Predetermined performance consistency tracking control method and system for nonlinear multi-agent system

Abstract

The invention belongs to the related technical field of multi-agent control, and particularly discloses a predetermined performance consistency tracking control method and system for a nonlinear multi-agent system, and the method comprises the steps: constructing a Lyapunov function based on the consistency tracking error of the multi-agent system, and obtaining a control law; consistency tracking control of the multi-agent system is realized according to the control law; wherein the system state quantity in the control law is estimated through a distributed state observer; the distributed state observer is designed through the following method: according to a universal approximation principle, a nonlinear function in a multi-agent system dynamic model is approximated based on a fuzzy logic system, and then the distributed state observer is obtained by combining the multi-agent system dynamic model. According to the method, the precision and robustness of the consistency tracking process of the multi-agent system can be remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to multi-agent control, and more specifically, relates to a predetermined performance consistency tracking control method and system for a nonlinear multi-agent system. Background Art

[0002] In recent years, with the rapid development of communication technology and computer technology, multi-agents and their networked systems have attracted research attention in various fields, and have shown great theoretical research value and broad industrial application prospects. With the help of networked systems, agents can complete specific complex tasks through information exchange. Among them, consistency tracking control is an important aspect of research in the field of multi-agent systems. It aims to design a reasonable control protocol based on the information of neighboring agents so that the states and outputs of all agents tend to be common quantities. It is the basis for achieving advanced tasks such as clustering, swarming, formation, and encirclement.

[0003] Currently, the commonly used consistency control methods mainly include output feedback control based on leader-follower network topology, control based on average consistency protocol, and distributed control based on graph theory, etc. These methods have shown good performance in different application scenarios.

[0004] However, with the continuous expansion of application fields, the consistency tracking control method faces many difficulties and challenges. For example, due to the accuracy and performance of measurement equipment such as sensors, the state variables of the intelligent agent in the actual system have measurement errors or are even unavailable, which makes it difficult to achieve output feedback consistency control; in addition, the dynamic characteristics of the intelligent agent system itself, the time-varying characteristics of the external environment, and the interaction within the system make the controlled object have high uncertainty, which puts higher requirements on the robustness of the control algorithm; in addition, due to physical limitations or safety considerations, the input and output of the controller need to be limited to a certain range, so how to achieve consistency tracking control of the intelligent agent system under the constraints of input saturation and output limitation is also a topic worth studying at present.

[0005] Therefore, for nonlinear multi-agent systems under output disturbances, studying more adaptive and robust control methods is of great significance for the consistency tracking control of multi-agents and helps to achieve more efficient, stable and reliable operation of the system. Summary of the invention

[0006] In view of the above defects or improvement needs of the prior art, the present invention provides a predetermined performance consistency tracking control method and system for a nonlinear multi-agent system, which aims to improve the accuracy and robustness of the consistency tracking process of the nonlinear multi-agent system.

[0007] To achieve the above object, according to one aspect of the present invention, a method for tracking control of predetermined performance consistency of a nonlinear multi-agent system is proposed, comprising the following steps:

[0008] Based on the consistency tracking error of the multi-agent system, the Lyapunov function is constructed, and then the control law is obtained; the consistency tracking control of the multi-agent system is realized according to the control law;

[0009] Among them, the system state quantity in the control law is estimated by a distributed state observer; the distributed state observer is designed by the following method: according to the universal approximation principle, the nonlinear function in the multi-agent system dynamics model is approximated based on the fuzzy logic system, and then the distributed state observer is obtained in combination with the multi-agent system dynamics model.

[0010] As a further preferred embodiment, the multi-agent system dynamics model is expressed as:

[0011]

[0012] Where i = 1, ..., N, N represents the number of agents; j = 1, ..., n, n represents the highest order of the state quantity; x i,j 、x i,j+1 、x i,n 、x i,1 They represent the j-th, j+1-th, n-th, and 1-th order states of the i-th agent respectively; Respectively represent x i,j 、x i,n The derivative of is the system state quantity; They represent the nonlinear functions related to the state quantity in the j-th and n-th order state equations of the ith agent respectively; u i represents the control input of the ith agent, represents the actual output of the ith agent under output perturbation, ρ i (t,y i ) represents a time-varying function, t represents time, y i represents the ideal system output when the i-th agent is not affected by the output disturbance.

[0013] As a further preferred embodiment, the nonlinear function in the multi-agent system dynamics model is approximated based on the fuzzy logic system, which is expressed as:

[0014]

[0015]

[0016] in, is the approximation error, is the fuzzy basis function vector; is the optimal weight vector in the j-th order state equation, U i,j are the fuzzy weight vector and its compact set, is the system state Tight set.

[0017] As a further preferred embodiment, the distributed state observer is expressed as:

[0018]

[0019] in, x i,j 、x i,n The derivative of the estimate, The x i,j+1 、x i,1 、x m,1 ,y i estimated value, m is the number of the agent adjacent to the i-th agent; l i,j , l i,n is the observer gain, θ i is the adaptive parameter to deal with output disturbances, a i,m is an element in the adjacency matrix of agent i, which is used to describe the connection status between agents; is the observed value of the system state quantity, are the optimal weight vector and fuzzy basis function vector in the state equation of the nth order system respectively.

[0020] As a further preferred embodiment, a Lyapunov function is constructed based on the consistency tracking error of the multi-agent system, including:

[0021] Combined with the performance boundary function, the consistency tracking error of the multi-agent system is transformed, and the Lyapunov function is constructed based on the transformed error.

[0022] As a further preferred embodiment, the performance boundary function It is expressed as:

[0023]

[0024] Among them, ρ0 is the initial value of the performance boundary function, β is the decay rate of the function; ρ ∞ is the convergence value of the performance boundary function when time t→∞.

[0025] As a further preferred embodiment, the error after transformation is specifically:

[0026]

[0027] Among them, Φ i,1 is the transformation error after the performance boundary function is introduced, Φ i,j , Φ i,n is the error between the observer output and the virtual control input, h i,1 is the consistency tracking error; x i,j 、x i,n An estimated value of is the virtual control law.

[0028] As a further preferred embodiment, the control law is expressed as:

[0029]

[0030]

[0031]

[0032] in, are the first-order and j-th-order virtual control inputs respectively; τ i,1 , k i,1 , τ i,j , k i,j , τ i,n , k i,n All are custom parameters, Δ i represents the degree of the ith agent, is the reference trajectory y d The derivative of .

[0033] As a further preferred embodiment, when the consistency tracking control of the multi-agent system is realized according to the control law, the parameter adaptation law is:

[0034]

[0035]

[0036] Among them, η i,1 , η i,n , η i,j , κ i is the gain of the adaptive parameter.

[0037] According to another aspect of the present invention, a predetermined performance consistency tracking control system for a nonlinear multi-agent system is provided, comprising a processor, wherein the processor is used to execute the above-mentioned predetermined performance consistency tracking control method for a nonlinear multi-agent system.

[0038] In general, the above technical solution conceived by the present invention has the following technical advantages compared with the prior art:

[0039] 1. The present invention combines a fuzzy logic system and a distributed state observer to realize online observation of state variables under output disturbances, and derives control laws based on Lyapunov stability theory to realize predetermined performance control of the system under output disturbances; it can improve the accuracy and robustness of the consistency tracking process of nonlinear multi-agent systems.

[0040] 2. Based on the fuzzy logic system, the nonlinear function in the controller design process is adaptively approximated online, which reduces the computational burden and can better cope with environmental changes and the uncertainty of internal parameters, significantly improving the robustness of the uncertain system and the versatility of the control algorithm.

[0041] 3. In order to solve the output disturbance problem in multi-agent systems, a distributed state observer is introduced to estimate the system state quantities online, avoiding the problem of decreased tracking accuracy caused by the unmeasurable state quantities or low measurement accuracy in actual systems.

[0042] 4. Introducing the error performance boundary function to achieve predetermined performance control and ensure that the consistency tracking error is always limited within the error boundary can make the system have better transient and steady-state performance, make the control strategy more robust, and be able to adapt to complex and changing scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a schematic diagram of a multi-agent and control system framework according to an embodiment of the present invention;

[0044] Figure 2 A schematic diagram of a network topology connection method between multiple agents according to an embodiment of the present invention;

[0045] Figure 3 This is a diagram showing the consistency tracking effect of multiple agents under output disturbances according to an embodiment of the present invention;

[0046] Figure 4 Schematic diagram of the consistency error and performance boundary function of the multi-agent system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0048] An embodiment of the present invention provides a method for tracking and controlling a predetermined performance consistency of a nonlinear multi-agent system, comprising the following steps:

[0049] S1. Construct a dynamic model of a nonlinear multi-agent system considering output disturbances.

[0050] Specifically, the system dynamics model is expressed as:

[0051]

[0052] Where i=1,...,N represents the number of agents, j=1,...,n represents the order of the state quantity; is a nonlinear function in the system dynamics model, depending on the actual physical model. x i,j represents the j-th state quantity of the ith agent, Respectively represent x i,j 、x i,n The derivative of u i is the control input of the ith agent, is the actual output of the system under output disturbance; ρ i (t,y i ) represents a time-varying function related to the system output, which is used to describe the uncertainty of the system. Specifically, ρ i (t,y i )=α i y i , t represents time, so the ideal system output y i It is expressed as:

[0053]

[0054] To ensure the effectiveness of the control algorithm, it is necessary to assume that the output disturbance function is bounded, that is, θ i An adaptive parameter to cope with output disturbances.

[0055] S2. Perform online adaptive approximation of nonlinear functions in the system dynamics model based on fuzzy logic system.

[0056] According to the universal approximation principle, there exists a fuzzy logic system that can approximate any continuous function with arbitrary precision. Specifically, for the continuous function Under a given accuracy l>0, the fuzzy logic system is defined as H *T M(x) can be used to approximate nonlinear functions Right now:

[0057]

[0058] The above universal approximation principle provides theoretical support for the subsequent nonlinear function approximation process.

[0059] Based on this, the nonlinear function in the above system dynamics model is expressed as:

[0060]

[0061] in, is the approximation error and satisfies the boundedness is the optimal weight vector, which can be expressed as:

[0062]

[0063] Among them, M(x) is the fuzzy basis function vector, U i,j are the fuzzy weight vector and its compact set, is the system state Tight set.

[0064] S3. Design a distributed state observer for the multi-agent system to realize online observation of the state variables under output disturbances, laying the foundation for subsequent feedback control and disturbance compensation.

[0065] Specifically, the system output considering the influence of disturbance cannot be directly used for feedback control, and a distributed observer is used to estimate the system state, thereby improving the robustness of the system under environmental disturbances.

[0066] Combining the system dynamics model in S1 and the fuzzy approximation function in S2, the distributed state observer is expressed as:

[0067]

[0068] in, x i,j 、x i,n The derivative of the estimate, The x i,j+1 、x i,1 、x m,1 ,y i Estimated value, m is the number of the agent adjacent to the i-th agent; the constant l i,j is the observer gain, represents the consistency error between the ith agent and its neighboring agents, a i,m is an element in the adjacency matrix of agent i, which is used to describe the connection status between agents; is the observed value of the system state quantity.

[0069] S4. Introduce the performance index function and transform the consistency error. Based on the Lyapunov function and stability theory, the control law is obtained to achieve the predetermined performance control of the system under output disturbance.

[0070] S41. Define the consistency error of the agent Among them, a ij is an element in the adjacency matrix, which is used to describe the connection status between agents in a directed graph. When agent j can receive information from agent i, a ij =1, otherwise a ij =0.d i is a constant describing the connection relationship between the follower and the leader in the network topology. If the follower i can receive instructions from the leader, then d i =1, otherwise d i =0.y d The expected trajectory information output by the leader.

[0071] S42. According to the relevant theory of predetermined performance control, the error performance index, i.e., the performance boundary function, is introduced. The commonly used performance indicators are monotonically decreasing exponential functions, which are specifically defined as:

[0072]

[0073] Among them, ρ0 is the initial value of the performance boundary function, β represents the decay rate of the function, and the function satisfies The above three parameters are all positive values.

[0074] Based on this, the predetermined performance control can strictly limit the consistency error to the following range:

[0075]

[0076] S43. Combined with the performance boundary function, the consistency error of the multi-agent system is transformed as follows:

[0077]

[0078] Among them, Φ i,1 is the transformation error after the performance boundary function is introduced, Φ i,j , Φ i,n are the errors between the observer output and the virtual control input in the backstepping controller design process, h i,1 is the consistency tracking error; x i,j 、x i,n An estimated value of is the virtual control law.

[0079] S44. Based on the transformed error, the Lyapunov function is defined and the corresponding control law is derived as follows:

[0080]

[0081]

[0082]

[0083] Among them, τ i,j , k i,j These are all parameters in the control law and need to be adjusted according to the specific model; represents the degree of agent i, When controlling, Determined by a distributed state observer.

[0084] Furthermore, the parameter adaptation law in the controller is expressed as follows:

[0085]

[0086] Among them, η i,j , κ i is the gain of the adaptive parameter.

[0087] The following are specific embodiments:

[0088] For a nonlinear multi-agent system consisting of four single-joint robotic arms, the model of the i-th robotic arm is as follows:

[0089]

[0090] Among them, i=1,2,3,4, θ i is the joint angle of the ith robot arm, g = 9.8 m / s 2 , joint torque

[0091] System status Then the second-order multi-agent model in the form of state space equation is:

[0092]

[0093] in, Consider the input disturbance α i (t) = 1 + 0.1cos(10t).

[0094] The topological connection between agents in a multi-agent system is as follows: Figure 2 shown.

[0095] According to the method of the present invention, the joint angles of the above-mentioned robot arm multi-agent system are tracked and controlled in a consistent manner. The control effect is as follows: Figure 3 , Figure 4 shown. Figure 3 , Figure 4The tracking effect of the intelligent agent on the desired trajectory and the error convergence of the predetermined performance control are demonstrated respectively. It can be seen that the system still has a good consistency tracking effect under the influence of the output disturbance, and the consistency error is always limited within the boundary of the performance function, indicating that the control method of the present invention exhibits good control performance.

[0096] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for tracking control of predetermined performance consistency of nonlinear multi-agent systems, characterized in that: The steps include: Based on the consistency tracking error of the multi-agent system, the Lyapunov function is constructed, and then the control law is obtained; the consistency tracking control of the multi-agent system is realized according to the control law; Among them, the system state quantity in the control law is estimated by a distributed state observer; the distributed state observer is designed by the following method: according to the universal approximation principle, the nonlinear function in the multi-agent system dynamics model is approximated based on the fuzzy logic system, and then the distributed state observer is obtained in combination with the multi-agent system dynamics model.

2. The method for tracking and controlling the predetermined performance consistency of a nonlinear multi-agent system according to claim 1, characterized in that: The multi-agent system dynamics model is expressed as: Where i = 1, ..., N, N represents the number of agents; j = 1, ..., n, n represents the highest order of the state quantity; x i,j 、x i,j+1 、x i,n 、x i,1 They represent the j-th, j+1-th, n-th, and 1-th order states of the i-th agent respectively; Respectively represent x i,j 、x i,n The derivative of is the system state quantity; They represent the nonlinear functions related to the state quantity in the j-th and n-th order state equations of the ith agent respectively; u i represents the control input of the ith agent, represents the actual output of the ith agent under output perturbation, ρ i (t,y i ) represents a time-varying function, t represents time, y i represents the ideal system output when the i-th agent is not affected by the output disturbance.

3. The method for tracking and controlling the predetermined performance consistency of a nonlinear multi-agent system according to claim 2, characterized in that: Based on the fuzzy logic system, the nonlinear function in the multi-agent system dynamics model is approximated and expressed as: in, is the approximation error, is the fuzzy basis function vector; is the optimal weight vector in the j-th order state equation, U i,j are the fuzzy weight vector and its compact set, is the system state Tight set.

4. The method for tracking and controlling the predetermined performance consistency of a nonlinear multi-agent system according to claim 3, characterized in that: The distributed state observer is expressed as: in, x i,j 、x i,n The derivative of the estimate, The x i,j+1 、x i,1 、x m,1 ,y i estimated value, m is the number of the agent adjacent to the i-th agent; l i,j , l i,n is the observer gain, θ i is the adaptive parameter to deal with output disturbances, a i,m is an element in the adjacency matrix of agent i, which is used to describe the connection status between agents; is the observed value of the system state quantity, are the optimal weight vector and fuzzy basis function vector in the state equation of the nth order system respectively.

5. The method for tracking and controlling the predetermined performance consistency of a nonlinear multi-agent system according to claim 4, characterized in that: The Lyapunov function is constructed based on the consistent tracking error of the multi-agent system, including: Combined with the performance boundary function, the consistency tracking error of the multi-agent system is transformed, and the Lyapunov function is constructed based on the transformed error.

6. The method for tracking and controlling the predetermined performance consistency of a nonlinear multi-agent system according to claim 5, characterized in that: The performance boundary function It is expressed as: Among them, ρ0 is the initial value of the performance boundary function, β is the decay rate of the function; ρ ∞ is the convergence value of the performance boundary function when time t→∞.

7. The method for tracking and controlling the predetermined performance consistency of a nonlinear multi-agent system according to claim 6, characterized in that: The error after transformation is: Among them, Φ i,1 is the transformation error after the performance boundary function is introduced, Φ i,j , Φ i,n is the error between the observer output and the virtual control input, h i,1 is the consistency tracking error; x i,j 、x i,n An estimated value of is the virtual control law.

8. The method for tracking and controlling the predetermined performance consistency of a nonlinear multi-agent system according to claim 7, characterized in that: The control law is expressed as: in, are the first-order and j-th-order virtual control inputs respectively; τ i,1 , k i,1 , τ i,j , k i,j , τ i,n , k i,n All are custom parameters, Δ i represents the degree of the ith agent, is the reference trajectory y d The derivative of .

9. The method for tracking and controlling the predetermined performance consistency of a nonlinear multi-agent system according to claim 8, characterized in that: When the consistency tracking control of the multi-agent system is realized according to the control law, the parameter adaptation law is: Among them, η i,1 , η i,n , η i,j , κ i is the gain of the adaptive parameter.

10. A predetermined performance consistency tracking control system for a nonlinear multi-agent system, characterized in that: It includes a processor, which is used to execute the predetermined performance consistency tracking control method for a nonlinear multi-agent system as described in any one of claims 1-9.

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