptly, or external disturbances occur, additional verification of whether the initial conditions are met is required; if not, a new performance function must be selected, significantly increasing the complexity of controller design and implementation. Existing solutions mainly use tuning functions to adjust the error or construct symmetric performance functions with infinitely large initial values. However, the former cannot clearly define the performance boundaries of the transient phase (such as overshoot), while the latter easily leads to poor transient behavior (such as excessively large error peaks).

[0006] Second, there is the problem of rigid constraints on fixed performance boundaries. Existing predetermined performance control methods typically select a pair of fixed, monotonically changing functions to construct performance boundaries, pre-defining the required transient and steady-state responses. However, in some practical applications, sudden disturbances (such as large-amplitude disturbances) and drastic fluctuations in reference values ​​can lead to a significant increase in errors, even touching or exceeding the performance boundaries, ultimately causing control failure. A typical example is the scenario of unmanned aerial vehicles (UAVs) flying against the wind, where the flight controller needs to achieve a dynamic balance between control performance and the aircraft's own capabilities to ensure safe and stable flight.

[0007] Third, the limitations of symmetric performance constraints. In practical engineering systems, the performance constraints of error control often exhibit significant asymmetric characteristics, meaning that the allowable deviation tolerance, convergence rate, and other constraint indicators often differ when the error fluctuates in the positive and negative directions. Traditional symmetric performance constraint schemes are difficult to adapt to such practical needs, easily leading to problems such as decreased control accuracy, weakened stability, or increased energy consumption.

[0008] Therefore, developing a predetermined performance control method with self-adjustment capabilities that can simultaneously handle initial condition feasibility, sudden disturbance adaptability, and asymmetric performance constraints is of great practical significance and application value for improving the reliability of consistency control in multi-agent systems. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and provide a self-adjusting predetermined performance consistency control method for multi-agent systems. This method not only ensures that the dynamic process and steady-state performance (including overshoot, convergence time and steady-state accuracy) of synchronization error can be preset as needed and automatically meet the initial conditions, but also flexibly relaxes the performance boundary when the system encounters strong disturbances with sudden amplitude changes, thereby substantially enhancing the system's adaptability and robustness.

[0010] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0011] A self-regulating predetermined performance consistency control method for a multi-agent system includes:

[0012] Establish a mathematical model of a multi-agent system that includes follower agents and leader agents, and define the synchronization error of the follower agents;

[0013] Based on graph theory, describe the information interaction relationships between agents in a multi-agent system;

[0014] Define the performance constraints of synchronization error and the self-adjusting performance boundary function, and introduce a boundary adjustment mechanism with safe interval detection to dynamically adapt to disturbances;

[0015] By using error transformation and barrier functions, the synchronization error constrained by the predetermined performance boundary is mapped to an unconstrained variable, thereby transforming the constrained control problem into a stability control problem for the unconstrained variable.

[0016] Based on the backstepping method, we recursively design virtual controllers of each order, the final actual controller, and the adaptive rate to ensure that all signals in the closed-loop system are bounded and to achieve cooperative tracking control of the multi-agent system.

[0017] Furthermore, the first The dynamic model of a follower agent is as follows:

[0018] (1);

[0019] in, , The total number of follower agents; and It is the system state vector. Represents the system state; Representing the The total order of the follower agents; Represents system control input; Representing the The output of a follower agent; and It is an unknown smooth nonlinear function; and Represents a bounded external disturbance, satisfying , ,in and It is an unknown constant;

[0020] The dynamics of the leader agent are as follows:

[0021] (2);

[0022] in, This represents the output signal of the leader agent. The derivative of the leader agent's output signal is given; the leader agent's output signal and its derivative are known, smooth, and bounded.

[0023] Furthermore, considering the practical situation, follower agents cannot obtain global information, but only local information, and define... For the first The set of neighbors of a follower agent is defined as the set of the i-th agent. The synchronization error of each follower agent is:

[0024] (3);

[0025] in, For the first The follower agent receives the neighbor's... Information weights of each agent For the first Each follower agent receives information weights from the leader agent.

[0026] Furthermore, graph theory is used to describe the information interaction relationships between agents in a multi-agent system, including:

[0027] Networked communication in multi-agent systems is achieved through directed graphs. This indicates a directed graph. Contains a set of nodes Edge sets used to define legal communication channels and the adjacency matrix used to quantize link weights. When the intelligent agent From intelligent agents When receiving information, At this time, the intelligent agent For intelligent agents Neighbors; exclude self-joins, i.e. The in-degree of each agent is determined by the in-degree matrix. It means that, among them The dynamic process of information propagation is encoded in the Laplace matrix. In; simultaneously define Let be the communication weight matrix, when Time represents intelligent agent It can receive information from the leader, and it is assumed that... This ensures that at least one follower agent can obtain information from the leader agent; the extended graph notation is... ,in , , ;

[0028] Extended diagram There exists a spanning tree where the leader node is its root node; Let be a non-singular matrix; , and The following inequalities describe the synchronization error. With actual tracking error The relationship between them:

[0029] (4);

[0030] In the formula, This represents the smallest eigenvalue of the matrix.

[0031] Furthermore, performance constraints on synchronization errors and performance boundary functions for self-adjustment are defined, including:

[0032] The performance constraints on synchronization errors are defined as follows:

[0033] (5);

[0034] in, and The expression is:

[0035] (6);

[0036] The self-adjusting performance boundary function includes the following parts:

[0037] 1) Inverse tuning function and initial value of synchronization error ;2) Performance scalar function and 3) Boundary adjustment function and .

[0038] Furthermore, the inverse tuning function Used for subsequent error transformation, defined as:

[0039] (7);

[0040] in, Represents the convergence time; As adjustable design parameters, their determination The convergence speed of is such that the larger the value, the faster the convergence.

[0041] satisfy:

[0042] It is at least a second-order continuously differentiable function and ;

[0043] when Tend to hour, And for , ;

[0044] Performance scalar function It serves as a benchmark function. It is used to ensure the critical transient and steady-state performance of the system, and is defined as follows:

[0045] (8);

[0046] hour, from Monotonically decrease to And in Keep as .parameter control The convergence speed of is such that the larger the value, the faster the convergence.

[0047] Boundary adjustment function The expression is:

[0048] (9);

[0049] in Design parameters; For adaptive rate; and This is a dynamic adjustment factor; the adjustment factor is generated by the following auxiliary system:

[0050] (10);

[0051] (11);

[0052] Here, , , These are design parameters, and are set during initialization. , ; Symbolic function; function and The pre-defined detection function for the performance boundary is as follows:

[0053] (12).

[0054] Furthermore, the working logic of the boundary adjustment function is as follows:

[0055] Boundary detection: when synchronization error Located within the preset safety zone, i.e., satisfying At that time, driving item This makes the regulating factor and Keep it at zero, and then adjust the boundary function. At this point, the performance boundary does not need to be corrected. and Determine the size of the safe interval;

[0056] Outbound response: If If the safe zone is exceeded, then the corresponding driving item... , making the regulatory factor and The dynamic increase drives the boundary adjustment function through equation (9). and Changes occur, allowing for relaxation of performance boundaries, whereby... and Determine the degree of boundary adjustment;

[0057] Boundary restoration: when After returning to the safe range, the adjustment factor and In the parameters and It converges to zero at the dominant exponential rate, thus restoring the performance boundary to its original setting.

[0058] Furthermore, to meet the requirements of feasible initial conditions, the synchronization error is transformed using the tuning function defined in equation (7); the introduced error variable Its initial value is zero, and it is defined as follows:

[0059] (13);

[0060] Under this transformation, the performance constraint defined by equation (5) is equivalently converted to the following form:

[0061] (14);

[0062] The new boundary function and The definition is as follows:

[0063] (15);

[0064] If equation (14) holds, then the system is guaranteed to have the following performance:

[0065] The initial conditions are naturally satisfied: because and , pushed It is naturally established;

[0066] Transient performance is bounded: within the time interval within, from Export By adjusting parameters and This enables the pre-determining of transient indicators such as overshoot.

[0067] Steady-state accuracy guarantee: when At that time, the system satisfies ;when ,have This ensures the steady-state accuracy of the synchronization error;

[0068] To achieve the performance constraints described in equation (14), the constrained error variable is... Mapping to unconstrained variables The transformation relationship is as follows:

[0069] (16).

[0070] Furthermore, a backstepping control method is employed to construct virtual controllers of various orders. , Actual controller and adaptive rate , ,include:

[0071] Define error variables :

[0072] (17);

[0073] in, This is the output of a first-order filter, and the expression for this first-order filter is:

[0074] (18);

[0075] In the formula, For design parameters, For the virtual controller to be designed;

[0076] Design a virtual controller based on the recursive process of the backstep method. as follows:

[0077] (19);

[0078] In the formula, , , For design parameters, and For adaptive rate, intermediate variable and Defined as:

[0079] (20);

[0080] (twenty one);

[0081] Design a practical controller and adaptive rate , as follows:

[0082] (twenty two);

[0083] (twenty three);

[0084] In the formula, , Design parameters, intermediate variables and Defined as:

[0085] (twenty four);

[0086] (25);

[0087] In the formula, , These are design parameters.

[0088] Compared with existing technologies, the principles and advantages of this technical solution are as follows:

[0089] 1. By integrating the inverse tuning function, error transformation function, and barrier function, the constrained synchronization error control problem is transformed into a stability control problem for unconstrained variables. This scheme can simultaneously and quantitatively control overshoot, convergence time, and steady-state accuracy, while naturally satisfying initial conditions. Even in the event of system restart or sudden changes in reference values, there is no need to re-verify the initial conditions, significantly reducing the complexity of controller design.

[0090] 2. Existing performance control methods typically employ a fixed, monotonically changing performance boundary function. In practical applications, sudden disturbances (such as large-scale disturbances) or drastic fluctuations in reference values ​​can significantly increase system errors, even triggering or exceeding the preset performance boundary, leading to control failure. To address this, this technical solution addresses the issue of performance boundary functions... Introducing boundary adjustment function When the error exceeds the preset detection function... The self-adjusting function dynamically adjusts the performance boundaries and appropriately relaxes the constraints, thereby ensuring the stable operation of the system under abnormal conditions. Once the disturbance is eliminated, the system can automatically restore its original high-precision tracking performance.

[0091] 3. In practical engineering systems, performance constraints for error control often exhibit significant asymmetric characteristics. That is, the allowable deviation tolerance, convergence rate, and other constraint indicators often differ when the error fluctuates in the positive and negative directions. Traditional symmetric performance constraint schemes are difficult to adapt to such practical needs, easily leading to problems such as decreased control accuracy, weakened stability, or increased energy consumption. To address this, this technical solution designs a pair of asymmetric self-adjusting performance boundary functions, which can flexibly fit the asymmetric error constraint requirements. The parameter configuration of this scheme is simple and intuitive: the convergence time and steady-state accuracy can be configured separately through parameters. and The maximum overshoot can be set directly, while the maximum overshoot can be set via parameters. and Adjustments can be made. Furthermore, this scheme provides a tighter performance envelope. This tighter envelope effectively guides the controller to generate more precise control signals, thereby simultaneously optimizing the system's dynamic performance (such as shortening settling time and suppressing overshoot) and steady-state performance (such as reducing steady-state error and enhancing anti-interference capabilities). Attached Figure Description

[0092] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0093] Figure 1 This is a flowchart illustrating the principle of a self-regulating predetermined performance consistency control method for a multi-agent system according to an embodiment of the present invention.

[0094] Figure 2 A diagram showing the communication topology of a multi-agent system;

[0095] Figure 3 A tracking trajectory diagram for a multi-agent follower;

[0096] Figure 4 Synchronization error diagram for follower multi-agent systems;

[0097] Figure 5 The tracking trajectory diagram of a multi-agent follower under sudden disturbances;

[0098] Figure 6 This is a synchronization error diagram of follower multi-agents under sudden disturbances. Detailed Implementation

[0099] The present invention will be further described below with reference to specific embodiments:

[0100] like Figure 1As shown in this embodiment, a self-adjusting predetermined performance consistency control method for a multi-agent system includes the following steps:

[0101] S1. Establish a mathematical model of a multi-agent system that includes follower agents and leader agents, and define the synchronization error of the follower agents;

[0102] In this step, the first The dynamic model of a follower agent is as follows:

[0103] (1);

[0104] in, , The total number of follower agents; and It is the system state vector. Represents the system state; Representing the The total order of the follower agents; Represents system control input; Representing the The output of a follower agent; and It is an unknown smooth nonlinear function; and Represents a bounded external disturbance, satisfying , ,in and It is an unknown constant;

[0105] The dynamics of the leader agent are as follows:

[0106] (2);

[0107] in, This represents the output signal of the leader agent. The derivative of the leader agent's output signal is given; the leader agent's output signal and its derivative are known, smooth, and bounded.

[0108] Considering the practical situation, follower agents cannot obtain global information, but only local information; therefore, the definition is... For the first The set of neighbors of a follower agent is defined as the set of the i-th agent. The synchronization error of each follower agent is:

[0109] (3);

[0110] in, For the first The follower agent receives the neighbor's... Information weights of each agent For the first Each follower agent receives information weights from the leader agent.

[0111] S2. Describe the information interaction relationships between agents in a multi-agent system based on graph theory;

[0112] This step specifically includes:

[0113] Networked communication in multi-agent systems is achieved through directed graphs. This indicates a directed graph. Contains a set of nodes Edge sets used to define legal communication channels and the adjacency matrix used to quantize link weights. When the intelligent agent From intelligent agents When receiving information, At this time, the intelligent agent For intelligent agents Neighbors; exclude self-joins, i.e. The in-degree of each agent is determined by the in-degree matrix. It means that, among them The dynamic process of information propagation is encoded in the Laplace matrix. In; simultaneously define Let be the communication weight matrix, when Time represents intelligent agent It can receive information from the leader, and it is assumed that... This ensures that at least one follower agent can obtain information from the leader agent; the extended graph notation is... ,in , , ;

[0114] Extended diagram There exists a spanning tree where the leader node is its root node; Let be a non-singular matrix; , and The following inequalities describe the synchronization error. With actual tracking error The relationship between them:

[0115] (4);

[0116] In the formula, This represents the smallest eigenvalue of the matrix.

[0117] S3. Define the performance constraints of synchronization error and the self-adjusting performance boundary function, and introduce a boundary adjustment mechanism with safe interval detection to dynamically adapt to disturbances;

[0118] In this step, to achieve the predetermined performance tracking, a pair of self-adjusting performance boundary functions are defined. and Used for synchronization error Constraints are applied. As long as the synchronization error consistently satisfies the constraints of the performance boundary function, tracking control with specified transient and steady-state performance can be achieved.

[0119] The performance constraints on synchronization errors are defined as follows:

[0120] (5);

[0121] in, and The expression is:

[0122] (6);

[0123] The self-adjusting performance boundary function includes the following parts:

[0124] 1) Inverse tuning function and initial value of synchronization error ;2) Performance scalar function and 3) Boundary adjustment function and .

[0125] Inverse tuning function Used for subsequent error transformation, defined as:

[0126] (7);

[0127] in, Represents the convergence time; As adjustable design parameters, their determination The convergence speed of is such that the larger the value, the faster the convergence.

[0128] satisfy:

[0129] It is at least a second-order continuously differentiable function and ;

[0130] when Tend to hour, And for , ;

[0131] Performance scalar function It serves as a benchmark function. It is used to ensure the critical transient and steady-state performance of the system, and is defined as follows:

[0132] (8);

[0133] hour, from Monotonically decrease to And in Keep as .parameter control The convergence speed of is such that the larger the value, the faster the convergence.

[0134] To achieve a dynamic response to system disturbances, the boundary adjustment function is configured as an active adjustment mechanism with safe zone detection. Its specific definition and operation process are as follows:

[0135] Boundary adjustment function The expression is:

[0136] (9);

[0137] in Design parameters; For adaptive rate; and This is a dynamic adjustment factor; the adjustment factor is generated by the following auxiliary system:

[0138] (10);

[0139] (11);

[0140] Here, , , These are design parameters, and are set during initialization. , ; Symbolic function; function and The pre-defined detection function for the performance boundary is as follows:

[0141] (12).

[0142] The working logic of the boundary adjustment function is as follows:

[0143] Boundary detection: when synchronization error Located within the preset safety zone, i.e., satisfying At that time, driving item This makes the regulating factor and Keep it at zero, and then adjust the boundary function. At this point, the performance boundary does not need to be corrected. and Determine the size of the safe interval;

[0144] Outbound response: If If the safe zone is exceeded, then the corresponding driving item... , making the regulatory factor and The dynamic increase drives the boundary adjustment function through equation (9). and Changes occur, allowing for relaxation of performance boundaries, whereby... and Determine the degree of boundary adjustment;

[0145] Boundary restoration: when After returning to the safe range, the adjustment factor and In the parameters and It converges to zero at the dominant exponential rate, thus restoring the performance boundary to its original setting.

[0146] This mechanism ensures that the synchronization error is always constrained within a feasible performance envelope by detecting the error status in real time and dynamically adjusting the boundaries, thereby effectively avoiding performance constraint violations and improving the reliability of the control system under disturbances.

[0147] S4. By using error transformation and barrier functions, the synchronization error constrained by the predetermined performance boundary is mapped to an unconstrained variable, thereby transforming the constrained control problem into a stability control problem for the unconstrained variable.

[0148] In this step, to meet the requirements of feasible initial conditions, the synchronization error is transformed using the tuning function defined in equation (7); the introduced error variable Its initial value is zero, and it is defined as follows:

[0149] (13);

[0150] Under this transformation, the performance constraint defined by equation (5) is equivalently converted to the following form:

[0151] (14);

[0152] The new boundary function and The definition is as follows:

[0153] (15);

[0154] If equation (14) holds, then the system is guaranteed to have the following performance:

[0155] The initial conditions are naturally satisfied: because and , pushed It is naturally established;

[0156] Transient performance is bounded: within the time interval within, from Export By adjusting parameters and This enables the pre-determining of transient indicators such as overshoot.

[0157] Steady-state accuracy guarantee: when At that time, the system satisfies ;when ,have This ensures the steady-state accuracy of the synchronization error;

[0158] To achieve the performance constraints described in equation (14), the constrained error variable is... Mapping to unconstrained variables The transformation relationship is as follows:

[0159] (16).

[0160] Within this framework, subsequent control processes only need to ensure Boundedness ensures that the error is correct. The constraints of equation (14) are always satisfied, thus achieving the predetermined synchronization error performance required by equation (5) equivalently. Simultaneously, key indicators such as the convergence time, overshoot, and steady-state error of the control system can be quantitatively determined. This transformation converts the constrained control problem of synchronization error into a stability control problem for unconstrained variables, simplifying the controller design and analysis process.

[0161] S5. Based on the backstepping method, recursively design virtual controllers of each order, the final actual controller, and the adaptive rate to ensure that all signals in the closed-loop system are bounded and to achieve cooperative tracking control of the multi-agent system.

[0162] This step includes:

[0163] Using a backstepping control method, virtual controllers of various orders are constructed. , Actual controller and adaptive rate , ,include:

[0164] Define error variables :

[0165] (17);

[0166] in, This is the output of a first-order filter, and the expression for this first-order filter is:

[0167] (18);

[0168] In the formula, For design parameters, For the virtual controller to be designed;

[0169] Design a virtual controller based on the recursive process of the backstep method. as follows:

[0170] (19);

[0171] In the formula, , , For design parameters, and For adaptive rate, intermediate variable and Defined as:

[0172] (20);

[0173] (twenty one);

[0174] Design a practical controller and adaptive rate , as follows:

[0175] (twenty two);

[0176] (twenty three);

[0177] In the formula, , Design parameters, intermediate variables and Defined as:

[0178] (twenty four);

[0179] (25);

[0180] In the formula, , These are design parameters.

[0181] By employing the controller described above, it can be ensured that all signals in the closed-loop system are bounded. Due to the variables... The boundedness is guaranteed, and the synchronization error predetermined performance constraint required by equation (5) is realized.

[0182] Meanwhile, actual tracking error It is bounded, its range of variation always remains within a pre-defined interval, and it converges to a preset region within a specified time. Based on this, the outputs of all follower agents will asymptotically converge to the output of the leader agent, ultimately achieving the cooperative tracking control objective with predetermined performance.

[0183] To demonstrate the effectiveness of the present invention, a simulation example is provided below.

[0184] Construct a multi-agent system consisting of one leader agent (labeled 0) and four follower agents (labeled 1 to 4), with the following communication topology: Figure 2 As shown. Among them, the first The dynamic model of a follower agent is defined as follows:

[0185] (26)

[0186] In the formula, and They represent the first The control inputs and outputs of an intelligent agent; and Indicates the first The state variables of an agent; and It is an unknown nonlinear function; It is a time-varying external perturbation. The initial state of each follower agent is: , , , The output signal of the leader agent is The control objective is to... Internal synchronization error satisfies To achieve this goal, the key performance parameters selected are: , , , , Other control parameters are as follows: , , , , , , , , , , , , , , .

[0187] Simulation results are as follows Figure 3 and Figure 4 As shown. Figure 3 This indicates the output of each follower agent. Both can quickly track leader signals ; Figure 4 The synchronization error is given. The evolution trajectory. It can be seen that all synchronization errors are limited within the preset performance boundaries, and in... Always satisfied .

[0188] To test the anti-interference capability of the proposed control method, in Apply high-intensity burst perturbations to follower agent 4 during the specified time period: The simulation results in this case are as follows: Figure 5 and Figure 6 As shown, under the self-adjusting predetermined performance control scheme, the system maintains stable operation throughout the entire disturbance period. Figure 5 The results show that follower agent 4 exhibits significant oscillations in its output during the disturbance, but quickly resumes tracking the leader signal after the disturbance ends. Figure 6 This indicates that the synchronization error briefly relaxes the performance constraint boundary during interference to ensure system stability, and then converges back to the specified error range after the interference ends. This fully verifies that the method of the present invention has excellent robustness and anti-interference ability.

[0189] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Therefore, any changes made in accordance with the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A self-regulating predetermined performance consistency control method for a multi-agent system, characterized in that, include: Establish a mathematical model of a multi-agent system that includes follower agents and leader agents, and define the synchronization error of the follower agents; Based on graph theory, describe the information interaction relationships between agents in a multi-agent system; Define the performance constraints of synchronization error and the self-adjusting performance boundary function, and introduce a boundary adjustment mechanism with safe interval detection to dynamically adapt to disturbances; By using error transformation and barrier functions, the synchronization error constrained by the predetermined performance boundary is mapped to an unconstrained variable, thereby transforming the constrained control problem into a stability control problem for the unconstrained variable. Based on the backstepping method, we recursively design virtual controllers of each order, the final actual controller, and the adaptive rate to ensure that all signals in the closed-loop system are bounded and to achieve cooperative tracking control of the multi-agent system.

2. The self-regulating predetermined performance consistency control method for a multi-agent system according to claim 1, characterized in that, No. The dynamic model of a follower agent is as follows: （1）； in, , The total number of follower agents; and It is the system state vector. Represents the system state; Representing the The total order of the follower agents; Represents system control input; Representing the The output of a follower agent; and It is an unknown smooth nonlinear function; and Represents a bounded external disturbance, satisfying , ,in and It is an unknown constant; The dynamics of the leader agent are as follows: (2)； in, This represents the output signal of the leader agent. The derivative of the leader agent's output signal is given; the leader agent's output signal and its derivative are known, smooth, and bounded.

3. The self-regulating predetermined performance consistency control method for a multi-agent system according to claim 2, characterized in that, Considering the practical situation, follower agents cannot obtain global information, but only local information; therefore, the definition is... For the first The set of neighbors of a follower agent is defined as the set of the i-th agent. The synchronization error of each follower agent is: (3)； in, For the first The follower agent receives the neighbor's... Information weights of each agent For the first Each follower agent receives information weights from the leader agent.

4. The self-regulating predetermined performance consistency control method for a multi-agent system according to claim 3, characterized in that, Graph theory is used to describe the information interaction relationships between agents in a multi-agent system, including: Networked communication in multi-agent systems is achieved through directed graphs. This indicates a directed graph. Contains a set of nodes Edge sets used to define legal communication channels and the adjacency matrix used to quantize link weights. When the intelligent agent From intelligent agents When receiving information, At this time, the intelligent agent For intelligent agents Neighbors; exclude self-joins, i.e. The in-degree of each agent is determined by the in-degree matrix. It means that, among them The dynamic process of information propagation is encoded in the Laplace matrix. In; simultaneously define Let be the communication weight matrix, when Time represents intelligent agent It can receive information from the leader, and it is assumed that... This ensures that at least one follower agent can obtain information from the leader agent; the extended graph notation is... ,in , , ; Extended diagram There exists a spanning tree where the leader node is its root node; Let be a non-singular matrix; , and The following inequalities describe the synchronization error. With actual tracking error The relationship between them: (4)； In the formula, This represents the smallest eigenvalue of the matrix.

5. The self-regulating predetermined performance consistency control method for a multi-agent system according to claim 4, characterized in that, Define the performance constraints for synchronization errors and the performance boundary functions for self-adjustment, including: The performance constraints on synchronization errors are defined as follows: (5)； in, and The expression is: (6)； The self-adjusting performance boundary function includes the following parts: 1) Inverse tuning function and initial value of synchronization error ;2) Performance scalar function and 3) Boundary adjustment function and .

6. The self-regulating predetermined performance consistency control method for a multi-agent system according to claim 5, characterized in that, Inverse tuning function Used for subsequent error transformation, defined as: (7)； in, Represents the convergence time; As adjustable design parameters, their determination The convergence speed of is such that the larger the value, the faster the convergence. satisfy: It is at least a second-order continuously differentiable function and ; when Tend to hour, And for , ; Performance scalar function It serves as a benchmark function. It is used to ensure the critical transient and steady-state performance of the system, and is defined as follows: (8)； hour, from Monotonically decrease to And in Keep as ;parameter control The convergence speed of is such that the larger the value, the faster the convergence. Boundary adjustment function The expression is: (9)； in Design parameters; For adaptive rate; and This is a dynamic adjustment factor; the adjustment factor is generated by the following auxiliary system: (10)； (11)； Here, , , These are design parameters, and are set during initialization. , ; Symbolic function; function and The pre-defined detection function for the performance boundary is as follows: (12)。 7. The self-regulating predetermined performance consistency control method for a multi-agent system according to claim 6, characterized in that, The working logic of the boundary adjustment function is as follows: Boundary detection: when synchronization error Located within the preset safety zone, i.e., satisfying At that time, driving item This makes the regulating factor and Keep it at zero, and then adjust the boundary function. At this point, the performance boundary does not need to be corrected. and Determine the size of the safe interval; Outbound response: If If the safe zone is exceeded, then the corresponding driving item... , making the regulatory factor and The dynamic increase drives the boundary adjustment function through equation (9). and Changes occur, allowing for relaxation of performance boundaries, whereby... and Determine the degree of boundary adjustment; Boundary restoration: when After returning to the safe range, the adjustment factor and In the parameters and It converges to zero at the dominant exponential rate, thus restoring the performance boundary to its original setting.

8. The self-regulating predetermined performance consistency control method for a multi-agent system according to claim 6, characterized in that, To meet the requirements of feasible initial conditions, the synchronization error is transformed using the tuning function defined in equation (7); the introduced error variable Its initial value is zero, and it is defined as follows: (13)； Under this transformation, the performance constraint defined by equation (5) is equivalently converted to the following form: (14)； The new boundary function and The definition is as follows: (15) If equation (14) holds, then the system is guaranteed to have the following performance: The initial conditions are naturally satisfied: because and , pushed It is naturally established; Transient performance is bounded: within the time interval within, from Export By adjusting parameters and This enables the pre-determining of transient indicators such as overshoot. Steady-state accuracy guarantee: when At that time, the system satisfies ;when ,have This ensures the steady-state accuracy of the synchronization error; To achieve the performance constraints described in equation (14), the constrained error variable is... Mapping to unconstrained variables The transformation relationship is as follows: (16)。 9. The self-regulating predetermined performance consistency control method for a multi-agent system according to claim 8, characterized in that, Using a backstepping control method, virtual controllers of various orders are constructed. , Actual controller and adaptive rate , ,include: Define error variables : (17)； in, This is the output of a first-order filter, and the expression for this first-order filter is: (18)； In the formula, For design parameters, For the virtual controller to be designed; Design a virtual controller based on the recursive process of the backstep method. as follows: (19)； In the formula, , , For design parameters, and For adaptive rate, intermediate variable and Defined as: (20)； (21)； Design a practical controller and adaptive rate , as follows: (22)； (23)； In the formula, , Design parameters, intermediate variables and Defined as: (24)； (25)； In the formula, , These are design parameters.

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