A leader-following quasi-bipartite consensus control method for time-varying multi-agent systems

Abstract

The application provides a networked discrete time-varying multi-agent system considering hybrid attacks and random nonlinear disturbances, and a method for realizing leader-following quasi-bipartite consensus under an event-triggering mechanism, and belongs to the field of networked multi-agent cooperative control. Technical points of the application include: establishing mathematical models of leaders and followers; designing a leader-following quasi-bipartite consensus control protocol based on clouds; in order to reduce unnecessary transmission, an event-triggering mechanism model is established; in view of network security problems, a hybrid attack model is established; by using a direction-dependent tracking error of the follower relative to the leader, linear matrix inequality conditions that gains and ellipsoid parameters of the control protocol satisfy are obtained, so that the system realizes leader-following quasi-bipartite consensus. The application overcomes the influence of hybrid attacks and random nonlinear disturbances, introduces an event-triggering mechanism and cloud control, reduces control cost, saves network resources, and has the characteristics of easy implementation and easy solution.

Description

Technical Field

[0001] This invention relates to a leader-follower pseudo-binary consensus control method for time-varying multi-agent systems. Background Technology

[0002] Networked multi-agent systems are systems in which multiple agents are interconnected and work collaboratively through a network. Consistency is an important research direction in networked multi-agent systems, which mainly refers to designing control protocols for multi-agent systems to achieve consistency in certain key quantities.

[0003] In networked multi-agent systems, information transmitted over a network may be susceptible to random, mixed attacks, leading to data leaks and even irreparable economic losses. Furthermore, the presence of random, nonlinear perturbations may degrade system performance.

[0004] Given the ever-increasing scale of multi-agent systems, cloud-based control protocols can handle the difficulties and challenges brought about by big data. At the same time, network resources are always limited, and adopting event-triggered mechanisms can effectively reduce unnecessary transmissions and save network resources. Summary of the Invention

[0005] This invention will study a leader-follower quasi-binary consensus control method for time-varying multi-agent systems, and adopt a cloud-based output feedback control protocol to solve the problem.

[0006] This invention provides a leader-follower quasi-binary consensus control method for time-varying multi-agent systems, which is implemented through the following scheme:

[0007] Step 1: Establish discrete time-varying dynamic models of leaders and followers, and consider stochastic nonlinear perturbations in the system model of followers;

[0008] Step 2: Based on the dynamic model of leaders and followers established in Step 1, design a cloud-based leader-follower pseudo-binary consensus control protocol;

[0009] Step 3: Based on the control signals generated in Step 2, establish an event triggering mechanism model to obtain the triggered control signals;

[0010] Step 4: Based on the triggered control signal obtained in Step 3, establish a hybrid attack model to obtain the control signal received by the executor;

[0011] Step 5: Substitute the control signals received by the actuator in Step 4 into the follower system model and augment it to obtain the augmented closed-loop expressions for all followers;

[0012] Step Six: Utilize the follower's direction-dependent tracking error relative to the leader to obtain the follower and leader tracking error system. Based on the definition of leader-follower quasi-binary consensus, derive the gain of the cloud-based leader-follower quasi-binary consensus control protocol. and ellipsoid parameters The linear matrix inequality conditions that should be satisfied;

[0013] Step 7: Using the Linear Matrix Inequality Toolbox in MATLAB, solve for the gain of the cloud-based leader-follower quasi-binary consensus control protocol. and ellipsoid parameters and will Substituting this into the cloud-based leader-follower quasi-binary consensus control protocol in step two, the networked discrete-time-varying multi-agent system, which considers hybrid attacks and random nonlinear disturbances, can achieve the desired leader-follower quasi-binary consensus under an event-triggered mechanism.

[0014] Further explanation of the above steps:

[0015] Furthermore, step one specifically includes:

[0016] Using symbolic directed graphs to indicate The communication relationships between the agents. The set of leaders represents the entire set of leaders; clearly, this patent only considers the case of a single leader. Symbolic directed subgraph. Used to represent The communication relationships between followers. yes A set of indexes for followers; It is an edge set; It is a weighted adjacency matrix. If and only if At that time, on the side It indicates that an intelligent agent is needed. To calculate the relevant signals of the intelligent agent The control signal. If , representing intelligent agents and intelligent agents There is a cooperative relationship between them; if This indicates the existence of an adversarial relationship. Furthermore, an agent cannot interact with itself, meaning... . Represents intelligent agents The set of neighboring nodes. express An adjacency matrix between followers and leaders. If the leader directs to the agent... Sending a message, ,otherwise . The Laplace matrix is ​​defined as ,in, , .

[0017] for A follower subjected to random nonlinear perturbations has the following discrete time-varying state-space description:

[0018] (1)

[0019] in, For the first in the follower system One follower The state at any given moment, For the first An intelligent agent in The measurement output at time, Indicates the first Control input for an intelligent agent , , All are time-related with appropriate dimensions Given matrix functions, positive numbers It is a pre-defined time constant. (Stochastic nonlinear function) The expectation is Furthermore, the covariance of random nonlinear perturbations of different agents at the same time is... The variance of random nonlinear perturbations of the same agent at the same time satisfies the following inequality:

[0020] (2)

[0021] here, , It is a known matrix.

[0022] for There are several followers, assuming the leader can generate an external reference signal for them to follow. The leader has the following dynamic model:

[0023] (3)

[0024] here, , These represent the leader's status information and output information, respectively.

[0025] Step two is:

[0026] Based on the previously given symbolic directed graph The cloud-based leader-follower quasi-binary consensus control protocol of the dynamic model (1)-(3) is designed as follows:

[0027] (4)

[0028] in, It is the time-varying gain to be designed; function Represents a symbolic function. Variable. Specifically, if This indicates that the intelligent agent A cooperative relationship with the leader; conversely, if This indicates that the intelligent agent The relationship with the leader is adversarial.

[0029] Step three is:

[0030] To reduce unnecessary transmissions and conserve network resources, the following event triggering mechanism is established:

[0031] Triggering time The selection criteria are ,in, Represents intelligent agents The At the next trigger time, satisfying ; It is a pre-defined trigger threshold matrix; update error Defined as:

[0032] (5)

[0033] in, This indicates that the cloud-based leader-follower quasi-binary consistency control protocol was triggered at the most recent time. To intelligent agents The actuator sends updated control signals.

[0034] Step four is:

[0035] Using the triggered control signal obtained in step three The hybrid attack model is established as follows:

[0036] (6)

[0037] in, This indicates the input signal that has been affected by the attack. This indicates that the attacker sent a deceptive signal, and the conditions that are met are: , And assume It is a known positive definite matrix. and These are independent random variables that follow a Bernoulli distribution and are used to describe the switching behavior of different attacks. Expectations Variance is expressed as... express; Expectations Variance is expressed as... It is indicated that all are known. And for ease of representation, it is defined as follows: , Expectations This indicates that, combined with equation (6), we can derive:

[0038] (7)

[0039] in, .

[0040] Furthermore, combining with (4), we can deduce the intelligent agent. The actuator in Control signals received at all times It can be represented as:

[0041] (8)

[0042] Step five is:

[0043] Substituting the control signal (8) received by the actuator in step four into the system model (1) and augmenting it, the augmented closed-loop expression for all followers is obtained as follows:

[0044] (9)

[0045] as well as .

[0046] in,

[0047]

[0048] Step six is:

[0049] The tracking error of the follower relative to the leader's direction of dependence is defined as... and order Then there is Therefore, the expression for the direction-dependent tracking error system of the follower relative to the leader can be obtained as follows:

[0050] (10)

[0051] To achieve leader-following quasi-binary consistency, i.e.: given a directed graph with symbols... and a series of positive definite ellipsoid parameters In the case of, if For any , satisfy If the system achieves leader-follower quasi-binary consistency, then the follower's tracking error relative to the leader depends on the direction of the leader. Should meet: If we take Decomposed into Then it exists satisfy , making .make ,but This can be further expressed as:

[0052] (11)

[0053] definition Substituting (11) into (10) yields:

[0054] (12)

[0055] in,

[0056]

[0057]

[0058] Therefore, if a series of matrices exist and a series of positive scalars , , , ( Makes the following linear matrix inequalities hold:

[0059] (13)

[0060] Therefore, systems (1)-(3) can achieve leader-following quasi-binary consistency. Among them,

[0061]

[0062]

[0063]

[0064] Step seven is:

[0065] Using the Linear Matrix Inequality Toolbox in MATLAB, solve the following optimization problem:

[0066] (14)

[0067] Gains can be obtained from cloud-based leader-follower quasi-dichotomous control protocols. and ellipsoid parameters ,in, Represents a matrix Tracing the trail. Substituting this into the cloud-based leader-follower quasi-binary consensus control protocol in step two, it enables networked discrete-time-varying multi-agent systems that consider hybrid attacks and random nonlinear perturbations to achieve the desired leader-follower quasi-binary consensus under an event-triggered mechanism.

[0068] The most prominent feature and significant beneficial effect of this invention are:

[0069] This invention studies a method for achieving leader-following quasi-binary consensus in networked discrete-time-varying multi-agent systems. It considers the impact of randomly occurring mixed attacks and nonlinear perturbations on the system, and introduces a cloud-based output feedback control protocol to control the agents in the network, while also considering event-triggered mechanisms. Compared with existing consensus control protocols where the controller is designed locally by the agent, this invention's control protocol design method can overcome the effects of randomly occurring mixed attacks and random nonlinear perturbations, and also reduces unnecessary data transmission, saves network resources, and alleviates network burden. Using mathematical tools such as graph theory and stochastic analysis, the feedback gain matrix is ​​solved based on recursive linear matrix inequalities, enabling the system to achieve the desired leader-following quasi-binary consensus. Attached Figure Description

[0070] Figure 1 This is a flowchart illustrating the steps involved in implementing the present invention.

[0071] Figure 2 This is a topology diagram of the multi-agent system involved in the present invention;

[0072] Figure 3 The trajectory of the first state component of the open-loop system;

[0073] Figure 4 The trajectory of the second state component of the open-loop system;

[0074] Figure 5 The trajectory of the first state component of the closed-loop system;

[0075] Figure 6 The trajectory of the second state component of the closed-loop system; Detailed Implementation

[0076] The significant effects of this invention are verified using the following implementation examples:

[0077] This case considers a networked discrete-time-varying multi-agent system consisting of one leader and four followers (1)-(3), where,

[0078]

[0079] A stochastic nonlinear function is described as: , .in, and It is zero-mean Gaussian white noise with unit variance. , They are states The two components.

[0080] , ,

[0081] The communication relationships between the five agents are represented by a symbolic directed graph. Description, in which, and As shown below:

[0082]

[0083] And assume That is, agents 1 and 2 have a cooperative relationship with the leader; That is, agents 3 and 4 are in an adversarial relationship with the leader. In this simulation, it is assumed that the desired outcome is... and They are respectively , , , , , , , For randomly occurring mixed attacks, bounded signals They are respectively , , , The thresholds for the event triggering functions are respectively... , , , . The initial states of the agents are set as follows:

[0084]

[0085] Figure 3 and Figure 5 For comparison, Figure 4 and Figure 6 In comparison, it is clear that, under the control protocol based on the cloud, the networked discrete time-varying multi-agent system considering hybrid attacks and random nonlinear disturbances achieves leader-follower quasi-binary consensus under the event-triggered mechanism.

[0086] 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 leader-follower quasi-binary consensus control method for time-varying multi-agent systems, characterized in that, The specific steps of this method are as follows: Step 1: Establish discrete time-varying dynamic models of leaders and followers, and consider stochastic nonlinear perturbations in the system model of followers; Step Two: Based on the dynamic model of leaders and followers established in Step One, design a cloud-based leader-follower pseudo-binary consensus control protocol as follows: （4） in, It is the time-varying gain to be designed; function Represents a symbolic function; a variable Specifically, if This indicates that the intelligent agent A cooperative relationship with the leader; conversely, if This indicates that the intelligent agent The relationship with the leader is adversarial; symbolic directed graphs are used. to indicate The communication relationships between individual agents; among which... The set of leaders, considering only the case of a single leader; symbolic directed subgraph. Used to represent The communication relationships between followers; among which... yes A set of indexes for followers; It is an edge set; It is a weighted adjacency matrix; if and only if At that time, on the side It indicates that an intelligent agent is needed. Use relevant signals to calculate the intelligent agent The control signal; if , representing intelligent agents and intelligent agents There is a cooperative relationship between them; if This indicates the existence of an adversarial relationship; furthermore, an agent cannot interact with itself, that is... ; Represents intelligent agents The set of neighboring nodes; express An adjacency matrix between followers and leaders; if the leader directs to an agent... Sending a message, ,otherwise ; For the first An intelligent agent in The measurement output at time, This represents the leader's output information; Step 3: Based on the control signals generated in Step 2, establish an event triggering mechanism model to obtain the triggered control signals; Step 4: Based on the triggered control signal obtained in Step 3, establish a hybrid attack model to obtain the control signal received by the executor; Step 5: Substitute the control signals received by the actuator in Step 4 into the follower system model and augment it to obtain the augmented closed-loop expressions for all followers; Step Six: Utilize the follower's direction-dependent tracking error relative to the leader to obtain the follower-leader tracking error system, and apply the definition of leader-follower quasi-binary consistency (i.e., in a given symbolic directed graph) to... and a series of positive definite ellipsoid parameters In the case of, if For any , satisfy If so, the system is said to have achieved leader-follower quasi-binary consistency, where Represents the direction-dependent tracking error of the follower relative to the leader, a positive integer. (The time constant is given in advance), to obtain the gain of the cloud-based leader-follower quasi-binary consensus control protocol. and ellipsoid parameters The linear matrix inequality conditions that should be satisfied; Step 7: Using the Linear Matrix Inequality Toolbox in MATLAB, solve for the gain of the cloud-based leader-follower quasi-binary consensus control protocol. and ellipsoid parameters and will Substituting this into the cloud-based leader-follower quasi-binary consensus control protocol in step two, this enables the networked discrete-time-varying multi-agent system, considering hybrid attacks and random nonlinear perturbations, to achieve the desired leader-follower quasi-binary consensus (i.e., the follower's direction-dependent tracking error relative to the leader) under an event-triggered mechanism. satisfy ).

2. The leader-follower quasi-binary consensus control method for a time-varying multi-agent system according to claim 1, wherein step one is: for A follower subjected to random nonlinear perturbations has the following discrete time-varying state-space description: （1） in, For the first in the follower system One follower The state at any given moment, For the first An intelligent agent in The measurement output at time, Indicates the first Input of an agent, , , All are time-related with appropriate dimensions Given matrix functions, positive integers It is a pre-given time constant; a random nonlinear function The expectation is Furthermore, the covariance of random nonlinear perturbations of different agents at the same time is... The variance of random nonlinear perturbations of the same agent at the same time satisfies the following inequality: （2） here, , It is a known matrix; for For each follower, the leader can generate an external reference signal for tracking; the leader has the following dynamic model: （3） here, , These represent the leader's status information and output information, respectively.

3. The leader-follower quasi-binary consensus control method for a time-varying multi-agent system according to claim 2, wherein step three is: To reduce unnecessary transmissions and conserve network resources, the following event triggering mechanism is established: Triggering time The selection criteria are ,in, Represents intelligent agents The At the next trigger time, the following conditions are met. ; It is a pre-defined trigger threshold matrix; update error Defined as: （5） in, This indicates that the cloud-based leader-follower quasi-binary consistency control protocol was triggered at the most recent time. To intelligent agents The executor sends an updated signal.

4. The leader-follower quasi-binary consensus control method for a time-varying multi-agent system according to claim 3, wherein step four is: Using the triggered control signal obtained in step three The hybrid attack model is established as follows: （6） in, Indicates the input signal affected by the attack; This indicates that the attacker sent a deceptive signal, and the conditions that are met are: , ,and It is a known positive definite matrix; and They are independent random variables that follow a Bernoulli distribution and are used to describe the switching behavior of different attacks; Expectations Variance is expressed as... express; Expectations Variance is expressed as... It is indicated that all are known; and for convenience, it is defined as follows: , Expectations express; Combining equation (6), we get: （7） in, ; Furthermore, in conjunction with (4), we introduce intelligent agents. The actuator in Control signals received at all times Represented as: （8）。 5. The leader-follower quasi-binary consensus control method for a time-varying multi-agent system according to claim 4, step five is as follows: Substituting the control signal (8) received by the actuator in step four into the original system model (1) and augmenting it, the augmented closed-loop expression for all followers is obtained as follows: （9） as well as ; in, 。 6. The leader-follower quasi-binary consensus control method for a time-varying multi-agent system according to claim 5, wherein step six is: The tracking error of the follower relative to the leader's direction of dependence is defined as... and order Then there is Therefore, the expression for the direction-dependent tracking error system of the follower relative to the leader is obtained as follows: （10） To achieve leader-following quasi-binary consistency, i.e.: given a directed graph with symbols... and a series of positive definite ellipsoid parameters In the case of, if For any , satisfy If the system achieves leader-follower quasi-binary consistency, then the follower's tracking error relative to the leader depends on the direction of the leader. Should meet If Decomposed into Then it exists satisfy , making ;make ,but Further expressed as: （11） definition Substituting (11) into (10) yields: （12） in, Therefore, if a series of matrices exist and a series of positive scalars , , , ( Make the following linear matrix inequalities hold: （13） Therefore, systems (1)-(3) achieve leader-following quasi-binary consistency; among which, 。 7. The leader-follower quasi-binary consensus control method for a time-varying multi-agent system according to claim 6, step seven is as follows: Using the Linear Matrix Inequality Toolbox in MATLAB, solve the following optimization problem: （14） Gains from cloud-based leader-follower quasi-binary consensus control protocols and ellipsoid parameters ,in, Represents a matrix Seeking traces; to trace Substituting this into the cloud-based leader-follower quasi-binary consensus control protocol in step two, the networked discrete-time-varying multi-agent system considering hybrid attacks and random nonlinear disturbances can achieve the desired leader-follower quasi-binary consensus under the event-triggered mechanism.

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