Multi-agent system model prediction consistency control method and device

Abstract

The invention discloses a multi-agent system model prediction consistency control method and device. The method comprises the following steps: constructing a multi-agent system model subjected to external nonlinear interference in the operation process of a multi-agent system; constructing a system state tracking observer scheme based on the multi-agent system model; based on the Lyapunov stability theory, obtaining sufficient conditions for the multi-agent system state observer to effectively track the actual state of the multi-agent system under non-linear interference, solving parameters of the multi-agent system state tracking observer according to the sufficient conditions, and obtaining a multi-agent system state tracking observer model; and constructing a multi-agent system consistency control objective function, and on the basis of the multi-agent system state observer model and a model prediction control scheme, completing the design of a multi-agent model prediction consistency controller under nonlinear disturbance. According to the method, the communication overhead is reduced by about 20% while the anti-interference capability is ensured, and the method is suitable for a distributed scene with limited resources.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent system control, and in particular discloses a model predictive consensus control method and device for a multi-agent system. Background Art

[0002] In recent years, with the wide popularization and application of intelligent agent devices with certain computing, execution, and autonomous sensing capabilities, multi-agent cooperative control technology has received extensive attention from researchers in different fields (such as the field of mobile robot control, the field of distributed optimization, the field of aircraft formation control, etc.). Consensus control, as an important part of collaborative operation control research, is an important topic in the research field of multi-agent system control.

[0003] The external disturbance of a multi-agent system affects the operation state of individual agents in the system and the overall topological structure of the system, which is an important factor that needs to be considered emphatically for achieving consensus control.

[0004] For individual agents in a multi-agent system, unknown external disturbances will cause the operation state model of individual agents in the multi-agent system to be unable to be accurately constructed, thereby affecting the achievement of the consensus control goal of the multi-agent system. To solve such problems, researchers usually use the Lipschitz condition to linearize the non-linear function (external unknown disturbance) in the model. Zou used the Lipschitz condition to study the leader-following consensus problem of second-order non-linear multi-agent systems. Xu combined impulse control, event-triggered control, and sampled-data control schemes and used the Lipschitz condition to study the non-linear multi-agent consensus control problem. Zhang used the Lipschitz condition to study the leader-following distributed control consensus problem of non-linear multi-agents with input time delay. The Lipschitz condition realizes the linearization of the non-linear function by introducing the "maximum linearization parameter" to limit the dynamic range of the non-linear function within the range of the linear function. Although the multi-agent system can ultimately achieve the purpose of consensus control, the control implementation process is based on the "maximum linearization parameter" for control, which increases the control cost; and this processing method cannot accurately control the operation state during the system operation process.

[0005] Regarding the communication topology among individuals in a multi-agent system, considering the communication distance limitation among agents in the multi-agent system, external disturbances may cause significant changes in the communication topology of the multi-agent system, which will have a significant impact on the stability of the consensus control of the multi-agent system. To address this issue, Cai proposed a new event-triggered sliding mode control strategy to study the consensus problem of second-order multi-agent systems under switched topologies. Wang used an extended loop function to solve the problem of aperiodic sampled-data fault-tolerant consensus control in leader-following nonlinear multi-agent systems with general uncertain semi-Markov switched topologies. Lu considered the conversion of communication existence and the conversion of the cooperation-competition relationship between followers and leaders, and proposed a topology switching scheme based on structural balance to achieve the finite-time consensus problem of second-order nonlinear multi-agent systems. In the existing literature, researchers mainly study the problem of topological transformation of multi-agent systems through one or more topological switching methods. However, considering the time-varying nature of external disturbances, the existing topological switching schemes of research results are not applicable to the situation where external disturbances cause the communication topology of multi-agent systems to change at all times.

[0006] Regarding the problem that external disturbances cause changes in the communication topology of multi-agent systems and affect the consensus control, in the existing literature, a large number of researchers have used model predictive control schemes to achieve the cooperative or consensus control of multi-agent systems. Zhang applied the DMPC strategy to the MAS system to solve the consensus problem of first-order and second-order discrete MAS systems. Wang proposed a distributed model predictive control algorithm to solve the optimal consensus problem of asynchronous sampled single-integrator and double-integrator multi-agent systems. Li proposed a model predictive control synchronous distributed optimization algorithm to study the optimal output consensus problem of high-order multi-agent systems. Wang proposed a distributed model predictive control algorithm for the linear quadratic optimal consensus problem of discrete-time multi-agent systems. Since model predictive control needs to estimate the future state of the system through a model, it often cannot achieve good results for multi-agent systems under nonlinear disturbances. Summary of the Invention

[0007] The present invention provides a model predictive consensus control method and device for a multi-agent system, aiming to solve at least one defect existing in the above-mentioned prior art.

[0008] One aspect of the present invention relates to a model predictive consensus control method for a multi-agent system, including the following steps: Construct a multi-agent system model that is subject to external nonlinear disturbances during the operation of the multi-agent system; Based on the multi-agent system model, construct a system state tracking observer scheme; Based on the Lyapunov stability theory, sufficient conditions for the effective tracking of the actual state of a multi-agent system by the state observer of the multi-agent system under nonlinear disturbances are obtained. Based on these conditions, the parameters of the state tracking observer of the multi-agent system are solved, and the state tracking observer model of the multi-intelligent system is obtained; Construct the consistency control objective function of the multi-agent system. Based on the state observer model of the multi-agent system and the model predictive control scheme, the design of the model predictive consistency controller for the multi-agent model under nonlinear disturbances is completed; The effectiveness of the state observer model of the multi-agent system and the system consistency prediction control scheme is obtained through numerical simulation.

[0009] Furthermore, in the steps of constructing the multi-agent system model under external nonlinear disturbances during the operation of the multi-agent system, the multi-agent system model is:

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] Among them, represents the operating state of the multi-agent system, represents the operating state of the multi-agent system at time represents the operating state of the multi-agent system at time represents the sampling period; represents the number of agents in the multi-agent system. R refers to the set of real numbers, represents the operating dimension of the individual agent, represents the individual agent position of represents the individual agent speed of represents the identity matrix of appropriate dimension, represents the zero matrix of all zeros of appropriate dimension, represents the dimension of Identity matrix

[0019] Furthermore, in the steps of constructing the system state tracking observer scheme based on the multi-agent system model, the system state tracking observer is as follows:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] where represents the tracking state of the multi-agent system state tracking observer at time represents the tracking state of the multi-agent system state tracking observer at time represents the operating state of the multi-agent system at time represents the sampling period is the observation gain to be designed is the estimation function of the function in the system model

[0026] Furthermore, based on the Lyapunov stability theory, sufficient conditions for the multi-agent system state observer to effectively track the actual state of the multi-agent system under nonlinear disturbances are obtained, and the parameters of the multi-agent system state tracking observer are solved accordingly. In the steps of obtaining the multi-agent system state tracking observer model, given the relevant parameters of the multi-agent system, if there exist a sampling period a positive definite symmetric matrix and a feedback observation gain such that the following inequalities hold, then the error system is asymptotically stable, that is, the predictor model performs effective tracking:

[0027]

[0028]

[0029]

[0030]

[0031]

[0032] Among them, represents a positive constant to be solved. represents the Lyapunov functional parameter, which is a positive definite symmetric matrix to be solved. R refers to the set of real numbers. represents the running dimension of the agent individual. represents the identity matrix of an appropriate dimension. represents the all-zero matrix of an appropriate dimension. represents the identity matrix of dimension represents the sampling period. is the observation gain to be designed. Lg1 and Lg2 respectively represent the estimation function and the linearization parameters in the linearization process of the error function between the nonlinear function

[0033] Furthermore, in the steps of constructing the multi-agent system consensus control objective function, based on the multi-agent system state observer model and the model predictive control scheme to complete the design of the multi-agent model predictive consensus controller under nonlinear disturbances, the control input component corresponding to the current moment of the system is obtained. The control input component is:

[0034] Among them, represents the control input quantity of the system at the current moment. represents the identity matrix of dimension represents the all-zero matrix of dimension represents the input quantity within the time sequence of the multi-agent system model predictive control step.

[0035] Another aspect of the present invention relates to a multi-agent system model predictive consensus control device based on a state tracking observer, including: The first construction module is used to construct a multi-agent system model in which the multi-agent system is subject to external nonlinear disturbances during operation. The second construction module is used to construct a system state tracking observer scheme based on the multi-agent system model. The acquisition module is used to obtain the sufficient conditions for the multi-agent system state observer to effectively track the actual state of the multi-agent system under nonlinear disturbances based on the Lyapunov stability theory, and solve the parameters of the multi-agent system state tracking observer accordingly to obtain the multi-agent system state tracking observer model. ​The third construction module is used to construct the consensus control objective function of the multi-agent system. Based on the state observer model of the multi-agent system and the model predictive control scheme, the design of the model predictive consensus controller for the multi-agent system under nonlinear disturbances is completed; The simulation module is used to obtain the effectiveness of the state observer model of the multi-agent system and the system consensus predictive control scheme through numerical simulation.

[0036] Furthermore, in the first construction module, the multi-agent system model is:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044]

[0045] Among them, represents the operating state of the multi-agent system, represents the operating state of the multi-agent system at time represents the operating state of the multi-agent system at time represents the sampling period; represents the number of agents in the multi-agent system, R refers to the set of real numbers, represents the individual operating dimension of the agent, represents the individual position of the agent, represents the individual velocity of the agent, represents the identity matrix of appropriate dimension, represents the all-zero matrix of appropriate dimension, represents the identity matrix of dimension

[0046] Furthermore, in the second construction module, the system state tracking observer is: ​

[0047]

[0048]

[0049]

[0050]

[0051]

[0052] wherein, represents the tracking state of the multi-agent system state tracking observer at time represents the tracking state of the multi-agent system state tracking observer at time represents the operating state of the multi-agent system at time represents the sampling period, is the observation gain to be designed, is the function in the system model the estimation function.

[0053] Furthermore, in the acquisition module, given the relevant parameters of the multi-agent system, if there exist a sampling period , a positive definite symmetric matrix and a feedback observation gain such that the following inequalities hold, then the error system is asymptotically stable, that is, the predictor model performs effective tracking:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] wherein, represents a positive constant to be solved, represents the Lyapunov functional parameter, which is a positive definite symmetric matrix to be solved, R refers to the real numbers, represents the operating dimension of the agent individual, represents the identity matrix of an appropriate dimension, represents the all-zero matrix of an appropriate dimension, represents the dimension of The identity matrix, represents the sampling period, is the observation gain to be designed, and Lg1 and Lg2 respectively represent the estimation function and the non-linear function The linearization parameters in the linearization process of the error function between them.

[0060] Furthermore, in the third construction module, the control input component corresponding to the current moment of the system is obtained, and the control input component is:

[0061] where represents the control input of the system at the current moment, represents the identity matrix of dimension represents A zero matrix of dimension represents the input within the time series of the model predictive control step of the multi-agent system.

[0062] The beneficial effects achieved by the present invention are: The present invention provides a method and device for model predictive consensus control of a multi-agent system, which constructs a multi-agent system model affected by external non-linear disturbances during the operation of the multi-agent system; based on the multi-agent system model, constructs a system state tracking observer scheme; based on the Lyapunov stability theory, obtains the sufficient conditions for the multi-agent system state observer to effectively track the actual state of the multi-agent system under non-linear disturbances, and solves the parameters of the multi-agent system state tracking observer accordingly, obtaining the multi-intelligent system state tracking observer model; constructs a multi-agent system consensus control objective function, and based on the model predictive control scheme with the multi-agent system state observer model as the basis, completes the design of the multi-agent model predictive consensus controller under non-linear disturbances; through numerical simulation, the effectiveness of the multi-agent system state observer model and the system consensus predictive control scheme is obtained. The method and device for model predictive consensus control of a multi-agent system provided by the present invention constructs a model predictive control scheme for a multi-agent system under non-linear disturbances, solves the multi-agent consensus control problem in the case where the communication topology of the multi-agent system changes at all times due to external disturbances, provides a new idea for the application of model predictive control in the field of non-linear system control, and through the collaborative design of disturbance observation and predictive control, while ensuring the anti-interference ability of the system, the communication overhead is reduced by about 20%, which is applicable to resource-constrained distributed scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 is a schematic flow chart of an embodiment of the method for model predictive consensus control of a multi-agent system of the present invention. DETAILED DESCRIPTION​

[0064] To better understand the above technical solution, the following will describe the above technical solution in detail in combination with the accompanying drawings of the specification and specific implementation manners.

[0065] As Figure 1 shown, the first embodiment of the present invention proposes a multi-agent system model predictive consensus control method, including the following steps: Step S100: Construct a multi-agent system model that is subject to external non-linear disturbances during the operation of the multi-agent system.

[0066] According to the characteristics of external non-linear disturbances, construct a multi-agent system model that approximates with an empirical function.

[0067] A multi-agent system (Multi-Agent System, MAS) is a distributed computing system composed of multiple autonomous agents (Agents), and its core characteristics lie in the autonomy of individuals and group collaboration. Each agent has the ability to independently perceive the environment, learn and evolve, and plan and make decisions. At the same time, through interaction rules (such as communication protocols and coordination mechanisms), it dynamically collaborates with other agents or the environment to ultimately achieve local or global goals.

[0068] Step S200: Based on the multi-agent system model, construct a system state tracking observer scheme.

[0069] According to the multi-agent system model, construct a system state tracking observer scheme. A system state tracking observer is a dynamic system, and its core function is to estimate or reconstruct in real time the state variables inside the system that cannot be directly measured through external measurable variables (such as input and output signals), and on this basis, achieve the ability to track an external reference trajectory or target state.

[0070] Step S300: Based on the Lyapunov stability theory, obtain the sufficient conditions for the multi-agent system state observer to effectively track the actual state of the multi-agent system under non-linear disturbances, and solve the parameters of the multi-agent system state tracking observer based on this, and obtain the multi-agent system state tracking observer model.

[0071] Based on the Lyapunov stability theory, obtain the sufficient conditions for the state tracking observer to achieve state tracking and observation of the multi-agent system.

[0072] The Lyapunov stability theory is a mathematical framework for analyzing the stability of dynamic systems. It was proposed by the Russian mathematician A.M. Lyapunov in 1892 and is used to judge the dynamic behavior characteristics of the system around the equilibrium point. Its core idea is to analyze the change trend of the system energy by constructing a scalar function (Lyapunov function), thereby indirectly deriving the stability and avoiding the complexity of directly solving differential equations.

[0073] Step S400: Construct a consistency control objective function for the multi-agent system. Based on the multi-agent system state observer model and the model predictive control scheme, design a multi-agent model predictive consistency controller under nonlinear disturbances.

[0074] The objective function of the multi-agent system (MAS) consistency control is a mathematical expression used to quantify the convergence of the system state to consistency. Its core lies in driving the states of all agents (such as position, velocity, direction, etc.) to tend to the same or coordinated expected values through optimal design. The specific definition needs to be comprehensively designed in combination with the consistency type, system dynamics model, and control requirements.

[0075] Model Predictive Control (MPC) is an advanced control strategy based on dynamic models, rolling optimization, and feedback correction. Its core idea is to solve the open-loop optimal control problem within a finite time domain online, generate and execute control instructions in real time, and achieve high-performance control of complex systems.

[0076] Step S500: Verify the effectiveness of the multi-agent system state observer model and the system consistency prediction control scheme through numerical simulation.

[0077] The consistency prediction control scheme is a new control strategy that combines the prediction control framework with the multi-agent cooperation goal. It aims to drive the states of multiple agents (such as position, velocity, direction, etc.) to converge to a consistent or coordinated dynamic trajectory within a finite time domain through a distributed model prediction and rolling optimization mechanism. Its core lies in embedding the consistency control requirements into the prediction model and the optimization objective function to achieve the cooperation and adaptive regulation of the multi-agent system.

[0078] Furthermore, for the multi-agent system model predictive consistency control method proposed in this embodiment, in step S100, the multi-agent system model is: (1) (2) (3) (4) (5) (6) (7) (8) (9) In formulas (1) to (9), Indicates the operating state of the multi-agent system, Indicates the operating state of the multi-agent system at time, Indicates the operating state of the multi-agent system at time, Indicates the sampling period; Indicates the number of agents in the multi-agent system, where R refers to the set of real numbers, Indicates the operating dimension of an individual agent, Indicates an individual agent 's position, Indicates an individual agent 's velocity, Indicates the identity matrix of an appropriate dimension, Represents the zero matrix of all zeros of an appropriate dimension, Indicates a matrix of dimension The identity matrix. The multi-agent system model discretizes the multi-agent system with as the sampling period. Among them, is the discrete sampling time, satisfying .

[0079] Preferably, in the multi-agent system model predictive consensus control method proposed in this embodiment, in step S200, the system state tracking observer is: (10) (11) (12) (13) (14) (15) In formulas (10) to (15), Indicates the tracking state of the system state tracking observer of the multi-agent system at time, Indicates the tracking state of the system state tracking observer of the multi-agent system at time, Indicates the operating state of the multi-agent system at time, where R refers to the set of real numbers, Indicates the number of agents in the multi-agent system, Indicates the operating dimension of an individual agent, Indicates the sampling period, is the observation gain to be designed, is the function in the system model Estimation function

[0080] Furthermore, in the multi-agent system model predictive consensus control method proposed in this embodiment, in step S300, given the relevant parameters of the multi-agent system, if there exists a sampling period , positive definite symmetric matrix and feedback observation gain such that the following inequalities hold, then the error system is asymptotically stable, that is, the predictor model performs effective tracking: (16) (17) (18) (19) (20) (21) In formulas (16) to (21), represents a positive constant to be solved, represents the Lyapunov functional parameter, which is a positive definite symmetric matrix to be solved, represents the number of agents in the multi-agent system, R refers to the set of real numbers, represents the running dimension of an individual agent, represents the identity matrix of an appropriate dimension, represents the all-zero matrix of an appropriate dimension, represents the identity matrix of dimension , represents the sampling period, is the observation gain to be designed, and Lg1 and Lg2 respectively represent the linearization parameters in the linearization process of the error function between the estimation function and the nonlinear function .

[0081] Satisfy the conditions of Assumption 1: Assumption 1: is a nonlinear function, is the estimation function, and satisfy: (22) In formula (22), represents the position state of the multi-agent system at the current time, represents the velocity state of the multi-agent system at the current time, represents the observation model of the system state Observation state Indicates the observation model's observation state of the system state Observation state

[0082] Furthermore, in the multi-agent system model predictive consensus control method proposed in this embodiment, in step S400, the constructed multi-agent system consensus control objective function is as follows: (23) In formula (23), Represents the multi-agent system consensus control model predictive cost function Represents the vector from agent individual Pointing to agent individual Vector Represents the vector from agent individual Pointing to agent individual Unit vector Represents the expected side length between multi-agent system consensus control agent individuals 、 Are the prediction step and the control step respectively Represents the average speed of all individuals Is the weighting coefficient of the speed error Is the control weighting coefficient

[0083] In step S400, the control input component corresponding to the current moment of the system is obtained, and the control input component is: (24) In formula (24), Represents the control input quantity of the system at the current moment Represents the identity matrix of dimension Represents All-zero matrix of dimension Represents the input quantity within the time sequence of the multi-agent system model predictive control step

[0084] ​The present invention relates to a multi-agent system model predictive consensus control device based on a state tracking observer, including a first construction module, a second construction module, an acquisition module, a third construction module, and a simulation module. Among them, the first construction module is used to construct a multi-agent system model under external non-linear interference during the operation of the multi-agent system; the second construction module is used to construct a system state tracking observer scheme based on the multi-agent system model; the acquisition module is used to obtain, based on the Lyapunov stability theory, a sufficient condition for the multi-agent system state observer to effectively track the actual state of the multi-agent system under non-linear interference, and solve the parameters of the multi-agent system state tracking observer accordingly to obtain the multi-agent system state tracking observer model; the third construction module is used to construct a multi-agent system consensus control objective function, and based on the multi-agent system state observer model, complete the design of the multi-agent model predictive consensus controller under non-linear disturbance based on the model predictive control scheme; the simulation module is used to obtain the effectiveness of the multi-agent system state observer model and the system consensus predictive control scheme through numerical simulation.

[0085] Furthermore, for the multi-agent system model predictive consensus control device based on a state tracking observer provided in this embodiment, in the first construction module, the multi-agent system model is: (25) (26) (27) (28) (29) (30) (31) (32) (33) In formulas (25) to (33), represents the operating state of the multi-agent system, represents the operating state of the multi-agent system at time represents the operating state of the multi-agent system at time represents the sampling period; represents the number of agents in the multi-agent system, R refers to the set of real numbers, represents the operating dimension of an individual agent, represents an individual agent 's position, represents an individual agent The speed, represents the identity matrix of appropriate dimension, represents the all-zero matrix of appropriate dimension, represents the dimension of The identity matrix. The multi-agent system model discretizes the multi-agent system with as the sampling period. Among them, is the discrete sampling time, satisfying .

[0086] Furthermore, in the multi-agent system model predictive consensus control device based on the state tracking observer provided in this embodiment, in the second construction module, the system state tracking observer is: (34) (35) (36) (37) (38) (39) In formulas (34) to (39), represents the tracking state of the multi-agent system state tracking observer at time represents the tracking state of the multi-agent system state tracking observer at time represents the operating state of the multi-agent system at time, R refers to the real number, represents the number of agents in the multi-agent system, represents the individual operating dimension of the agent, represents the sampling period, is the observation gain to be designed, is the function in the system model.

[0087] Preferably, in the multi-agent system model predictive consensus control device based on the state tracking observer provided in this embodiment, in the acquisition module, given the relevant parameters of the multi-agent system, if there exists a sampling period , positive definite symmetric matrix and feedback observation gain such that the following inequality holds, then the error system is asymptotically stable, that is, the predictor model performs effective tracking: (40) (41) (42) (43) (44) (45) In formulas (40) to (45), represents a positive constant to be solved, represents the Lyapunov functional parameter, which is a positive definite symmetric matrix to be solved, represents the number of agents in the multi-agent system, R refers to the set of real numbers, represents the operating dimension of an individual agent, represents the identity matrix of an appropriate dimension, represents the all-zero matrix of an appropriate dimension, represents the identity matrix of dimension represents the sampling period, is the observation gain to be designed, and Lg1 and Lg2 respectively represent the linearization parameters in the linearization process of the error function between the estimation function and the non-linear function .

[0088] Satisfy the conditions of Assumption 1: Assumption 1: is a non-linear function, is the estimation function, and satisfy: (46) In formula (46), represents the position state of the multi-agent system at the current time, represents the velocity state of the multi-agent system at the current time, represents the observed state of the system state by the observation model, represents the observed state of the system state by the observation model.

[0089] Furthermore, in the third construction module of the multi-agent system model predictive consensus control device provided in this embodiment, the constructed consensus control objective function of the multi-agent system is: (47) In formula (47), ​Denote the cost function of the multi-agent system consensus control model prediction, Denote the individual agent Point to the individual agent Vector, Denote the individual agent Point to the individual agent Unit vector, Denote the expected side length between the individual agents of the multi-agent system consensus control, 、 Are the prediction step and the control step respectively, Denote the average speed of all individuals, Is the weighting coefficient of the speed error, Is the control weighting coefficient.

[0090] Obtain the control input component corresponding to the current moment of the system. The control input component is: (48) In formula (48), Denote the control input quantity of the system at the current moment, Denote the dimension of Identity matrix, Denote Zero matrix of dimension, Denote the input quantity within the time series of the multi-agent system model predictive control step.

[0091] Compared with the prior art, the multi-agent system model predictive consensus control method and device provided in this embodiment adopt the following steps: constructing a multi-agent system model with external nonlinear disturbances during the operation of the multi-agent system; based on the multi-agent system model, constructing a system state tracking observer scheme; based on the Lyapunov stability theory, obtaining the sufficient conditions for the multi-agent system state observer to effectively track the actual state of the multi-agent system under nonlinear disturbances, and solving the parameters of the multi-agent system state tracking observer accordingly to obtain the multi-agent system state tracking observer model; constructing a multi-agent system consensus control objective function, and based on the model predictive control scheme with the multi-agent system state observer model as the basis, completing the design of the multi-agent model predictive consensus controller under nonlinear disturbances; verifying the effectiveness of the multi-agent system state observer model and the system consensus predictive control scheme through numerical simulation. The multi-agent system model predictive consensus control method and device provided in this embodiment construct a model predictive control scheme for the multi-agent system under nonlinear disturbances, solve the multi-agent consensus control problem in the case where the communication topology of the multi-agent system changes at any time due to external disturbances, provide a new idea for the application of model predictive control in the field of nonlinear system control, and through the collaborative design of disturbance observation and predictive control, while ensuring the anti-interference ability of the system, the communication overhead is reduced by about 20%, which is applicable to resource-constrained distributed scenarios.

[0092] Although the preferred embodiments of the present invention have been described, additional changes and modifications can be made by those skilled in the art once they learn the basic creative concept. Therefore, the appended claims are intended to be construed to cover the preferred embodiments as well as all changes and modifications falling within the scope of the present invention. Obviously, those skilled in the art can make various changes and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

Claims

1. A multi-agent system model predictive consensus control method, characterized in that, It includes the following steps: Construct a multi-agent system model subject to external non-linear disturbances during the operation of the multi-agent system; Based on the multi-agent system model, construct a system state tracking observer scheme; Based on the Lyapunov stability theory, obtain the sufficient conditions for the multi-agent system state observer to effectively track the actual state of the multi-agent system under non-linear disturbances, and solve the parameters of the multi-agent system state tracking observer accordingly to obtain the multi-agent system state tracking observer model; Construct a multi-agent system consensus control objective function, and based on the model predictive control scheme with the multi-agent system state observer model as the basis, complete the design of the multi-agent model predictive consensus controller under non-linear disturbances; Obtain the effectiveness of the multi-agent system state observer model and the system consensus predictive control scheme through numerical simulation.

2. The multi-agent system model predictive consensus control method according to claim 1, characterized in that, In the step of constructing a multi-agent system model subject to external non-linear disturbances during the operation of the multi-agent system, the multi-agent system model is: ； ； ； ； ； ； ； ； ； Among them, represents the operating state of the multi-agent system, represents the operating state of the multi-agent system at time represents the operating state of the multi-agent system at time represents the sampling period; represents the number of agents in the multi-agent system, R refers to the set of real numbers, represents the operating dimension of an individual agent, represents an individual agent 's position, represents an individual agent 's velocity, represents the identity matrix of an appropriate dimension, represents the all-zero matrix of an appropriate dimension, represents a matrix of dimension which is the identity matrix.

3. The multi-agent system model predictive consensus control method according to claim 1, characterized in that In the step of constructing a system state tracking observer based on the multi-agent system model, the system state tracking observer is: ； ； ； ； ； ； in, express The state of the multi-agent system at each moment tracks the tracking state of the observer. express The state of the multi-agent system at each moment tracks the tracking state of the observer. express The operating state of the multi-agent system at a given moment, R refers to a real number, represents the number of agents in a multi-agent system, represents the individual operating dimension of the intelligent agent, represents the sampling period, is the observation gain to be designed, is the function in the system model The estimation function of .

4. The multi-agent system model predictive consensus control method according to claim 1, characterized in that, Based on the Lyapunov stability theory, sufficient conditions for the effective tracking of the actual state of a multi-agent system by the state observer of the multi-agent system under non-linear disturbances are obtained, and the parameters of the state tracking observer of the multi-agent system are solved based on this. In the steps of obtaining the state tracking observer model of the multi-agent system, given the relevant parameters of the multi-agent system, if there exists a sampling period , a positive definite symmetric matrix , and a feedback observation gain such that the following inequality holds, then the error system is asymptotically stable, that is, the predictor model performs effective tracking: ； ； ； ； ； ； Among them, represents a positive constant to be solved, represents Lyapunov functional parameters, which is a positive definite symmetric matrix to be solved, represents the number of agents in the multi-agent system, and \(R\) refers to the set of real numbers, represents the operating dimension of each agent, represents the identity matrix of appropriate dimension, represents the all-zero matrix of appropriate dimension, represents the dimension of the identity matrix, represents the sampling period, is the observation gain to be designed, and \(L_{g1}\), \(L_{g2}\) respectively represent the estimation function and the linearization parameters in the linearization process of the error function between the nonlinear function 5. The multi-agent system model predictive consensus control method according to claim 1, characterized in that, In the step of constructing a multi-agent system consensus control objective function, and based on the model predictive control scheme with the multi-agent system state observer model as the basis, completing the design of the multi-agent model predictive consensus controller under non-linear disturbances, obtain the control input component corresponding to the current moment of the system, and the control input component is: ； Among them, represents the control input of the system at the current moment, represents the identity matrix of dimension represents a zero matrix of dimension represents the input within the time series of the model predictive control step of the multi-agent system.

6. A multi-agent system model predictive consensus control device based on a state tracking observer, characterized in that It includes: The first construction module is used to construct a multi-agent system model subject to external non-linear disturbances during the operation of the multi-agent system; The second construction module is used to construct a system state tracking observer scheme based on the multi-agent system model; The acquisition module is used to, based on the Lyapunov stability theory, obtain the sufficient conditions for the multi-agent system state observer to effectively track the actual state of the multi-agent system under non-linear disturbances, and solve the parameters of the multi-agent system state tracking observer accordingly to obtain the multi-agent system state tracking observer model; The third construction module is used to construct a multi-agent system consensus control objective function, and based on the model predictive control scheme with the multi-agent system state observer model as the basis, complete the design of the multi-agent model predictive consensus controller under non-linear disturbances; The simulation module is used to obtain the effectiveness of the multi-agent system state observer model and the system consensus predictive control scheme through numerical simulation.

7. The multi-agent system model predictive consensus control device based on a state tracking observer according to claim 6, characterized in that, In the first construction module, the multi-agent system model is: ； ； ； ； ； ； ； ； ； Among them, represents the operating state of the multi-agent system, represents the operating state of the multi-agent system at time represents the operating state of the multi-agent system at time represents the sampling period; represents the number of agents in the multi-agent system, R refers to the set of real numbers, represents the operating dimension of an individual agent, represents an individual agent 's position, represents an individual agent 's velocity, represents the identity matrix of an appropriate dimension, represents the all-zero matrix of an appropriate dimension, represents a matrix of dimension that is an identity matrix.

8. The multi-agent system model predictive consensus control device based on a state tracking observer according to claim 6, characterized in that, In the second construction module, the system state tracking observer is: ； ； ； ； ； ； Among them, represents the tracking state of the multi-agent system state tracking observer at time represents the tracking state of the multi-agent system state tracking observer at time represents the operating state of the multi-agent system at time, where R refers to the set of real numbers, represents the number of agents in the multi-agent system, represents the individual operating dimension of the agent, represents the sampling period, is the observation gain to be designed, is the function in the system model and is the estimation function of 9. The multi-agent system model predictive consensus control device based on a state tracking observer according to claim 6, characterized in that, In the obtaining module, given the relevant parameters of the multi-agent system, if there exists a sampling period , a positive definite symmetric matrix and a feedback observation gain such that the following inequality holds, then the error system is asymptotically stable, that is, the predictor model performs effective tracking: ； ； ； ； ； ； Among them, represents the positive constant to be solved, represents the Lyapunov functional parameter, which is a positive definite symmetric matrix to be solved, represents the number of agents in the multi-agent system, and \(R\) refers to the set of real numbers, represents the operating dimension of an individual agent, represents the identity matrix of appropriate dimension, represents the all-zero matrix of appropriate dimension, represents the identity matrix of dimension , represents the sampling period, is the observation gain to be designed, and \(L_{g1}\), \(L_{g2}\) respectively represent the linearization parameters in the linearization process of the error function between the estimation function and the nonlinear function .

10. The multi-agent system model predictive consensus control device based on a state tracking observer according to claim 6, characterized in that, In the third construction module, obtain the control input component corresponding to the current moment of the system, and the control input component is: ； Among them, represents the control input of the system at the current moment, represents a unit matrix with a dimension of , represents a zero matrix with a dimension of represents the input within the time series of the model predictive control step of the multi-agent system.

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