H infinite lag consistency control method of human-in-loop multi-agent system

Abstract

The invention discloses an H infinite lag consistency control method of a human-in-loop multi-agent system. The method belongs to the field of cooperative control, and comprises the following steps: firstly, constructing a mathematical model and a virtual leader model of a multi-agent system with external interference to facilitate the design of a subsequent controller; then, human intervention is added on part of the intelligent agents, and other intelligent agents perform autonomous control; secondly, based on the multi-agent system model and the virtual leader model, obtaining an error system; then, respectively designing appropriate control input for the human and the autonomous agent; and finally, constructing a corresponding Lyapunov functional for analyzing and obtaining sufficient conditions for the multi-agent system of the human-in-the-loop to realize H infinite lag consistency. Compared with the prior art, human intervention is added into the multi-agent system with external interference, the probability that the system makes a wrong decision in an unknown and complex environment is reduced, and the multi-agent system can achieve H infinite lag consistency.

Description

Technical Field

[0001] The present invention belongs to the technical field of collaborative control, and in particular relates to an H infinite lag consistency control method for a multi-agent system with a human in the loop. Background Art

[0002] The consistency problem is an important research direction in the coordinated control of multi-agent systems. The so-called consistency control refers to designing a suitable controller so that the states of the agents eventually tend to be the same over time. So far, many research results on the consistency of multi-agent systems have been reported. In fact, each agent's acquisition of its own state information lags significantly behind the acquisition of the virtual leader's state information. Therefore, some researchers have preliminarily studied the lagging consistency control problem of multi-agent systems, providing a theoretical basis for subsequent research.

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

[0004] In addition, agents are prone to make wrong decisions in unknown and complex environments. In view of this, some researchers have studied the consistency control problem of multi-agent systems with human in the loop. Obviously, it is also necessary to add human intervention when studying the H-infinite lag consistency 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 infinite lag consistency control method for a multi-agent system with a human in the loop, aiming to solve the H infinite lag consistency control problem of a multi-agent system with communication delay and external interference that has not been considered so far.

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

[0007] A method for H infinite lag consistency control of a multi-agent system with a human in the loop, the method comprising:

[0008] Construct mathematical models and virtual leader models of multi-agent systems with external interference;

[0009] Add human intervention to some intelligent agents, and autonomous control to other intelligent agents;

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

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

[0012] Construct Lyapunov functionals and establish criteria for achieving H infinite lag consistency in multi-agent systems.

[0013] The H infinite lag consensus control method for multi-agent systems with human in the loop has the following steps:

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

[0015]

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

[0017]

[0018] For any where κ1 and κ2 are positive constants, represents an o-dimensional real vector.

[0019] Step 2: Considering that intelligent agents are prone to making wrong decisions in unknown and complex environments, adding human intervention to some intelligent agents can obtain the following model:

[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) means the agent is controlled by humans, Represents autonomous control of the agent.

[0026] The virtual leader model is as follows:

[0027]

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

[0029] The dynamic model of a person considered by the present invention is expressed as follows:

[0030]

[0031] In the above formula, i∈M, 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 o×o-dimensional real matrix.

[0032] A multi-agent system can achieve H infinite lag consensus if the following conditions can be met:

[0033]

[0034] 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.

[0035] Step 3: In order to ensure that the multi-agent system can achieve H infinite lag consistency, the present invention designs the following control inputs with communication delay for humans and autonomous agents:

[0036]

[0037] In the above formula, 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 an N×N dimensional real matrix.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] The present invention proposes an H infinite lag consistency control method for a multi-agent system with a human in the loop; considering that a multi-agent system is prone to make wrong decisions in an unknown and complex environment, the present invention adds human intervention to the H infinite lag consistency control of a multi-agent system with external interference for the first time, designs control inputs with communication time lags 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 of instability of the entire system due to the mistakes of the autonomous agents; from an implementation perspective, the present invention requires fewer computing resources and the required control quantities are easier to obtain; the H infinite lag consistency control method for a multi-agent system with a human in the loop is applicable to any actual system modeled by the mathematical model of a single agent considered by the present invention, and has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Flow chart of H infinite lag consensus control for multi-agent systems with human in the loop;

[0041] Figure 2 It is the communication topology diagram of the multi-agent system;

[0042] Figure 3 This is a graph showing the position of the multi-agent system changing over time at different times under the control protocols (6) and (7) of the present invention.

[0043] Figure 4 This is a graph showing the speed of the multi-agent system changing with time at different times under the control protocols (6) and (7) of the present invention. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0045] like Figure 1 As shown, step 1: Construct the mathematical model of the multi-agent system with external interference as follows:

[0046]

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

[0048]

[0049] For any where κ1 and κ2 are positive constants, represents an o-dimensional real vector.

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

[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) means the agent is controlled by humans, Represents autonomous control of the agent.

[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 dynamic model of a person considered by the present invention is expressed as follows:

[0061]

[0062] In the above formula, i∈M, 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 o×o-dimensional real matrix.

[0063] A multi-agent system can achieve H infinite lag consensus if the following conditions can be met:

[0064]

[0065] 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.

[0066] Step 3: In order to ensure that the multi-agent system can achieve H infinite lag consistency, the present invention designs the following control inputs with communication delay for humans and autonomous agents:

[0067]

[0068]

[0069] In the above formula, represents the communication delay between agent i and agent j, 0 <c i ∈ Represents controller parameters, The coupling weight matrix between agents. If there is communication between agent i and agent j, then otherwise also, Represents an N×N dimensional real matrix.

[0070] Step 4: Definition 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 control protocols (6) and (7), the multi-agent system (1) can achieve H infinite lag consensus if there exists and The following conditions are established:

[0075]

[0076] In the above formula, [G] ε =G+G T , z2=Y+A+I No , ε2=(3κ2+κ1+2)I No ,ε1=(3κ1+κ2)I No .

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

[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 infinite lag consistency under the action of controllers (6) and (7).

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

[0090] The following nonlinear multi-agent system with external disturbances is considered:

[0091]

[0092] In the above formula, Respectively represent the position, speed, external disturbance and control input of the intelligent agent; select Obviously, it is easy to verify The following inequality is satisfied:

[0093]

[0094] For any Represents a real number.

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

[0096]

[0097] In the above formula, i∈M, They represent the state, input and output of a person respectively. The communication topology diagram is as follows Figure 2 As 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, we can find the following parameters to make conditions (9) and (10) true:

[0100] K=0.0939,ρ=7.5926,

[0101]

[0102] Therefore, the multi-agent system (14) can achieve H infinite lag consistency under the control protocols (6) and (7). Figure 3 and Figure 4 The curves of the position and velocity of the multi-agent system at different times changing with time under the control protocols (6) and (7) are shown respectively.

[0103] It should be understood that, although each step in the flow chart of each embodiment of the present invention is shown in sequence according to the indication of the arrow, these steps are not necessarily performed in sequence according to the order indicated by the arrow. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, and these steps can be performed in other orders. Moreover, at least a portion of the steps in each embodiment may include a plurality of sub-steps or a plurality of stages, and these sub-steps or stages are not necessarily performed at the same time, but can be performed at different times, and the execution order of these sub-steps or stages is not necessarily performed in sequence, but can be performed in turn or alternately with at least a portion of other steps or sub-steps or stages of other steps.

[0104] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and 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-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (SyncHlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0105] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0106] The above-mentioned embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

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

Claims

1. 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; Add human intervention to some intelligent agents, and autonomous control to other intelligent agents; 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 criteria for achieving H infinite lag consistency in multi-agent systems.

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: The mathematical model of the i-th multi-agent system is In the above formula, Represent the position vector, velocity vector, external disturbance and control input of the agent respectively, represents the internal dynamics of the agent, represents an o-dimensional real vector.

3. 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: 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, Represents autonomous control of the agent.

4. 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: The virtual leader model is as follows: In the above formula, and represent the position vector and velocity vector of the virtual leader respectively.

5. 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: The dynamic model of the person is expressed as follows: In the above formula, i∈M, 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 o×o-dimensional real matrix.

6. 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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