H∞ Lag Consensus Control Method for Human-in-the-Loop Multi-Agent Systems

Abstract

The present invention discloses an H-infinity lag consensus control method for a human-in-the-loop multi-agent system. Belonging to the field of cooperative control, it includes the following steps: First, construct a mathematical model of the multi-agent system with external disturbances and a virtual leader model to facilitate the subsequent design of the controller; Next, add human intervention to some agents, and other agents are autonomously controlled; Secondly, based on the multi-agent system model and the virtual leader model, obtain the error system; Then, design appropriate control inputs for humans and autonomous agents respectively; Finally, construct a corresponding Lyapunov functional to analyze and obtain the sufficient conditions for the human-in-the-loop multi-agent system to achieve H-infinity lag consensus. Compared with the prior art, the present invention adds human intervention to the multi-agent system with external disturbances, reduces the probability of the system making wrong decisions in unknown and complex environments, and enables the multi-agent system to achieve H-infinity lag consensus.

Description

Technical Field

[0001] The present invention belongs to the technical field of cooperative control, and particularly relates to an H-infinity lag consensus control method for a human-in-the-loop multi-agent system. Background Art

[0002] The consensus problem is an important research direction in the cooperative control of multi-agent systems. The so-called consensus control means that by designing a suitable controller, the states of agents will eventually tend to be the same as time goes by. So far, many research results on the consensus of multi-agent systems have been reported. In fact, each agent obtains its own state information significantly later than the acquisition of the state information of the virtual leader. Therefore, some researchers have preliminarily studied the lag consensus control problem of multi-agent systems, providing a theoretical basis for subsequent research.

[0003] In the process of achieving consensus, communication between agents is an indispensable link. However, the communication between agents is restricted by many factors (such as limited transmission speed, information congestion, etc.), and these factors will all lead to the generation of communication delays. So far, the consensus problem of multi-agent systems with communication delays has been studied. In addition, considering that multi-agent systems are often affected by external disturbances (such as wind force, temperature, etc.) in practical applications, some researchers have further studied the H-infinity consensus of multi-agent systems with communication delays and external disturbances. Obviously, it is also very meaningful to study the H-infinity lag consensus problem of multi-agent systems with communication delays and external disturbances, but so far the research in this area is still blank.

[0004] In addition, agents are prone to make wrong decisions in unknown and complex environments. In view of this, some researchers have studied the consensus control problem of human-in-the-loop multi-agent systems. Obviously, it is also very necessary to add human intervention when studying the H-infinity lag consensus of multi-agent systems with communication delays and external disturbances. Summary of the Invention

[0005] The purpose of the embodiments of the present invention is to provide an H-infinity lag consensus control method for a human-in-the-loop multi-agent system, aiming to solve the H-infinity lag consensus control problem of multi-agent systems with communication delays and external disturbances that has not been considered so far.

[0006] To achieve the above purpose, the present invention provides the following technical solutions:

[0007] An H-infinity lag consensus control method for a human-in-the-loop multi-agent system, the method comprising:

[0008] Construct a mathematical model of a multi-agent system with external disturbances and a virtual leader model;

[0009] Add human intervention to some agents, and other agents are autonomously controlled;

[0010] Based on the multi-agent system model and the virtual leader model, an error system is obtained;

[0011] Design appropriate control inputs for humans and autonomous agents respectively;

[0012] Construct a Lyapunov functional and establish a criterion for the multi-agent system to achieve H-infinity lag consensus.

[0013] The H-infinity lag consensus control method for a multi-agent system with humans in the loop is as follows:

[0014] Step 1: Construct a mathematical model of a multi-agent system with external disturbances. The model of the i-th multi-agent system is:

[0015]

[0016] In the above formula, respectively represent the position vector, velocity vector, external disturbance and control input of the agent, represents the internal dynamics of the agent and satisfies the following inequality:

[0017]

[0018] For any where κ 1 and κ 2 are positive constants, represents an o-dimensional real vector.

[0019] Step 2: Considering that agents are prone to make wrong decisions in unknown and complex environments, add human intervention to some agents, and the following model can be obtained:

[0020]

[0021] In the above formula, M represents the set of human-controlled agents,

[0022]

[0023] Next, rewrite the multi-agent system model as follows:

[0024]

[0025] In the above formula, p i represents the human control coefficient, p i = 1 (i ∈ M) indicates that the agent is controlled by humans, Indicates the autonomous control of the agent.

[0026] The virtual leader model is as follows:

[0027]

[0028] In the above formula, and respectively represent the position vector and velocity vector of the virtual leader.

[0029] The human dynamic model considered in the present invention is represented as follows:

[0030]

[0031] In the above formula, i ∈ M, respectively represent the state, input, and output of the human; is a constant matrix, represents ο 1 dimensional real vector, represents o 1 × o 1 dimensional real matrix, represents o 1 × o dimensional real matrix, represents o × o 1 dimensional real matrix, represents o × o dimensional real matrix.

[0032] The multi-agent system can achieve H-infinity lag consensus if the following conditions can be satisfied:

[0033]

[0034] In the above formula, represents the time delay between each agent and the virtual leader, V(·) is a non-negative function, represents a real number.

[0035] Step 3: To ensure that the multi-agent system can achieve H-infinity lag consensus, the present invention designs the following control input with communication time delay for humans and autonomous agents:

[0036]

[0037] In the above formula, represents the communication time delay between agent i and agent j, represents the controller parameter, is the coupling weight matrix between agents. If there is communication between agent i and agent j, then otherwise In addition, Represents an N×N dimensional real matrix.

[0038] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0039] The present invention proposes an H-infinity lag consensus control method for a human-in-the-loop multi-agent system; considering that the multi-agent system is prone to making wrong decisions in an unknown and complex environment, the present invention first adds human intervention to the H-infinity lag consensus control of the multi-agent system with external disturbances, designs control inputs with communication delays for humans and autonomous agents, reduces the error rate of the multi-agent system and improves the stability of the system, and effectively solves the problem that the entire system becomes unstable due to the mistakes of autonomous agents; from the perspective of implementation, the present invention requires less computing resources and the required control quantities are easier to obtain; the H-infinity lag consensus control method for the human-in-the-loop multi-agent system is applicable to any actual system modeled by the mathematical model of a single agent considered in the present invention, and has a wide range of applications. Description of the Drawings

[0040] Figure 1 Is a flowchart of the H-infinity lag consensus control for the human-in-the-loop multi-agent system;

[0041] Figure 2 Is a communication topology diagram of the multi-agent system;

[0042] Figure 3 Is a curve graph showing the change of the position of the multi-agent system with time at different times under the action of the control protocols (6) and (7) of the present invention.

[0043] Figure 4 Is a curve graph showing the change of the speed of the multi-agent system with time at different times under the action of the control protocols (6) and (7) of the present invention. Detailed Embodiment

[0044] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to 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 used to limit the present invention.

[0045] As Figure 1 shown, Step 1: Construct a mathematical model of the multi-agent system with external disturbances as follows:

[0046]

[0047] In the above formula, respectively represent the position vector, velocity vector, external disturbance and control input of the agent, represents the internal dynamics of the agent and satisfies the following inequality:

[0048]

[0049] For any where κ 1 and κ 2 are positive constants, represents an o-dimensional real vector.

[0050] Step 2: Considering that agents are prone to making wrong decisions in unknown and complex environments, adding human intervention to some agents, the following model can be obtained:

[0051]

[0052] In the above formula, M represents the set of human-controlled agents,

[0053]

[0054] Next, rewrite the multi-agent system model as follows:

[0055]

[0056] In the above formula, p i represents the human control coefficient, p i = 1 (i ∈ M) indicates that the agent is controlled by humans, represents the agent's autonomous control.

[0057] The virtual leader model is as follows:

[0058]

[0059] In the above formula, and represent the position vector and velocity vector of the virtual leader, respectively.

[0060] The human dynamic model considered in the present invention is represented as follows:

[0061]

[0062] In the above formula, i ∈ M, represent the state, input, and output of the human, respectively; is a constant matrix, represents ο 1 dimensional real vector, represents o 1 × o 1 dimensional real matrix, represents o 1 × o dimensional real matrix, Denote \(o\times o\) 1 a real matrix of dimension \(o\times o\), denote a real matrix of dimension \(o\times o\).

[0063] The multi - agent system can achieve \(H_{\infty}\) lag consensus if the following conditions can be satisfied:

[0064]

[0065] In the above formula, denotes the time - delay between each agent and the virtual leader, \(V(\cdot)\) is a non - negative function, denotes a real number.

[0066] Step 3: To ensure that the multi - agent system can achieve \(H_{\infty}\) lag consensus, the present invention designs the following control input with communication time - delay for humans and autonomous agents:

[0067]

[0068]

[0069] In the above formula, denotes the communication time - delay between agent \(i\) and agent \(j\), \(0\lt c\) i \(\in\) denotes the controller parameter, the coupling weight matrix between agents. If there is communication between agent \(i\) and agent \(j\), then otherwise In addition, denotes a real matrix of dimension \(N\times N\).

[0070] Step 4: Define and According to (2), (3), (6) and (7), the following error model can be obtained:

[0071]

[0072] In the above formula,

[0073]

[0074] Step 5: Under the action of the control protocols (6) and (7), the multi - agent system (1) can achieve \(H_{\infty}\) lag consensus if there exist and such that the following conditions hold:

[0075]

[0076] In the above formula, \([G]\)ε = G + G T , z 2 = Y + A + I No , ε 2 = (3κ 2 + κ 1 + 2)I No , ε 1 = (3κ 1 + κ 2 )I No 。

[0077] For the error system (8), construct the following Lyapunov functional:

[0078]

[0079] In the above formula,

[0080] Taking the derivative of the above formula, we can get

[0081]

[0082] In the above formula,

[0083] From (12), we can get

[0084]

[0085] In the above formula, and

[0086] According to (13), we can get

[0087]

[0088] Therefore, the multi-agent system (1) can achieve H-infinity lag consensus under the action of the controllers (6) and (7).

[0089] Step 6: Select an example for simulation verification;

[0090] Consider the following nonlinear multi-agent system with external disturbances:

[0091]

[0092] In the above formula, respectively represent the position, velocity, external disturbance and control input of the agent; select Obviously, it is easy to verify Satisfy the following inequalities:

[0093]

[0094] For any represent real numbers.

[0095] Let agents 1, 2, and 3 be human - controlled agents, then M = {1, 2, 3}. The dynamics of humans are as follows:

[0096]

[0097] In the above formula, i ∈ M, respectively represent the state, input, and output of humans. Among them, the communication topology diagram is as Figure 2 shown. Let D = diag(4.2, 5.5, 5.8, 6.2, 7.9), σ = 0.6, and

[0098]

[0099] Using the YALMIP toolbox in MATLAB, the following parameters can be obtained to make conditions (9) and (10) hold:

[0100] K = 0.0939, ρ = 7.5926,

[0101]

[0102] Therefore, the multi - agent system (14) can achieve H - infinity lag consensus under the action of control protocols (6) and (7). Figure 3 and Figure 4 respectively show the curves of the positions and velocities of the multi - agent system changing with time at different times under the action of control protocols (6) and (7).

[0103] It should be understood that although the steps in the flowcharts of the embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless there is a clear description in this article, the execution of these steps has no strict order limit, and these steps can be executed in other orders. Moreover, at least a part of the steps in each embodiment may include multiple sub - steps or multiple stages. These sub - steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub - steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a part of other steps or sub - steps or stages of other steps.

[0104] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the various embodiments provided in the present application can include non-volatile and / or volatile memories. Non-volatile memories can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memories can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link (SyncHlink) DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0105] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the various technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0106] The above-described embodiments merely represent several implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent for the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent for the present invention should be subject to the appended claims.

[0107] The above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. H infinite lag consistency control method for multi-agent systems with human in the loop, characterized in that: The method comprises: Construct mathematical models and virtual leader models of multi-agent systems with external interference; The mathematical model of the i-th multi-agent system is In the above formula, They represent the position vector, velocity vector, external disturbance and control input of the agent respectively, t is the time variable, represents the internal dynamics of the agent, represents an o-dimensional real vector; The virtual leader model is as follows: In the above formula, and represent the position vector and velocity vector of the virtual leader respectively; Add human intervention to some intelligent agents, and autonomous control to other intelligent agents; Intelligent agents are prone to making wrong decisions in unknown and complex environments, so human intervention is added to some intelligent agents to obtain the following model: In the above formula, M represents the set of human-controlled agents, Next, rewrite the multi-agent system model as follows: In the above formula, p i represents the human control coefficient, p i =1(i∈M) means the agent is controlled by humans, Indicates autonomous control of the agent; The dynamic model of the person is expressed as follows: In the above formula, They represent the state, input and output of a person respectively; is a constant matrix, represents a 1-dimensional real vector, represents an o1×o1 dimensional real matrix, represents an o1×o dimensional real matrix, represents an o×o1-dimensional real matrix, represents an o1×o-dimensional real matrix; Based on the multi-agent system model and the virtual leader model, the error system is obtained; Design appropriate control inputs for humans and autonomous agents respectively; Construct Lyapunov functionals and establish the criterion for achieving H infinite lag consistency in multi-agent systems; Can get In the above formula, and According to (13), we can obtain H infinite lag consistency; A multi-agent system can achieve H infinite lag consensus if the following conditions can be met: In the above formula, represents the time lag between each agent and the virtual leader, V(·) is a non-negative function, represents a real number, β i (t) represents external disturbance.

2. The H infinite lag consistency control method for a multi-agent system with a human in the loop according to claim 1, characterized in that: Design the following control inputs with communication delay for humans and autonomous agents: In the above formula, represents the time lag between each agent and the virtual leader, represents the communication delay between agent i and agent j, Represents controller parameters, is the coupling weight matrix between agents. If there is communication between agent i and agent j, then otherwise also, represents a real number, Represents an N×N dimensional real matrix.

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