Fixed time inclusion control method and system of second-order nonlinear multi-agent system

Abstract

The invention discloses a fixed time inclusion control method and system for a second-order nonlinear multi-agent system, and the method comprises the steps: defining a state tracking error according to a control target, augmenting the state tracking error into a matrix form, and designing an integral sliding mode surface for suppressing disturbance; designing a distributed fixed time inclusion consistency protocol and a dynamic event triggering mechanism based on position information and speed information according to the integral sliding mode surface; and controlling the multi-agent system model to reach an integral sliding mode surface according to a distributed fixed time inclusion consistency protocol and a dynamic event triggering mechanism, then sliding on the integral sliding mode surface, and controlling the state of the multi-agent system model to realize inclusion consistency within fixed time. According to the invention, the energy consumption of the system and the updating frequency of the controller can be reduced, the service life of the system is prolonged, and under a new distributed fixed time inclusion consistency protocol, the system firstly reaches the sliding mode surface and then slides on the sliding mode surface, so that the inclusion consistency of the system state is finally realized within fixed time.

Description

Technical Field

[0001] The present invention belongs to the field of multi-agent technology, and in particular to a fixed-time inclusion control method and system for a second-order nonlinear multi-agent system. Background Art

[0002] At present, most of the work on the consistency of multi-agent systems is mainly the study of general consistency, that is, all agents eventually tend to a state value. Then, in some practical applications, the state of multi-agents is expected to be in a certain area, that is, in the convex hull formed by the leader's state trajectory. Therefore, the study of inclusive control is a hot issue in the field of cooperative control of multi-agent systems.

[0003] For multi-agent systems, it is inevitable that agents are subject to external interference during information transmission, which may lead to system performance degradation or even instability. In addition, in multi-agent systems, communication resources are often limited. The use of existing control methods will lead to a waste of communication resources, especially when the system state does not change much. Summary of the invention

[0004] The present invention provides a fixed-time inclusion control method and system for a second-order nonlinear multi-agent system, which are used to solve the technical problems that may lead to waste of communication resources and degradation or even instability of system performance.

[0005] In a first aspect, the present invention provides a fixed-time inclusion control method for a second-order nonlinear multi-agent system, comprising: Construct a second-order multi-leader-follower multi-agent system model; The state tracking error is defined according to the control objective and expanded into a matrix form, and the integral sliding surface that suppresses disturbance is designed; Design a distributed fixed-time inclusive consensus protocol and a dynamic event triggering mechanism based on position and speed information; After the multi-agent system model reaches the integral sliding surface according to the distributed fixed-time inclusion consistency protocol and the dynamic event triggering mechanism, it slides on the integral sliding surface to control the state of the multi-agent system model to achieve inclusion consistency within a fixed time.

[0006] In a second aspect, the present invention provides a fixed-time inclusion control system for a second-order nonlinear multi-agent system, comprising: A building module configured to build a second-order multi-leader-follower multi-agent system model; A first design module is configured to define a state tracking error according to a control objective and augment it into a matrix form, and to design an integral sliding surface for suppressing disturbances; A second design module is configured to design a distributed fixed-time inclusion consistency protocol and a dynamic event triggering mechanism based on position information and speed information; The control module is configured to control the multi-agent system model to reach the integral sliding surface according to the distributed fixed-time inclusion consistency protocol and the dynamic event triggering mechanism, and then slide on the integral sliding surface to control the state of the multi-agent system model to achieve inclusion consistency within a fixed time.

[0007] According to a third aspect, an electronic device is provided, comprising: at least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can perform the steps of the fixed-time inclusion control method for a second-order nonlinear multi-agent system according to any embodiment of the present invention.

[0008] In a fourth aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, wherein when the program instructions are executed by a processor, the processor executes the steps of the fixed-time control method for a second-order nonlinear multi-agent system of any embodiment of the present invention.

[0009] The fixed-time inclusion control method and system of the second-order nonlinear multi-agent system of the present application give a second-order multi-leader-follower multi-agent system model, and in response to the external disturbances existing in the system, a suitable double-power approach rate is selected to design a sliding surface to improve the convergence speed and suppress external disturbances. At the same time, a dynamic event trigger mechanism based on position information and speed information is designed to further reduce the energy consumption of the system and the number of controller updates, thereby extending the service life of the system. The dynamic event trigger mechanism is then combined with the sliding surface to design a new distributed fixed-time inclusion consistency protocol. Under this control protocol, the system will first reach the sliding surface, then slide on the sliding surface, and ultimately the system state will achieve inclusion consistency within a fixed time. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0011] Figure 1 A flowchart of a fixed-time inclusion control method for a second-order nonlinear multi-agent system provided by one embodiment of the present invention; Figure 2A structural block diagram of a fixed-time inclusion control system for a second-order nonlinear multi-agent system provided by one embodiment of the present invention; Figure 3 It is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0012] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0013] See also Figure 1 , which shows a flow chart of a fixed-time inclusion control method for a second-order nonlinear multi-agent system of the present application.

[0014] like Figure 1 As shown, the fixed-time inclusion control method of the second-order nonlinear multi-agent system specifically includes the following steps: Step S101, construct a second-order multi-leader-follower multi-agent system model.

[0015] In this step, the dynamic equation of the follower in the multi-agent system model is: , In the formula, is the derivative of the follower’s position state, is the velocity state of the follower, is the derivative of the velocity state of the follower, is a nonlinear function, is the control input, is the external disturbance of the follower, is the number of followers, is the position status of the follower; The dynamic equation of the leader in the multi-agent system model is: , In the formula, is the derivative of the leader’s position state, is the speed state of the leader, is the derivative of the leader's velocity state, External disturbances that exist for leaders, is the number of leaders, The position status of the leader.

[0016] Step S102, defining the state tracking error according to the control target and expanding it into a matrix form, and designing an integral sliding surface for suppressing disturbances.

[0017] In this step, the state tracking error includes the position error function of the follower and the speed error function of the follower, wherein the expressions of the position error function and the speed error function are respectively: , In the formula, is the position state error, is the speed state error, is the correlation weight between followers, , are the position state of the i-th follower agent and the j-th follower agent, respectively. is the correlation weight between the follower and the leader, is the position state of the leader agent, , are the speed state of the i-th follower agent and the speed state of the j-th follower agent, respectively. is the leader agent speed state; The matrix form is: , In the formula, is the matrix form of the follower’s position error, is the matrix form of the follower’s velocity error, is a non-singular matrix, is the Kronecker product, is the n-th order unit vector, is the weight matrix between followers and leaders, is the matrix form of the follower’s position state, , is the position state of the Nth agent, is the matrix form of the leader's position state, , is the position state of the N+Mth agent, is the matrix form of the velocity state of the follower, , is the speed state of the Nth agent, is the matrix form of the leader's velocity state, , is the speed state of the N+Mth agent, is the transpose symbol.

[0018] It should be noted that the expression of the integral sliding surface is: , In the formula, is the sliding surface function, is the speed error, is the Kronecker product, is the Sigmoid function, is the n-th order unit vector, is a non-singular matrix, , are all positive constants, is the ratio of two positive odd numbers, is the matrix form of the position error of the follower; , In the formula, is the derivative of the sliding surface function, is the position error, is the sliding surface function, is a constant, , is a constant, , , and are all positive constants, is a symbolic function; When the multi-agent system model reaches the integral sliding surface, ,but: , In the formula, is the derivative of the velocity error, For followers The velocity error matrix form at the moment is: is the matrix form of the velocity error of the follower.

[0019] Step S103, designing a distributed fixed-time inclusion consistency protocol and a dynamic event triggering mechanism based on position information and speed information.

[0020] In this step, the expression of the distributed fixed-time inclusion consensus protocol is: , In the formula, , , , and are all positive constants, is the symbolic function, is the matrix form of the follower’s position error, is the matrix form of the follower’s velocity error, is the ratio of two positive odd numbers, is the speed error, is the position error, is the Sigmoid function, is the sliding surface function, For followers The velocity error matrix form at the moment is: is a constant, .

[0021] It should be noted that the dynamic event triggering mechanism specifically includes: When the dynamic event trigger function and the internal dynamic variables meet the preset conditions, the event is triggered. The expression of the preset conditions is: , In the formula, is the k+1 moment of the ith agent, For time, To trigger the function for dynamic events, It is an internal dynamic variable; The expression of the dynamic event trigger function is: , In the formula, is the dynamic event triggering function of the ith agent, is the measurement error of the system, , , are all normal numbers, is the sliding surface function of the ith agent, is a constant, is a constant, ; The expression of the internal dynamic variable is: , In the formula, is the derivative of the internal dynamic variable, is an internal dynamic variable, , All are normal numbers.

[0022] Step S104, after controlling the multi-agent system model to reach the integral sliding surface according to the distributed fixed-time inclusion consistency protocol and the dynamic event triggering mechanism, the model slides on the integral sliding surface to control the state of the multi-agent system model to achieve inclusion consistency within a fixed time.

[0023] In summary, the method of this application provides a second-order multi-leader-follower multi-agent system model. In view of the external disturbances in the system, a suitable double-power approach rate is selected to design a sliding surface to improve the convergence speed and suppress external disturbances. At the same time, a dynamic event trigger mechanism based on position information and speed information is designed to further reduce the energy consumption of the system and the number of controller updates, thereby extending the service life of the system. The dynamic event trigger mechanism is then combined with the sliding surface to design a new distributed fixed-time inclusive consistency protocol. Under this control protocol, the system will first reach the sliding surface, then slide on the sliding surface, and finally achieve inclusive consistency of the system state within a fixed time.

[0024] In a specific embodiment, the event triggering strategy is an important means to avoid continuous communication between agents. Usually, the control input is updated and the data is transmitted when the absolute value of the error reaches the set threshold. If it is triggered infinitely in a short period of time, the Zeno phenomenon will occur. The definition of the Zeno phenomenon is given as follows: If exists , A custom constant that triggers the time sequence satisfy , then the system is said to have Zeno behavior.

[0025] In order to reduce the control cost and improve the convergence speed, a dynamic event-triggered consensus protocol based on integral sliding mode was proposed.

[0026] Design a new measurement error suitable for this system: , In the formula, , , , and are all positive constants, is the symbolic function, is the matrix form of the follower’s position error, is the matrix form of the follower’s velocity error, is the ratio of two positive odd numbers, is the speed error, is the position error, is the Sigmoid function, is the sliding surface function, For followers The velocity error matrix form at the moment is: is a constant, , for The value of the sliding surface function at time .

[0027] A distributed event-triggered sampling control is proposed. Each agent's control update is only performed at its own event triggering moment. Based on the zero-order holder, the control input is constant within each triggering interval.

[0028] See also Figure 2 , which shows a structural block diagram of a fixed-time inclusion control system of a second-order nonlinear multi-agent system of the present application.

[0029] like Figure 2 As shown, the fixed time includes a control system 200 , including a construction module 210 , a first design module 220 , a second design module 230 and a control module 240 .

[0030] Among them, the construction module 210 is configured to construct a second-order multi-leader-follower multi-agent system model; the first design module 220 is configured to define the state tracking error according to the control target and augment it into a matrix form, and design an integral sliding surface that suppresses disturbances; the second design module 230 is configured to design a distributed fixed-time inclusion consistency protocol, and a dynamic event triggering mechanism based on position information and speed information; the control module 240 is configured to control the multi-agent system model to reach the integral sliding surface according to the distributed fixed-time inclusion consistency protocol and the dynamic event triggering mechanism, and then slide on the integral sliding surface to control the state of the multi-agent system model to achieve inclusion consistency within a fixed time.

[0031] It should be understood that Figure 2 Modules and references documented in Figure 1 Therefore, the operations and features described above for the method and the corresponding technical effects are also applicable to Figure 2 The modules in it will not be described in detail here.

[0032] In some other embodiments, the embodiments of the present invention further provide a computer-readable storage medium having a computer program stored thereon, wherein when the program instructions are executed by a processor, the processor is caused to execute the fixed-time inclusion control method for a second-order nonlinear multi-agent system in any of the above method embodiments; As an implementation mode, the computer-readable storage medium of the present invention stores computer-executable instructions, and the computer-executable instructions are configured as follows: Construct a second-order multi-leader-follower multi-agent system model; The state tracking error is defined according to the control objective and expanded into a matrix form, and the integral sliding surface that suppresses disturbance is designed; Design a distributed fixed-time inclusive consensus protocol and a dynamic event triggering mechanism based on position and speed information; After the multi-agent system model reaches the integral sliding surface according to the distributed fixed-time inclusion consistency protocol and the dynamic event triggering mechanism, it slides on the integral sliding surface to control the state of the multi-agent system model to achieve inclusion consistency within a fixed time.

[0033] The computer-readable storage medium may include a program storage area and a data storage area, wherein the program storage area may store an operating system and an application required for at least one function; the data storage area may store data created according to the use of the fixed-time inclusion control system of the second-order nonlinear multi-agent system, etc. In addition, the computer-readable storage medium may include a high-speed random access memory, and may also include a memory, such as at least one disk storage device, a flash memory device, or other non-volatile solid-state storage device. In some embodiments, the computer-readable storage medium may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the fixed-time inclusion control system of the second-order nonlinear multi-agent system via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0034] Figure 3 is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention, such as Figure 3 As shown, the device includes: a processor 310 and a memory 320. The electronic device may also include: an input device 330 and an output device 340. The processor 310, the memory 320, the input device 330 and the output device 340 may be connected via a bus or other means. Figure 3 In the example, the connection through the bus is taken as an example. The memory 320 is the above-mentioned computer-readable storage medium. The processor 310 executes various functional applications and data processing of the server by running the non-volatile software programs, instructions and modules stored in the memory 320, that is, the fixed time inclusion control method of the second-order nonlinear multi-agent system of the above-mentioned method embodiment is realized. The input device 330 can receive input digital or character information, and generate key signal input related to the user setting and function control of the fixed time inclusion control system of the second-order nonlinear multi-agent system. The output device 340 may include a display device such as a display screen.

[0035] The electronic device can execute the method provided by the embodiment of the present invention, and has the functional modules and beneficial effects corresponding to the execution method. For technical details not described in detail in this embodiment, please refer to the method provided by the embodiment of the present invention.

[0036] As an implementation mode, the electronic device is applied to a fixed-time inclusion control system of a second-order nonlinear multi-agent system, and is used for a client, and includes: at least one processor; and a memory connected to the at least one processor in communication; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can: Construct a second-order multi-leader-follower multi-agent system model; The state tracking error is defined according to the control objective and expanded into a matrix form, and the integral sliding surface that suppresses disturbance is designed; Design a distributed fixed-time inclusive consensus protocol and a dynamic event triggering mechanism based on position and speed information; After the multi-agent system model reaches the integral sliding surface according to the distributed fixed-time inclusion consistency protocol and the dynamic event triggering mechanism, it slides on the integral sliding surface to control the state of the multi-agent system model to achieve inclusion consistency within a fixed time.

[0037] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods of each embodiment or some parts of the embodiment.

[0038] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fixed-time inclusion control method for a second-order nonlinear multi-agent system, characterized in that: include: Construct a second-order multi-leader-follower multi-agent system model; The state tracking error is defined according to the control objective and expanded into a matrix form, and the integral sliding surface that suppresses disturbance is designed; Design a distributed fixed-time inclusive consensus protocol and a dynamic event triggering mechanism based on position and speed information; After the multi-agent system model reaches the integral sliding surface according to the distributed fixed-time inclusion consistency protocol and the dynamic event triggering mechanism, it slides on the integral sliding surface to control the state of the multi-agent system model to achieve inclusion consistency within a fixed time.

2. The fixed-time inclusion control method for a second-order nonlinear multi-agent system according to claim 1, characterized in that: The dynamic equation of the follower in the multi-agent system model is: ， In the formula, is the derivative of the follower’s position state, is the velocity state of the follower, is the derivative of the velocity state of the follower, is a nonlinear function, is the control input, is the external disturbance of the follower, is the number of followers, is the position status of the follower; The dynamic equation of the leader in the multi-agent system model is: ， In the formula, is the derivative of the leader’s position state, is the speed state of the leader, is the derivative of the leader's velocity state, External disturbances that exist for leaders, is the number of leaders, The position status of the leader.

3. The fixed-time inclusion control method for a second-order nonlinear multi-agent system according to claim 1, characterized in that: The state tracking error includes a position error function of the follower and a speed error function of the follower, wherein the expressions of the position error function and the speed error function are respectively: ， In the formula, is the position state error, is the speed state error, is the correlation weight between followers, , are the position state of the i-th follower agent and the j-th follower agent, respectively. is the correlation weight between the follower and the leader, is the position state of the leader agent, , are the speed state of the i-th follower agent and the speed state of the j-th follower agent, respectively. is the leader agent speed state; The matrix form is: ， In the formula, is the matrix form of the follower’s position error, is the matrix form of the follower’s velocity error, is a non-singular matrix, is the Kronecker product, is the n-th order unit vector, is the weight matrix between followers and leaders, is the matrix form of the follower's position state, , is the position state of the Nth agent, is the matrix form of the leader's position state, , is the position state of the N+Mth agent, is the matrix form of the velocity state of the follower, , is the speed state of the Nth agent, is the matrix form of the leader's velocity state, , is the speed state of the N+Mth agent, is the transpose symbol.

4. The fixed-time inclusion control method for a second-order nonlinear multi-agent system according to claim 1, characterized in that: The expression of the integral sliding surface is: ， In the formula, is the sliding surface function, is the speed error, is the Kronecker product, is the Sigmoid function, is the n-th order unit vector, is a non-singular matrix, , are all positive constants, is the ratio of two positive odd numbers, is the matrix form of the position error of the follower; ， In the formula, is the derivative of the sliding surface function, is the position error, is the sliding surface function, is a constant, , is a constant, , , and are all positive constants, is a symbolic function; When the multi-agent system model reaches the integral sliding surface, ,but: ， In the formula, is the derivative of the velocity error, For followers The velocity error matrix form at the moment is: is the matrix form of the velocity error of the follower.

5. The fixed-time inclusion control method for a second-order nonlinear multi-agent system according to claim 1, characterized in that: The expression of the distributed fixed-time inclusion consistency protocol is: ， In the formula, , , , and are all positive constants, is the symbolic function, is the matrix form of the follower’s position error, is the matrix form of the follower’s velocity error, is the ratio of two positive odd numbers, is the speed error, is the position error, is the Sigmoid function, is the sliding surface function, For followers The velocity error matrix form at the moment is: is a constant, .

6. The fixed-time inclusion control method for a second-order nonlinear multi-agent system according to claim 1, characterized in that: The dynamic event triggering mechanism specifically includes: When the dynamic event trigger function and the internal dynamic variables meet the preset conditions, the event is triggered. The expression of the preset conditions is: ， In the formula, is the k+1 moment of the ith agent, For time, To trigger the function for dynamic events, It is an internal dynamic variable; The expression of the dynamic event trigger function is: ， In the formula, is the dynamic event triggering function of the ith agent, is the measurement error of the system, , , are all normal numbers, is the sliding surface function of the ith agent, is a constant, is a constant, ; The expression of the internal dynamic variable is: ， In the formula, is the derivative of the internal dynamic variable, is an internal dynamic variable, , All are normal numbers.

7. A fixed-time inclusion control system for a second-order nonlinear multi-agent system, characterized in that: include: A building module configured to build a second-order multi-leader-follower multi-agent system model; A first design module is configured to define a state tracking error according to a control objective and augment it into a matrix form, and to design an integral sliding surface for suppressing disturbances; A second design module is configured to design a distributed fixed-time inclusion consistency protocol and a dynamic event triggering mechanism based on position information and speed information; The control module is configured to control the multi-agent system model to reach the integral sliding surface according to the distributed fixed-time inclusion consistency protocol and the dynamic event triggering mechanism, and then slide on the integral sliding surface to control the state of the multi-agent system model to achieve inclusion consistency within a fixed time.

8. An electronic device, characterized in that: include: At least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

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