Control method of time-varying nonlinear multi-agent system based on dynamic trigger condition

Abstract

The invention belongs to the technical field of industrial intelligent control, and particularly relates to a control method of a time-varying nonlinear multi-agent system based on a dynamic trigger condition. The method is realized based on a model of a time-varying nonlinear multi-agent system, and comprises the following steps: establishing a centralized control method under a dynamic event triggering condition; establishing a distributed control method of the multi-agent system with the known topological structure; and establishing a distributed control method of the multi-agent system with the unknown topological structure. The method is applied to a centralized control method, the conservative property of a trigger interval is small, and the lower limit is larger; for a multi-agent system with a known topological structure, not only can each agent have different pulse time, but also the information transmission channel and communication cost can be reduced; for a multi-agent system with an unknown topological graph, a dynamic compensator is added to each agent, so that pulse events of the agents are different. The control efficiency can be practically improved, the system risk is reduced, and the consistency of the system is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial intelligent control, and particularly relates to a control method for a time-varying nonlinear multi-agent system based on dynamic triggering conditions. More specifically, it is a pulse control method for a time-varying nonlinear multi-agent system based on dynamic event triggering conditions. Background Art

[0002] Due to the successful application of multi-agent systems in fields such as energy management, mode control, and unmanned driving, the problem of their joint control has attracted extensive attention. In particular, many scholars are committed to studying the output state consensus problem of multi-agents.

[0003] Traditional control methods for multi-agent systems usually require the controller updates and agent-to-agent communications to maintain a continuous state, but this may cause energy loss and channel congestion. To solve this problem, many scholars have conducted in-depth research on control schemes, including reducing the sampling frequency through pulse control strategies. However, both the sampling time and the pulse time are set in advance, which will lead to more conservative choices of sampling and pulse points.

[0004] To further optimize the control strategy, some scholars have proposed event-triggered control strategies, allowing the controller to be updated according to specific events. However, the pulse control strategy based on event-triggering conditions still has some drawbacks. For example, the existing static event-triggering conditions are very conservative, most control strategies only consider linear multi-agent systems, and most existing pulse rules require all agents to update the controller simultaneously.

[0005] Therefore, there is an urgent need for a pulse control method based on dynamic event-triggering conditions that can better adapt to nonlinear multi-agent systems, effectively improving the control efficiency and reducing system risks. Summary of the Invention

[0006] Aiming at the deficiencies existing in the above-mentioned prior art, the present invention provides a control method for a time-varying nonlinear multi-agent system based on dynamic triggering conditions. Its purpose is to achieve the invention purpose of giving a pulse control method for multi-agent systems with known and unknown topological structures through a new dynamic event-triggering strategy with a larger triggering interval than the static mode, so that the system reaches consensus.

[0007] The technical solution adopted by the present invention to achieve the above purpose is as follows:

[0008] A control method for a time-varying nonlinear multi-agent system based on dynamic triggering conditions, comprising:

[0009] A centralized control method under dynamic event-triggered conditions, which performs centralized control on a known multi-agent system. By adding a piecewise continuous function term to the static control mode of pulse control at fixed times, a dynamic event-triggered condition under the pulse control mode is proposed. If the above conditions are met, the system achieves consensus.

[0010] A distributed control method for a multi-agent system with a known topological structure, which performs distributed control on a known multi-agent system. By applying centralized pulse control at different pulse times to a known time-varying nonlinear topological multi-agent system, an improved distributed control method based on centralized pulse control is proposed. If the above conditions are met, the system achieves consensus.

[0011] A distributed control method for a multi-agent system with an unknown topological structure, which performs distributed control on an unknown multi-agent system. By setting a dynamic compensator for each agent to make the pulse events different, if the above conditions are met, the system achieves consensus.

[0012] Furthermore, the model of the time-varying nonlinear multi-agent system is:

[0013]

[0014] where, x i (·) is an n-dimensional real vector, representing the state moment of the i-th agent; u i (·) is an m-dimensional real vector, representing the input moment of the i-th agent; represents the pulse moment of the i-th agent, x0(t) is the state of the system leader, g(·) is a vector function of a nonlinear structure, represents the left limit of, is the derivative of x0(t), is the derivative of x i (t), is the system input at the pulse moment of the i-th agent, is the system state at the pulse moment of the i-th agent, M1(t), M2(t) are system matrices, M s (t) = M s + ΔM s (t), M s is a known matrix, ΔM s (t) is an uncertain matrix;

[0015] ΔM1(t) = QΞ(t)Q1

[0016] ΔM2(t) = QΞ(t)Q2

[0017] where Q, Q1, and Q2 are known, time-invariant real matrices of dimension n*n, and Ξ(t) is a time-varying real matrix of dimension n*n.

[0018] For the nonlinear vector function g(·) and any x1, x2 belonging to the n-dimensional real number set, there exists a constant symmetric positive definite matrix L such that:

[0019] ∥g(x1) - g(x2)∥ 2 ≤(x1 - x2) T L(x1 - x2)

[0020] Considering that there is a direct communication channel between the system leader and the agents to transmit information, find appropriate and event-triggering conditions to make the system reach state consensus.

[0021] Furthermore, the centralized control method under the dynamic event-triggering condition includes:

[0022] In the centralized control method, the impulse time of the i-th agent is e i (t) = x i (t) - x0(t), which is the state error between the i-th agent and the leader. The vector composed of the state errors between each agent and the leader, so:

[0023]

[0024] where:

[0025]

[0026] In the above formula, is the derivative of e(t), M i (t) is the M1(t) and M2(t) mentioned above, which are system matrices, g(e(t)) is the vector function of the nonlinear structure of the state error, t is time, t k is the impulse time, T is the vector transpose operation, is the N-dimensional identity matrix, e(t k ) is the vector composed of the state errors between each agent's impulse time and the leader, is the vector composed of the state errors between each agent's left limit impulse time and the leader, u(t k ) is the input of each agent at the impulse time;

[0027] If e(t) approaches 0, the system reaches consensus;

[0028] Design the controller as shown in the following formula:

[0029]

[0030] where: u i (t k ) is the input of the i-th agent at the impulse moment, K i is the unknown matrix to be calculated, H is the information connection matrix of the multi-agent system, i is the agent number,

[0031] is the set of agent numbers, where R is the set of real numbers, n is the vector dimension, which is the same as the number of agents, is the n-dimensional identity matrix;

[0032] Among them, various variables need to satisfy: matrix P > 0, α > 0, ε1 > 0, ε2 > 0, λ > 0

[0033] 0 < γ < 1

[0034]

[0035] In the above formula: PQ is P * Q, PM1 is P * M1, PM2 is P * M2, L *T is the conjugate transpose matrix of the L matrix, ε1Q T 1 is the transpose matrix of ε1 * Q1, Q T 2 is the transpose matrix of Q2, is the n-dimensional identity matrix;

[0036] t k The impulse trigger moment depends on:

[0037]

[0038] The system can reach consensus, where:

[0039]

[0040] Among them, T > 0 is a constant, θ > 0, μ > 0, 0 < < δ1 - γ.

[0041] Furthermore, the distributed control method for the multi-agent system with the known topological structure includes:

[0042] Given Satisfying And b N > 0, a controller is given as follows:

[0043]

[0044] Among them, K i ∈R n×n represents an unknown matrix to be calculated, * is the conjugate, and col (i-1)n+1 (H i ) represents the (i - 1)n + 1-th column in the H i matrix; meanwhile,

[0045]

[0046] Among them, Δt i > 0 represents a positive constant that needs to be solved; represents the k-th pulse moment of the i-th agent, and Δt i represents the deviation between the (i + 1)-th agent and the i-th agent at the k-th pulse moment;

[0047] As long as there is a matrix P, K i ∈R n×n , where α > 0, ε1 > 0, ε2 > 0, λ > 0, 0 < γ < 1, γ i > 0 and s2 ∈ {s1 + 1, …, N}, Δt s > 0, such that P > 0 and satisfies the following conditions:

[0048]

[0049] depends on:

[0050]

[0051] The system can achieve consensus, where:

[0052]

[0053] T = min{Ω, T},

[0054]

[0055] In the above formula: diag{···} represents a matrix with the values in {} as the diagonal and zeros in other positions, and row represents a certain row of the matrix.

[0056] Furthermore, the distributed control method for the multi-agent system with unknown topological structure is as follows:

[0057]

[0058] Among them, is the derivative of the dynamic compensator system state, z i (t) is the derivative of the dynamic compensator system state, u i is the system input, z i (t) ∈ R n , unknown matrix K 1i , K 2i ∈ R n×n needs to be calculated;

[0059] Under this condition, as long as there is a matrix P i , K 1i , K 2i ∈ R n×n , α i > 0, ε 1i > 0, ε 2i > 0, ε 3i > 0, λ > 0, 0 < γ i < 1 and such that P i > 0;

[0060]

[0061] depends on:

[0062]

[0063] Satisfying the above conditions, the system can achieve consensus, where,

[0064]

[0065] T i > 0 is a given constant, θ i > 0, μ i > 0, 0 < δ i < 1 - γ i 。

[0066] Furthermore, the control method of the time-varying nonlinear multi-agent system based on dynamic triggering conditions also includes a verification method for the control method of the time-varying nonlinear multi-agent system based on dynamic triggering conditions. The symbols used for calculation are assigned values using the models of five agents to verify the control method, including:

[0067] The system parameters are selected as:

[0068]

[0069] g(x) = (g1(x1) g2(x2)) T, x = (x1 x2) T ,

[0070]

[0071] T = 0.5, T i = 0.5, i = 1,2,...,5;

[0072] The comparison of the number of pulses using the centralized control method is as follows:

[0073]

[0074] θ = 4, δ = 0.1, α = 2.7, μ = 3, γ = 0.85.

[0075] The distributed control method for the known topological structure is as follows:

[0076]

[0077] θ = 4, δ = 0.1, α = 2.5, μ = 3, γ = 0.85,

[0078] Δt1 = 0.01, Δt2 = 0.005, Δt3 = 0.01, Δt4 = 0.005.

[0079] The multi - agent control method for the unknown topological structure is as follows:

[0080]

[0081] θ i = 4, α i = 2.4, μ i = 3, i = 1, 2,...,5,

[0082] δ1 = 0.1, δ2 = 0.2, δ3 = 0.3, δ4 = 0.4, δ5 = 0.5,

[0083] γ1 = 0.5, γ2 = 0.45, γ3 = 0.4, γ4 = 0.35, γ5 = 0.3..

[0084] The control device for the time - varying non - linear multi - agent system based on the dynamic triggering condition, implemented based on the model of the time - varying non - linear multi - agent system, includes:

[0085] The centralized control method establishment module, used to establish the centralized control method under the dynamic event triggering condition, control the known multi - agent system, by adding a piece - wise continuous function term to the static control mode of pulse control at a fixed time, propose the dynamic event triggering condition under the pulse control mode, and the system achieves consensus when the above conditions are met;

[0086] The distributed control method establishment module for a multi-agent system with a known topological structure is used to establish a distributed control method for a multi-agent system with a known topological structure, control the known multi-agent system, and propose an improved distributed control method based on centralized impulsive control for the known time-varying non-linear topological multi-agent system at different impulsive times. If the above conditions are met, the system achieves consensus.

[0087] The distributed control method establishment module for a multi-agent system with an unknown topological structure is used to establish a distributed control method for a multi-agent system with an unknown topological structure, control the unknown multi-agent system, and make the impulsive events of each agent different by setting a dynamic compensator for each agent. If the above conditions are met, the system achieves consensus.

[0088] Furthermore, the centralized control method under the dynamic event-triggering condition includes:

[0089] In the centralized control method, the impulsive time of the i-th agent is e i (t) = x i (t) - x0(t), which is the state error between the i-th agent and the leader. The vector composed of the state errors between each agent and the leader. Therefore:

[0090]

[0091] Where:

[0092]

[0093] In the above formula, is the derivative of e(t), M i (t) is the M1(t) and M2(t) mentioned above, which are system matrices, g(e(t)) is the vector function of the non-linear structure of the state error, t is time, t k is the impulsive time, T is the vector transpose operation, is the N-dimensional identity matrix, e(t k ) is the vector composed of the state errors between each agent's impulsive time and the leader, is the vector composed of the state errors between each agent's left limit impulsive time and the leader, u(t k ) is the input quantity at each agent's impulsive time;

[0094] If e(t) approaches 0, the system reaches consensus;

[0095] Design the controller as shown in the following formula:

[0096]

[0097] where: u i (t k ) is the input of the i-th agent at the pulse moment, K i ∈R n×n , K i is the unknown matrix to be calculated, H is the information connection matrix of the multi-agent system, i is the agent number, is the set of agent numbers, where R is the set of real numbers, n is the vector dimension and is the same as the number of agents, is the n-dimensional identity matrix;

[0098] Among them, various variables need to satisfy: matrix P > 0, α > 0, ε1 > 0, ε2 > 0, λ > 0

[0099] 0 < γ < 1

[0100]

[0101] In the above formula: PQ is P*Q, PM1 is P*M1, PM2 is P*M2, L *T is the conjugate transpose matrix of the L matrix, ε1Q T 1 is the transpose matrix of ε1*Q1, Q T 2 is the transpose matrix of Q2, is the n-dimensional identity matrix;

[0102] t k The pulse trigger moment depends on:

[0103]

[0104] The system can reach consensus, where:

[0105]

[0106] Among them, T > 0 is a constant, θ > 0, μ > 0, 0 < < δ1 - γ.

[0107] A computer device includes a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor. When the processor executes the computer program, it implements the steps of any one of the control methods for a time-varying nonlinear multi-agent system based on dynamic trigger conditions.

[0108] A computer storage medium stores a computer program. When the computer program is executed by a processor, it implements the steps of any one of the control methods for a time-varying nonlinear multi-agent system based on dynamic trigger conditions.

[0109] The present invention has the following beneficial effects and advantages:

[0110] First, by adding a piecewise continuous function term to the static control mode, a series of new dynamic event-triggering conditions under the pulse control mode are proposed and applied in the centralized control method, with less conservatism and a larger lower limit for the triggering interval.

[0111] Second, for a multi-agent system with a known topological structure, an improved distributed control scheme based on centralized pulse control is proposed. It can not only make each agent have different pulse times but also reduce the information transmission channel and communication cost.

[0112] Third, for a multi-agent system with an unknown topological graph, a distributed pulse control scheme with dynamic event-triggering conditions is proposed. By adding a dynamic compensator to each agent, the pulse events are made different.

[0113] The dynamic event-triggering condition obtained by adding a piecewise continuous function term to the traditional static event-triggering condition in the present invention can make the control method have less conservatism and a larger lower bound for the triggering interval.

[0114] Compared with the existing methods that only consider linear systems and time-invariant systems, the present invention can effectively handle time-varying and non-linear difficulties through the Schur theorem, Gronwall inequality, and the characteristics of exponential functions, and solve the consensus problem of non-linear time-varying multi-agents.

[0115] Therefore, the method of the present invention can better adapt to the pulse control method based on dynamic event-triggering conditions for non-linear multi-agent systems, effectively improve the control efficiency, and reduce the system risk. A pulse control method is given for multi-agent systems with known and unknown topological structures, so that the system reaches consensus. BRIEF DESCRIPTION OF THE DRAWINGS

[0116] The above and / or additional aspects and advantages of the present invention will become apparent and be readily understood from the following description of the embodiments in conjunction with the accompanying drawings, where:

[0117] Figure 1 is the topological structure diagram of the multi-agent system of the present invention;

[0118] Figure 2 is the comparison diagram of the number of pulses between the traditional method and the centralized method of the present invention;

[0119] Figure 3 is the state deviation diagram of the agents of the centralized pulse control method of the present invention;

[0120] Figure 4 is the comparison diagram of the pulse conditions between the traditional method and the distributed method of the present invention for a system with a known topological structure;

[0121] Figure 5 It is the state deviation diagram of the agent of the distributed pulse control method for the known topological structure system of the present invention;

[0122] Figure 6 It is the comparison diagram of the pulse conditions between the traditional method and the present distributed method for the unknown topological structure system of the present invention;

[0123] Figure 7 It is the state deviation diagram of the agent of the distributed pulse control method for the unknown topological structure system of the present invention;

[0124] Figure 8 It is the flow chart of the method of the present invention.

[0125] In the figure: Agent 1 is Agent 1, Agent 2 is Agent 2, Agent 3 is Agent 3, Agent 4 is Agent 4, and Agent 5 is Agent 5. Specific embodiments

[0126] In order to more clearly understand the above objects, features and advantages of the present invention, the present invention will be further described in detail below in conjunction with the drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0127] Many specific details are set forth in the following description in order to fully understand the present invention. However, the present invention can also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0128] The following refers to Figures 1-8 Describe the technical solutions of some embodiments of the present invention.

[0129] Embodiment 1

[0130] The present invention provides an embodiment, which is a control method for a time-varying nonlinear multi-agent system based on dynamic trigger conditions. As Figure 8 shown, Figure 8 It is the flow chart of the method of the present invention.

[0131] The model of the time-varying nonlinear multi-agent system of the present invention is:

[0132]

[0133] wherein, x i (·) is an n-dimensional real vector, u i (·) is an m-dimensional real vector, which respectively represent the state time and input time of the i-th agent, Denote the impulsive moment of the \(i\) -th agent, \(x_0(t)\) is the state of the system leader, \(g(\cdot)\) is a vector function of non - linear structure, Denote the left - hand limit of is the derivative of \(x_0(t)\), is \(x\) i (t)'s derivative, is the system input at the impulsive moment of the \(i\) -th agent, is the system state at the impulsive moment of the \(i\) -th agent, \(M_1(t)\), \(M_2(t)\) are system matrices. \(M\) s (t)=M s +\(\Delta M\) s (t), \(M\) s is a known matrix, \(\Delta M\) s (t) is an uncertain matrix.

[0134] \(\Delta M_1(t)=Q\Xi(t)Q_1\)

[0135] \(\Delta M_2(t)=Q\Xi(t)Q_2\)

[0136] where \(Q\), \(Q_1\), \(Q_2\) are known, time - invariant real - valued matrices of dimension \(n\times n\) respectively, and \(\Xi(t)\) is a time - varying real - valued matrix of dimension \(n\times n\).

[0137] In addition, for the non - linear vector function \(g(\cdot)\) and any \(x_1\), \(x_2\) belonging to the \(n\) - dimensional real - number set, there exists a constant symmetric positive - definite matrix \(L\) such that:

[0138] \(\left\|\left|g(x_1)-g(x_2)\right|\right\|\) 2 \(\leq(x_1 - x_2)\) T \(L(x_1 - x_2)\)

[0139] In the present invention, there is a direct communication channel between the system leader and the agents to transmit information. Therefore, the main purpose of the present invention is to find appropriate and event - triggering conditions to make the system reach state consensus.

[0140] A control method for a time - varying non - linear multi - agent system based on dynamic triggering conditions of the present invention is implemented on the basis of the above - mentioned model of the time - varying non - linear multi - agent system, and specifically includes: a centralized control method under dynamic event - triggering conditions, a distributed control method for a multi - agent system with known topological structure, and a distributed control method for a multi - agent system with unknown topological structure.

[0141] (1) The centralized control method under dynamic event - triggering conditions.

[0142] A series of new dynamic event-triggering conditions under pulse control mode are proposed by adding piecewise continuous function terms to the static control mode with pulse control at fixed moments, and are applied in the centralized control method, which has less conservatism and a larger lower limit for the triggering interval.

[0143] Furthermore, the centralized control method under dynamic event-triggering conditions includes:

[0144] In the centralized control method, the pulse moment of the i-th agent is e i (t) = x i (t) - x0(t), which is the state error between the i-th agent and the leader. is the vector composed of the state errors between each agent and the leader. Therefore:

[0145]

[0146] Where:

[0147]

[0148] In the above formula, is the derivative of e(t), M i (t) is the M1(t) and M2(t) mentioned above, which are system matrices, g(e(t)) is similar to the previous one and is a vector function of the nonlinear structure of the state error, t is time, t k is the pulse moment, T is the vector transpose operation. is the N-dimensional identity matrix, e(t k ) is the vector composed of the state errors between each agent's pulse moment and the leader. is the vector composed of the state errors between each agent's left limit moment of the pulse and the leader, u(t k ) is the input at each agent's pulse moment.

[0149] Therefore, when e(t) approaches 0, the system reaches consensus.

[0150] According to these conditions, a controller is designed as shown in the following formula:

[0151]

[0152] Where: u i (t k ) is the input to the i-th agent at the pulse moment. K i ∈ R n×n and K iis an unknown matrix to be calculated, H is the information connection matrix of the multi-agent system, i is the serial number of the agent, is the set of agent serial numbers, where R is the set of real numbers, n is the vector dimension and is the same as the number of agents, is the n-dimensional identity matrix.

[0153] Among them, all kinds of variables need to satisfy: matrix P > 0, α > 0, ε1 > 0, ε2 > 0, λ > 0

[0154] 0 < γ < 1

[0155]

[0156] All the newly defined symbols in the above formula are symbols used for calculation and have no specific practical significance. PQ is P * Q, PM1 is P * M1, PM2 is P * M2, L *T is the conjugate transpose matrix of the L matrix, ε1Q T 1 is the transpose matrix of ε1 * Q1, Q T 2 is the transpose matrix of Q2, is the n-dimensional identity matrix.

[0157] And t k The pulse trigger moment depends on:

[0158]

[0159] The system can reach consensus, where:

[0160]

[0161]

[0162] Among them, T > 0 is a constant, θ > 0, μ > 0, 0 < < δ1 - γ

[0163] In the above formula, the newly added symbols are all for calculation and have no practical physical meaning.

[0164] (2) Distributed control method for multi-agent systems with known topological structures.

[0165] This method is obtained by researching on the basis of the centralized control method for multi-agent systems with known topological structures, that is, it is implemented on the basis of the above model of time-varying nonlinear multi-agent systems.

[0166] For a multi-agent system with a known time-varying non-linear topology, an improved distributed control scheme based on centralized impulsive control is proposed. It can not only enable each agent to have different impulsive times, but also reduce the information transmission channels and communication costs.

[0167] Furthermore, the distributed control method for a multi-agent system with a known topology includes:

[0168] Given a satisfying and b N > 0, the controller can be given as follows:

[0169]

[0170] where, K i ∈R n×n represents an unknown matrix to be calculated. * is the conjugate, and col (i-1)n+1 (H i ) represents the (i - 1)n + 1-th column in the H i matrix. At the same time,

[0171]

[0172] where, Δt i > 0 represents a positive constant that needs to be solved; represents the k-th impulsive time of the i-th agent, and Δt i represents the deviation of the k-th impulsive time between the (i + 1)-th agent and the i-th agent.

[0173] As long as there is a matrix P, K i ∈R n×n , where α > 0, ε1 > 0, ε2 > 0, λ > 0, 0 < γ < 1, γ i > 0 and s2 ∈ {s1 + 1, …, N}, Δt s > 0, such that P > 0, and the following conditions are also met.

[0174]

[0175] depends on:

[0176]

[0177] The system can achieve consensus, where:

[0178]

[0179] τ = min{Ω, T},

[0180]

[0181] In the above formula: diag{···} represents a matrix with the values in {} as the diagonal and zeros elsewhere, row represents a certain row of the matrix, and other positioning symbols are for calculation use and have no physical meaning.

[0182] (3) Distributed control method for multi-agent systems with unknown topological structures.

[0183] For the multi-agent system with an unknown topological graph, the present invention also proposes a distributed impulsive control scheme with dynamic event-triggering conditions. By adding a dynamic compensator to each agent, the impulsive events are made different.

[0184] Furthermore, the distributed control method for multi-agent systems with unknown topological structures is as follows:

[0185] To make the of all agents different, a dynamic compensator is set for each agent when designing the controller. The specific design method is as follows:

[0186]

[0187] Wherein, is the derivative of the system state of the dynamic compensator, z i (t) is the derivative of the system state of the dynamic compensator, u i is the system input, z i (t) ∈ R n , unknown matrix K 1i , K 2i ∈ R n×n needs to be calculated.

[0188] Under this condition, as long as there is a matrix P i , K 1i , K 2i ∈ R n×n , α i > 0, ε 1i > 0, ε 2i > 0, ε 3i > 0, λ > 0, 0 < γ i < 1 and such that P i > 0.

[0189]

[0190] Depending on:

[0191]

[0192] When the above conditions are met, the system can achieve consistency. Among them,

[0193]

[0194] T i > 0 is a given constant, θ i > 0, μ i > 0, 0 <δ i < 1 - γ i .

[0195] The newly added symbols in the above formula are parameters used in the calculation and have no physical meaning.

[0196] The above three control methods for different situations enable the multi - agent system to achieve state consistency. Among them:

[0197] Method (1) The centralized control method under dynamic event - triggering conditions and Method (2) The distributed control method for multi - agent systems with known topologies are used to control known multi - agent systems.

[0198] Method (2) The distributed control method for multi - agent systems with known topologies is an improvement of Method (1) The centralized control method under dynamic event - triggering conditions. Their effects are similar. Method (2) The distributed control method for multi - agent systems with known topologies has a heavier communication burden, and Method (1) The centralized control method under dynamic event - triggering conditions has a heavier instantaneous burden.

[0199] Method (3) The distributed control method for multi - agent systems with unknown topologies is used to control unknown multi - agent systems.

[0200] Embodiment 2

[0201] The present invention further provides an embodiment, which is a control method for a time - varying nonlinear multi - agent system based on dynamic triggering conditions. This embodiment verifies the three methods in Embodiment 1 as follows:

[0202] The system parameters are selected as:

[0203]

[0204] g(x) = (g1(x1) g2(x2)) T , x = (x1 x2) T ,

[0205]

[0206] T = 0.5, T i = 0.5, i = 1, 2, …, 5。

[0207] As Figure 2 shown, the comparison of the number of pulses between the traditional method and the centralized method of the present invention is as follows: The centralized control method is as follows:

[0208]

[0209] 0 = 4, δ = 0.1, α = 2.7, μ = 3, γ = 0.85.

[0210] Among them, the state deviation of the agent of the centralized pulse control method is as Figure 3 shown.

[0211] As Figure 4 shown, for the comparison of the pulse conditions between the traditional traditional method and the present distributed method for the system with known topological structure, the state deviation of the agent of the distributed pulse control method for the system with known topological structure is as Figure 5 shown.

[0212] The distributed control method for the known topological structure is as follows:

[0213]

[0214] θ = 4, δ = 0.1, α = 2.5, μ = 3, γ = 0.85,

[0215] △t1 = 0.01, △t2 = 0.005, △t3 = 0.01, △t4 = 0.005.

[0216] The control method for multi - agent with unknown topological structure is as follows:

[0217]

[0218] θ i = 4, α i = 2.4, μ i = 3, i = 1, 2, …, 5,

[0219] δ1 = 0.1, δ2 = 0.2, δ3 = 0.3, δ4 = 0.4, δ5 = 0.5,

[0220] γ1 = 0.5, γ2 = 0.45, γ3 = 0.4, γ4 = 0.35, γ5 = 0.3..

[0221] When verifying the three methods in Example 1 in this embodiment, Figure 1The models of the five agents included therein, including Agent 1, Agent 2, Agent 3, Agent 4, and Agent 5, assign values to the symbols that need to be calculated and the symbols used in the calculation in the method of the present invention to verify the feasibility of the method of the present invention and its advantage of being more sensitive compared to traditional static pulse control. Among them Figures 2-7 is a comparison diagram of images.

[0222] Embodiment 3

[0223] The present invention further provides an embodiment, which is a control device for a time-varying nonlinear multi-agent system based on dynamic trigger conditions, implemented based on the model of the time-varying nonlinear multi-agent system, including:

[0224] A centralized control method establishment module, used to establish a centralized control method under dynamic event trigger conditions, control a known multi-agent system, and propose a dynamic event trigger condition under the pulse control mode by adding a piecewise continuous function term to the static control mode of performing pulse control at fixed times;

[0225] A distributed control method establishment module for a multi-agent system with a known topological structure, used to establish a distributed control method for a multi-agent system with a known topological structure, control a known multi-agent system, and propose an improved distributed control method based on centralized pulse control for a known time-varying nonlinear topological structure multi-agent system at different pulse times;

[0226] A distributed control method establishment module for a multi-agent system with an unknown topological structure, used to establish a distributed control method for a multi-agent system with an unknown topological structure, control an unknown multi-agent system, and make the pulse events different by setting a dynamic compensator for each agent.

[0227] The control device for a time-varying nonlinear multi-agent system based on dynamic trigger conditions according to the present invention is used to implement the steps of the control method for a time-varying nonlinear multi-agent system based on dynamic trigger conditions described in Embodiment 1.

[0228] Embodiment 4

[0229] Based on the same inventive concept, an embodiment of the present invention further provides a computer device, including a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor. When the processor executes the computer program, it implements the steps of the control method for a time-varying nonlinear multi-agent system based on dynamic trigger conditions described in Embodiment 1.

[0230] Embodiment 5

[0231] Based on the same inventive concept, an embodiment of the present invention further provides a computer storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the control method of the time-varying nonlinear multi-agent system based on dynamic trigger conditions described in Embodiment 1 are implemented.

[0232] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0233] The present invention is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0234] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means, and the instruction means implement the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0235] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0236] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: it is still possible to modify the specific implementation manners of the present invention or make equivalent substitutions, and any modification or equivalent substitution that does not depart from the spirit and scope of the present invention shall be covered by the protection scope of the claims of the present invention.

Claims

1. A control method for a time-varying nonlinear multi-agent system based on dynamic trigger conditions, characterized by: include: Centralized control method under dynamic event triggering conditions, for known multi-agent systems, centralized control is performed, by adding piecewise continuous function terms to the static control mode of pulse control at fixed time, and dynamic event triggering conditions under pulse control mode are proposed. If the above conditions are met, the system achieves consistency; Distributed control method for multi-agent system with known topology, for distributed control of known multi-agent system, by controlling multi-agent system with known time-varying nonlinear topology at different pulse times, an improved distributed control method based on centralized pulse control is proposed, and the system achieves consistency if the above conditions are met; A distributed control method for a multi-agent system with an unknown topology structure performs distributed control on an unknown multi-agent system. By setting a dynamic compensator for each agent, the pulse events of the agents are different. If the above conditions are met, the system achieves consistency.

2. The control method of a time-varying nonlinear multi-agent system based on dynamic trigger conditions according to claim 1 is characterized in that: The model of the time-varying nonlinear multi-agent system is: Among them, x i (·) is an n-dimensional real vector, representing the state of the i-th agent at that moment; u i (·) is an m-dimensional real vector, representing the input time of the i-th agent; represents the pulse moment of the ith agent, x0(t) is the state of the system leader, g(·) is the vector function of the nonlinear structure, represent The left limit of is the derivative of x0(t), is x i The derivative of (t), is the system input at the pulse time of the ith agent, is the system state at the pulse time of the ith agent, M1(t), M2(t) are system matrices, M s (t) = M s +ΔM s (t), M s is a known matrix, ΔM s (t) is the uncertainty matrix; ΔM1(t)=QΞ(t)Q1 ΔM2(t)=QΞ(t)Q2 Among them, Q, Q1, Q2 are known, time-invariant real matrices of n*n dimensions, Ξ(t) is a time-varying n*n dimensional real matrix, For a nonlinear vector function g(·) and any x1, x2 belonging to the n-dimensional real number set, there exists a constant symmetric positive definite matrix L that satisfies: ∥g(x1)-g(x2)∥ 2 ≤(x1-x2) T L(x1-x2) Considering that there is a direct communication channel between the system leader and the intelligent agent to transmit information, find the appropriate and event triggering conditions to bring the system into a consistent state.

3. The control method of a time-varying nonlinear multi-agent system based on dynamic trigger conditions according to claim 1 is characterized by: The centralized control method under the dynamic event triggering condition includes: In the centralized control method, the pulse time of the ith agent is e i (t) = x i (t)-x0(t), is the state error between the ith agent and the leader, A vector consisting of the state errors between each agent and the leader, so: in: In the above formula, is the derivative of e(t), M i (t) is the M1(t) and M2(t) mentioned above, which are system matrices, g(e(t)) is the vector function of the nonlinear structure of the state error, t is time, t k is the pulse time, T is the vector transposition operation, is the N-dimensional identity matrix, e(t k ) is a vector of state errors between each agent’s pulse time and the leader’s. is a vector of state errors between each agent and the leader at the left limit moment of the pulse, u(t k ) is the input quantity of each agent at the pulse time; When e(t) approaches 0, the system reaches consistency; Design the controller as shown below: Where: u i (t k ) is the input to the ith agent at the pulse time, K i is the unknown matrix to be calculated, H is the information connection matrix of the multi-agent system, i is the serial number of the agent, is a set of agent serial numbers, where R is a real number set, n is the vector dimension, which is the same as the number of agents, is the n-dimensional identity matrix; The various variables need to satisfy: matrix P>0, α>0,ε1>0,ε2>0,λ>00<γ<1 In the above formula: PQ is P*Q, PM1 is P*M1, PM2 is P*M2, L *T is the conjugate transposed matrix of the L matrix, ε1Q T 1 is the transposed matrix of ε1*Q1, Q T 2 is the transposed matrix of Q2, is the n-dimensional identity matrix; t k The pulse triggering time depends on: The system can be consistent, where: Among them, T>0 is a constant number, θ>0, μ>0, 0<<δ1-γ.

4. The control method of a time-varying nonlinear multi-agent system based on dynamic trigger conditions according to claim 1 is characterized in that: The distributed control method of the multi-agent system with known topology structure comprises: Given satisfy And b N >0, the controller is given as follows: in, K i ∈R n×n Indicates that the unknown matrix needs to be calculated, * is conjugate, col (i-1)n+1 (H i ) represents H i The (i-1)n+1th column in the matrix; at the same time, Among them, Δt i >0 represents a positive constant and needs to be solved; represents the kth pulse time of the i-th agent, Δt i represents the deviation between the kth pulse time of the i+1th agent and the ith agent; As long as there is a matrix P,K i ∈R n×n ,in α>0,ε1>0,ε2>0,λ>0,0<γ<1,γ i >0 and s2∈{s1+1,…,N},Δt s >0, Make P>0 and meet the following conditions: depending on: The system can achieve consistency, where: τ=min{Ω,T}, In the above formula: diag{···} represents a matrix with the values ​​in {} as diagonals and other positions as zeros, and row represents a row of the matrix.

5. The control method of a time-varying nonlinear multi-agent system based on dynamic trigger conditions according to claim 1, characterized in that: The distributed control method of the unknown topology multi-agent system is as follows: in, is the derivative of the dynamic compensator system state, z i (t) is the derivative of the dynamic compensator system state, u i is the system input, z i (t)∈R n , Unknown matrix K 1i ,K 2i ∈R n×n Calculation is required; Under this condition, as long as there is a matrix P i ,K 1i ,K 2i ∈R n×n ,α i >0,ε 1i >0,ε 2i >0,ε 3i >0,λ>0,0<γ i <1 and Make P i >0; depending on: If the above conditions are met, the system can achieve consistency, among which, T i >0 is a given constant, θ i >0,μ i >0,0<δ i <1-γ i .

6. The control method of a time-varying nonlinear multi-agent system based on dynamic trigger conditions according to claim 1, characterized in that: It also includes a verification method for the control method of a time-varying nonlinear multi-agent system based on dynamic trigger conditions, using a model of five agents to assign values ​​to symbols that need to be calculated and used in the calculation, and verifying the control method, including: The system parameters are: g(x)=(g1(x1) g2(x2)) T ,x=(x1 x2) T , T=0.5,T i =0.5,i=1,2,…,5; The comparison of pulse times using the centralized control method is as follows: K5=I2, 0=4, δ=0.1, α=2.7, μ=3, γ=0.

85. The distributed control methods of known topologies are as follows: 0=4, δ=0.1, α=2.5, μ=3, γ=0.85, △t1=0.01,△t2=0.005,△t3=0.01,△t4=0.

005. The unknown topology multi-agent control method is as follows: i i =4,a i =2.4, m i =3, i =1, 2,..., 5, δ1=0.1, δ2=0.2, δ3=0.3, δ4=0.4, δ5=0.5, γ1=0.5, γ2=0.45, γ3=0.4, γ4=0.35, γ5=0.

3.

7. A control device for a time-varying nonlinear multi-agent system based on dynamic trigger conditions, characterized in that: Model implementation based on time-varying nonlinear multi-agent system, including: The centralized control method establishment module is used to establish a centralized control method under dynamic event triggering conditions. It controls the known multi-agent system and proposes dynamic event triggering conditions under the pulse control mode by adding piecewise continuous function terms to the static control mode of pulse control at a fixed time. If the above conditions are met, the system achieves consistency. A distributed control method establishment module for a multi-agent system with a known topology structure is used to establish a distributed control method for a multi-agent system with a known topology structure. The module controls the known multi-agent system and proposes an improved distributed control method based on centralized pulse control for the multi-agent system with a known time-varying nonlinear topology structure at different pulse times. If the above conditions are met, the system achieves consistency. The module for establishing the distributed control method of multi-agent system with unknown topology is used to establish the distributed control method of multi-agent system with unknown topology. The module controls the unknown multi-agent system by setting a dynamic compensator for each agent to make the pulse events of the agent different. If the above conditions are met, the system will be consistent.

8. The control device for a time-varying nonlinear multi-agent system based on dynamic trigger conditions according to claim 7, characterized in that: The centralized control method under the dynamic event triggering condition includes: In the centralized control method, the pulse time of the ith agent is e i (t) = x i (t)-x0(t), is the state error between the ith agent and the leader, A vector consisting of the state errors between each agent and the leader, so: in: In the above formula, is the derivative of e(t), M i (t) is the M1(t) and M2(t) mentioned above, which are system matrices, g(e(t)) is the vector function of the nonlinear structure of the state error, t is time, t k is the pulse time, T is the vector transposition operation, is the N-dimensional identity matrix, e(t k ) is a vector of state errors between each agent’s pulse time and the leader’s. is a vector of state errors between each agent and the leader at the left limit moment of the pulse, u(t k ) is the input quantity of each agent at the pulse time; When e(t) approaches 0, the system reaches consistency; Design the controller as shown below: Where: u i (t k ) is the input to the ith agent at the pulse time, K i is the unknown matrix to be calculated, H is the information connection matrix of the multi-agent system, i is the serial number of the agent, is a set of agent serial numbers, where R is a real number set, n is the vector dimension, which is the same as the number of agents, is the n-dimensional identity matrix; The various variables need to satisfy: matrix P>0, α>0,ε1>0,ε2>0,λ>00<γ<1 In the above formula: PQ is P*Q, PM1 is P*M1, PM2 is P*M2, L *T is the conjugate transposed matrix of the L matrix, ε1Q T 1 is the transposed matrix of ε1*Q1, Q T 2 is the transposed matrix of Q2, is the n-dimensional identity matrix; t k The pulse triggering time depends on: The system can be consistent, where: Among them, T>0 is a constant number, θ>0, μ>0, 0<<δ1-γ.

9. A computer device comprising a storage medium, a processor, and a computer program stored in the storage medium and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the control method of a time-varying nonlinear multi-agent system based on dynamic trigger conditions as described in any one of claims 1 to 6 are implemented.

10. A computer storage medium, characterized in that: The computer storage medium stores a computer program, which, when executed by a processor, implements the steps of the control method for a time-varying nonlinear multi-agent system based on dynamic trigger conditions as described in any one of claims 1 to 6.

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