Method for realizing containment proportional consensus of multi-agent system considering time delay

Abstract

The application provides a high-order discrete multi-agent system with time delay and provides a method for achieving restraint proportional consistency, and belongs to the field of networked multi-agent cooperative control. The technical points of the application include: a dynamic model of a discrete-time networked high-order multi-agent system considering time delay is established, a state predictor is constructed according to the model to perform state prediction, a restraint proportional consistency control protocol is designed, an expression of an incremental system is obtained according to the control protocol, a feedback gain matrix is obtained based on a linear matrix inequality, and the gain matrix is substituted into the designed restraint proportional consistency control protocol to achieve restraint proportional consistency of the high-order discrete multi-agent system with time delay. The application overcomes the influence of constant communication time delay, introduces a restraint control strategy to exert control on part of the agents in the network, reduces control cost, and adopts a tracking system to enable all the agents to proportionally reach a predicted expected state, so that the agent system reaches restraint proportional consistency without requiring the communication topology graph to be connected, and the application has the characteristics of easy implementation and easy solution.

Description

Technical Field

[0001] This invention relates to the study of a method for achieving consistency of the restraint ratio in high-order multi-agent systems that considers time delay. Background Technology

[0002] Consistency is an important research direction in networked multi-agent systems. It mainly refers to designing control protocols for multi-agent systems to achieve consistency in certain key quantities of the multi-agent system.

[0003] Networked multi-agent systems inevitably encounter communication delay problems. State predictive control methods are used to compensate for communication delays, and a state observer is designed.

[0004] Previous multi-agent systems often designed controllers for each agent. Now, a restraint control strategy is introduced to apply control to some key nodes, which can make all multi-agent systems reach consistency. Furthermore, a tracking system and proportionality coefficient are designed to ensure that all agents can reach the expected state proportionally. Summary of the Invention

[0005] This invention will study a method for achieving consistency of the restraint ratio in a high-order multi-agent system that considers time delays, and will use a networked multi-agent state prediction and control protocol to solve the communication time delay problem.

[0006] The present invention discloses a method for achieving consistency of the restraint ratio in a high-order multi-agent system considering time delay. This method is implemented through the following scheme:

[0007] Step 1: Establish a dynamic model of a discrete-time networked high-order multi-agent system that considers time delays;

[0008] Step 2: Construct a state predictor for the dynamic model of a discrete-time networked high-order multi-agent system that considers time delays, obtain the predicted state, and compensate for communication time delays;

[0009] Step 3: Based on the predicted state of the dynamic model of the discrete-time networked high-order multi-agent system considering time delay in Step 2, design a constraint proportional consistency control protocol that enables the system to reach the desired state.

[0010] Step 4: Based on the constraint ratio consistency control protocol designed in Step 3, obtain the expression for the incremental system;

[0011] Step 5: Using the expression for the incremental system, design the state predictor gain matrix. The gain matrix of the restraint controller is obtained based on the linear matrix inequality. , , and ;

[0012] Step Six: Apply the gain matrix obtained in Step Five , , , and Substitute the constraint ratio consistency control protocol from step three to achieve constraint ratio consistency in a discrete-time networked high-order multi-agent system that takes time delay into account.

[0013] Further explanation of the above steps:

[0014] Furthermore, step one specifically includes:

[0015] For a containing A network of intelligent agents ,in, It is a vertex set. It is an edge set. It connects unordered pairs One of the edges, Represents the adjacency matrix; if ,but ,and , ; Let be the Laplace matrix, where .

[0016] Establish a leader intelligent agent and In a discrete-time networked multi-agent system consisting of several follower agents, the dynamic model of the leader agent is as follows:

[0017] (1)

[0018] in, , , These represent the leader agent's state, control inputs, and measurement outputs, respectively. , , The constant matrix is ​​known to the system.

[0019] The dynamics of the follower are described as follows:

[0020] (2)

[0021] in, , , Representing the first The state, control inputs, and measurement outputs of a follower agent; , , Let be a known constant matrix of the system; assume that the states of all agents are not fully measurable, but... It is detectable.

[0022] Furthermore, the specific process of state prediction described in step two includes the following:

[0023] intelligent agent from arrive The state predictor at time step is designed as follows:

[0024] (3)

[0025] in, For constant communication time delay, For intelligent agents use Predicting the next step based on the state at any given moment The state at any given moment, For intelligent agents use Predicting the state at any given moment The state at any given moment, It is an intelligent agent use The output at each moment is used to predict the next step. The output at time, where It is the state observer gain matrix;

[0026] Using formula (3), we can obtain:

[0027] (4)

[0028] definition Time estimation error :

[0029] but (5)

[0030] Through iterative calculations, we can obtain:

[0031] (6)

[0032] To track the leader's desired state, a tracking and control system is introduced:

[0033] (7)

[0034] in, This indicates the known desired state to be tracked. This indicates a known proportionality coefficient.

[0035] Furthermore, the specific process of designing the system to achieve the desired state through a constraint ratio consistency control protocol, as described in step three, includes:

[0036] The control protocol for the design leader is:

[0037] (8)

[0038] The following is a protocol for controlling the proportion of followers' restraint:

[0039] (9)

[0040] (10)

[0041] in, , , , This represents the gain matrix of the controller. This represents the proportional weighted sum of the differences in predicted states between neighboring agents. This indicates the difference in the predicted state ratio between leaders and followers. , This indicates the communication relationship between the leader agent and the follower agents. When the leader agent can receive information from the follower agent, it means that the follower agent can receive information from the leader agent; otherwise... ; Indicates the restraint control gain, when the first When an intelligent agent is restrained ,otherwise ;

[0042] Assuming the topology of the system is disconnected, agents with lower node degrees should be constrained first, and isolated agents should also be constrained, because these agents receive limited information from other agents. After applying the constraining control strategy, all follower agents can receive information from the leader agent directly or indirectly.

[0043] Furthermore, the specific process of step four is as follows:

[0044] The incremental system is expressed as follows:

[0045] (11)

[0046] Among them, the state increment matrix of the multi-agent system Tracking the state increment matrix of the system , This represents the increment of the estimation error in a multi-agent system;

[0047] , ,

[0048] , , ;

[0049] , ,

[0050] , ,

[0051] , ,

[0052] , ,

[0053] for 1D identity matrix for 1D identity matrix for 1D identity matrix for 1D identity matrix Indicates the Kronecker product;

[0054] make If and only if the matrix and When Schur is stable, system (11) is asymptotically stable.

[0055] Furthermore, according to the specific process described in step five:

[0056] Solve the matrix according to the discrete-time Riccati equation (12). The conical complement linearization algorithm is used to solve for the gain matrix based on the linear matrix inequality (13):

[0057] (12)

[0058] in, Since it is a positive definite matrix, it can be solved. ;

[0059] (13)

[0060] in, It is a positive definite matrix.

[0061] Furthermore, according to the specific process described in step six:

[0062] The observer gain matrix obtained in step five Controller gain matrix , , and Substitute the constraint ratio consistency control protocol from step three to achieve constraint ratio consistency in a discrete-time networked high-order multi-agent system that takes time delay into account.

[0063] The most prominent feature and significant beneficial effect of this invention are:

[0064] This invention studies a method for achieving proportional consistency in high-order multi-agent systems that considers time delays. It takes into account the impact of constant communication delays on networked multi-agent systems, introduces a restraint control strategy to apply control to some agents in the network, reducing control costs. It utilizes a networked predictive control method to comprehensively consider the effective information of time delays. Compared with existing methods that directly use outdated agent information to design restraint proportional consistency protocols, this invention's protocol design method can proactively compensate for the impact of communication delays, providing a unified prediction process for all agents and overcoming the influence of constant communication delays on restraint proportional consistency control. Using mathematical tools such as graph theory and matrix theory, a tracking system is established, and the feedback gain matrix is ​​solved based on linear matrix inequalities, enabling the system to proportionally reach the expected state. It also has advantages such as short convergence time and ease of implementation. Attached Figure Description

[0065] Figure 1 This is a flowchart illustrating the steps involved in implementing the present invention.

[0066] Figure 2 This is a communication topology diagram;

[0067] Figure 3 It is an intelligent agent Error trajectory ;

[0068] Figure 4 It is an intelligent agent Error trajectory ;

[0069] Figure 5 It is an intelligent agent state components ;

[0070] Figure 6 It is an intelligent agent state components ; Detailed Implementation

[0071] The significant effects of this invention are verified using the following implementation examples:

[0072] The dynamic model of the multi-agent system is described by (1) and (2);

[0073]

[0074]

[0075] because It is detectable, and the gain matrix can be obtained by solving the Riccati equation (12). :

[0076]

[0077] According to the linear matrix inequality (13), we can obtain:

[0078]

[0079]

[0080]

[0081]

[0082] When the system communication delay The initial state is designed as follows:

[0083]

[0084]

[0085] The expected state of tracking .

[0086] The constraint gain matrix is ​​designed as follows:

[0087]

[0088] Depend on Figure 5 and Figure 6 It can be concluded that leaders and followers can reach the set reference state proportionally and achieve consistency.

[0089] The above description is merely one embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for achieving consistency of restraint ratios in a multi-agent system considering time delay, characterized in that, The specific steps of this method are as follows: Step 1: Establish a dynamic model of a discrete-time networked high-order multi-agent system that considers time delays; Step 2: Construct a state predictor for the dynamic model of a discrete-time networked high-order multi-agent system that considers time delays, obtain the predicted state, and compensate for communication time delays; Step 3: Based on the predicted state of the dynamic model of the discrete-time networked high-order multi-agent system considering time delays in Step 2, design the following constraint proportional consistency control protocol: The control protocol for the design leader is: （8） The following is a protocol for controlling the proportion of followers' restraint: （9） （10） in, , , , This represents the gain matrix of the controller. This represents the proportional weighted sum of the differences in predicted states between neighboring agents. This indicates the difference in the predicted state ratio between leaders and followers. , This indicates the communication relationship between the leader agent and the follower agents. When the follower agent receives information from the leader agent, otherwise... ; Indicates the restraint control gain, when the first When an agent is restrained ,otherwise ; The topology of this system is disconnected. Agents with lower node degree are constrained and isolated agents are constrained because these agents receive limited information from other agents. After applying the constraining control strategy, all follower agents can receive information from the leader agent directly or indirectly. Step 4: Based on the constraint ratio consistency control protocol designed in Step 3, obtain the expression for the incremental system; Step 5: Using the expression for the incremental system, design the state predictor gain matrix. The gain matrix of the restraint controller is obtained based on the linear matrix inequality. , , and ; Step Six: Apply the gain matrix obtained in Step Five , , , and Substitute the constraint ratio consistency control protocol from step three to achieve constraint ratio consistency in a discrete-time networked high-order multi-agent system that takes time delay into account.

2. The method for achieving consistency of restraint ratio in a multi-agent system considering time delay as described in claim 1, wherein step one is: For a containing A network of intelligent agents ,in, It is a vertex set. It is an edge set. It is a connection of unordered pairs One of the edges, Represents the adjacency matrix; like ,but ,and , ; Let be the Laplace matrix, where ; Establish a leader intelligent agent and In a discrete-time networked multi-agent system consisting of several follower agents, the dynamic model of the leader agent is as follows: （1） in, , , These represent the leader agent's state, control input, and measurement output, respectively. , , The constant matrix is ​​known to the system. The dynamics of the follower are described as follows: （2） in, , , Representing the first The states, control inputs, and measurement outputs of each follower agent; where the states of all agents are not fully measurable, but... It is detectable.

3. The method for achieving consistency of restraint ratio in a multi-agent system considering time delay as described in claim 2, wherein step two is as follows: intelligent agent from arrive The predicted state at time t is designed as follows: （3） in, For constant communication time delay, For intelligent agents use Predicting the next step based on the state at any given moment The state at any given moment, For intelligent agents use Predicting the state at any given moment The state at any given moment, in which It is the state observer gain matrix; Using formula (3), we get: （4） definition Time estimation error ; but (5) After iterative calculation, we obtained: （6） To track the desired state of leaders, an external tracking and control system is introduced: （7） in, This indicates that the desired known state should be tracked. This indicates a known proportionality coefficient.

4. In the method for achieving consistency of restraint ratios in a multi-agent system considering time delay as described in claim 3, the incremental system described in step four is expressed as follows: （11） in, State increment matrix of multi-agent system Tracking the state increment matrix of the system , This represents the increment of the estimation error in a multi-agent system; ， ， ， ， ； ， ， ， ， ， ， ， ， for 1D identity matrix for 1D identity matrix for 1D identity matrix for 1D identity matrix Indicates the Kronecker product; make If and only if the matrix and When Schur is stable, system (11) is asymptotically stable.

5. A method for achieving consistency of restraint ratios in a multi-agent system considering time delay, as described in claim 4, is characterized in that... Step five is as follows: Solve the matrix according to the discrete-time Riccati equation (12). The conical complement linearization algorithm is used to solve for the gain matrix based on the linear matrix inequality (10): （12） in, Given a positive definite matrix, solve for... ; （13） in, It is a positive definite matrix.

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