Fixed-Time Containment Control Method and System for Second-Order Nonlinear Multi-Agent Systems

Abstract

The present invention discloses a fixed-time containment control method and system for a second-order nonlinear multi-agent system. The method includes: defining a state tracking error according to a control target and augmenting it into a matrix form, and designing an integral sliding mode surface for suppressing disturbances; designing a distributed fixed-time containment consensus protocol according to the integral sliding mode surface, and a dynamic event-triggering mechanism based on position information and velocity information; after controlling the multi-agent system model to reach the integral sliding mode surface according to the distributed fixed-time containment consensus protocol and the dynamic event-triggering mechanism, making it slide on the integral sliding mode surface, and controlling the state of the multi-agent system model to achieve containment consensus within a fixed time. It can reduce the energy consumption of the system and the update times of the controller, extend the service life of the system, and under the new distributed fixed-time containment consensus protocol, the system will first reach the sliding mode surface and then slide on the sliding mode surface, finally enabling the system state to achieve containment consensus within a fixed time.

Description

Technical Field

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

[0002] At present, most of the work on the consensus of multi-agent systems mainly focuses on the research of ordinary consensus, that is, all agents finally converge to a state value. Then, in some practical applications, the desired state of multi-agents is within a certain region, that is, within the convex hull formed by the leader state trajectories. Therefore, the research on containment 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 disturbances during the information transmission process, which may lead to a decline in system performance or even instability. Moreover, in multi-agent systems, communication resources are often limited, and the use of existing control methods will result in a waste of communication resources, especially when the system state changes little. Summary of the Invention

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

[0005] In a first aspect, the present invention provides a fixed-time containment control method for a second-order nonlinear multi-agent system, including:

[0006] Constructing a second-order multi-leader-follower multi-agent system model;

[0007] Defining a state tracking error according to the control objective and augmenting it into a matrix form, and designing an integral sliding mode surface to suppress disturbances;

[0008] Designing a distributed fixed-time containment consensus protocol and a dynamic event-triggering mechanism based on position information and velocity information;

[0009] After controlling the multi-agent system model to reach the integral sliding mode surface according to the distributed fixed-time containment consensus protocol and the dynamic event-triggering mechanism, making it slide on the integral sliding mode surface, and controlling the state of the multi-agent system model to achieve containment consensus within a fixed time.

[0010] In a second aspect, the present invention provides a fixed-time containment control system for a second-order nonlinear multi-agent system, including:

[0011] A constructing module configured to construct a second-order multi-leader-follower multi-agent system model;

[0012] The first design module is configured to define a state tracking error according to a control target and augment it into a matrix form, and design an integral sliding mode surface for suppressing disturbances;

[0013] The second design module is configured to design a distributed fixed-time containment consensus protocol and a dynamic event-triggering mechanism based on position information and velocity information;

[0014] The control module is configured to control the multi-agent system model to slide on the integral sliding mode surface after reaching the integral sliding mode surface according to the distributed fixed-time containment consensus protocol and the dynamic event-triggering mechanism, and control the state of the multi-agent system model to achieve containment consensus within a fixed time.

[0015] In a third aspect, an electronic device is provided, which includes: 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 execute the steps of the fixed-time containment control method for a second-order nonlinear multi-agent system according to any embodiment of the present invention.

[0016] In a fourth aspect, the present invention further provides a computer-readable storage medium, on which a computer program is stored, and when the program instructions are executed by a processor, the processor is enabled to execute the steps of the fixed-time containment control method for a second-order nonlinear multi-agent system according to any embodiment of the present invention.

[0017] The fixed-time containment control method and system for the second-order nonlinear multi-agent system of the present application present a second-order multi-leader-follower multi-agent system model. In view of the external disturbances existing in the system, a suitable double-power reaching law is selected to design a sliding mode surface to improve the convergence speed and suppress external disturbances. At the same time, a dynamic event-triggering mechanism based on position information and velocity information is designed to further reduce the energy consumption of the system and the update times of the controller, extend the service life of the system, and then combine the dynamic event-triggering mechanism with the sliding mode surface to design a new distributed fixed-time containment consensus protocol. Under this control protocol, the system will first reach the sliding mode surface and then slide on the sliding mode surface, and finally enable the system state to achieve containment consensus within a fixed time. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0019] Figure 1Flowchart of a fixed-time containment control method for a second-order nonlinear multi-agent system provided by an embodiment of the present invention;

[0020] Figure 2 Block diagram of a fixed-time containment control system for a second-order nonlinear multi-agent system provided by an embodiment of the present invention;

[0021] Figure 3 Schematic structural diagram of an electronic device provided by an embodiment of the present invention. Detailed implementation manners

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0023] Please refer to Figure 1 , which shows a flowchart of a fixed-time containment control method for a second-order nonlinear multi-agent system of the present application.

[0024] As Figure 1 shown, the fixed-time containment control method for a second-order nonlinear multi-agent system specifically includes the following steps:

[0025] Step S101, construct a second-order multi-leader-follower multi-agent system model.

[0026] In this step, the dynamic equation of the follower in the multi-agent system model is:

[0027] ,

[0028] In the formula, is the derivative of the position state of the follower, 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 existing in the follower, is the number of followers, is the position state of the follower;

[0029] The dynamic equation of the leader in the multi-agent system model is:

[0030] ,

[0031] wherein, is the derivative of the position state of the leader, is the velocity state of the leader, is the derivative of the velocity state of the leader, is the external disturbance existing for the leader, is the number of leaders, is the position state of the leader.

[0032] Step S102: Define the state tracking error according to the control objective and augment it into matrix form, and design an integral sliding mode surface for suppressing the disturbance.

[0033] In this step, the state tracking error includes the position error function of the follower and the velocity error function of the follower. Among them, the expressions of the position error function and the velocity error function are respectively:

[0034] ,

[0035] wherein, is the position state error, is the velocity state error, is the correlation weight between followers, , are respectively the position states of the i-th follower agent and the j-th follower agent, is the correlation weight between the follower and the leader, is the position state of the leader agent, , are respectively the velocity states of the i-th follower agent and the j-th follower agent, is the velocity state of the leader agent;

[0036] The matrix form is:

[0037] ,

[0038] wherein, is the matrix form of the position error of the follower, is the matrix form of the velocity error of the follower, is a non-singular matrix, is the Kronecker product, is the n-order unit vector, is the weight matrix between the follower and the leader, is the matrix form of the position state of the follower, , is the position state of the N-th agent, is the matrix form of the position state of the leader, , is the position state of the (N + M)-th agent, is the matrix form of the velocity state of the follower, , is the velocity state of the N-th agent, is the matrix form of the velocity state of the leader, , is the velocity state of the (N + M)-th agent, is the transpose symbol.

[0039] It should be noted that the expression of the integral sliding surface is:

[0040] ,

[0041] wherein, is the sliding surface function, is the velocity error, is the Kronecker product, is the Sigmoid function, is the n-order unit vector, is a non-singular matrix, , are both positive constants, is the ratio of two positive odd numbers, is the matrix form of the position error of the follower;

[0042] ,

[0043] wherein, 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 both positive constants, is the sign function;

[0044] When the multi-agent system model reaches the said integral sliding surface, , then:

[0045] ,

[0046] wherein, is the derivative of the velocity error, is the matrix form of the velocity error of the follower at time , is the matrix form of the velocity error of the follower.

[0047] Step S103: Design a distributed fixed-time containment consensus protocol and a dynamic event-triggering mechanism based on position information and speed information.

[0048] In this step, the expression of the distributed fixed-time containment consensus protocol is:

[0049] ,

[0050] wherein, , , , and are all positive constants, is the sign function, is the matrix form of the position error of the followers, is the matrix form of the speed error of the followers, is the ratio of two positive odd numbers, is the speed error, is the position error, is the Sigmoid function, is the sliding mode surface function, is the follower at time is a constant, .

[0051] It should be noted that the dynamic event-triggering mechanism specifically includes:

[0052] An event is triggered when the dynamic event-triggering function and the internal dynamic variable meet the preset conditions, and the expression of the preset conditions is:

[0053] ,

[0054] wherein, is the time of the is the dynamic event-triggering function, is the internal dynamic variable;

[0055] Among them, the expression of the dynamic event-triggering function is:

[0056] ,

[0057] wherein, is the dynamic event-triggering function of the is the measurement error of the system, , , are all normal constants, is the sliding mode surface function of the i-th agent, is a constant, is a constant, ;

[0058] The expression of the internal dynamic variable is:

[0059] ,

[0060] In the formula, is the derivative of the internal dynamic variable, is the internal dynamic variable, , are both positive constants.

[0061] Step S104, after controlling the multi-agent system model to reach the integral sliding mode surface according to the distributed fixed-time inclusion consensus protocol and the dynamic event-triggering mechanism, and sliding on the integral sliding mode surface, control the state of the multi-agent system model to achieve inclusion consensus within a fixed time.

[0062] In summary, the method of this application gives a second-order multi-leader-follower multi-agent system model. For the external disturbances existing in the system, a suitable double power reaching law is selected to design a sliding mode surface to improve the convergence speed and suppress external disturbances. At the same time, a dynamic event-triggering mechanism based on position information and speed information is designed to further reduce the energy consumption of the system and the update times of the controller, and extend the service life of the system. Then, the dynamic event-triggering mechanism is combined with the sliding mode surface to design a new distributed fixed-time inclusion consensus protocol. Under this control protocol, the system will first reach the sliding mode surface and then slide on the sliding mode surface, and finally make the system state achieve inclusion consensus within a fixed time.

[0063] In a specific embodiment, the event-triggering strategy is an important means to avoid continuous communication between agents. Usually, when the absolute value of the error reaches the set threshold, the control input is updated and data is transmitted. If it is triggered infinitely many times in a very short time, the Zeno phenomenon will occur. The definition of the Zeno phenomenon is given as follows:

[0064] If there exists , is a user-defined constant, and the trigger time sequence satisfies , then it is said that the system has Zeno behavior.

[0065] In order to reduce the control cost and improve the convergence speed, a dynamic event-triggering consensus protocol based on integral sliding mode is proposed.

[0066] Design a new measurement error applicable to this system as:

[0067] ,

[0068] wherein, , , , and are all positive constants, is the sign function, is the matrix form of the position error of the follower, is the matrix form of the velocity error of the follower, is the ratio of two positive odd numbers, is the velocity error, is the position error, is the Sigmoid function, is the sliding mode surface function, is the follower at time is a constant, , is the value of the sliding mode surface function at time

[0069] proposes a distributed event-triggered sampling control. The control update of each agent is only at its own event-triggering moment. Based on the zero-order hold, the control input is constant within each triggering interval.

[0070] Please refer to Figure 2 , which shows the structural block diagram of a fixed-time containment control system for a second-order nonlinear multi-agent system of the present application.

[0071] As Figure 2 shown, the fixed-time containment control system 200 includes a construction module 210, a first design module 220, a second design module 230, and a control module 240.

[0072] 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 objective and augment it into a matrix form, and design an integral sliding mode surface for suppressing disturbances; the second design module 230 is configured to design a distributed fixed-time containment consensus protocol and a dynamic event-triggering mechanism based on position information and velocity information; the control module 240 is configured to control the multi-agent system model to reach the integral sliding mode surface according to the distributed fixed-time containment consensus protocol and the dynamic event-triggering mechanism, slide on the integral sliding mode surface, and control the state of the multi-agent system model to achieve containment consensus within a fixed time.

[0073] It should be understood that Figure 2The various modules described in Figure 1 correspond to the respective steps in the method described in the reference Figure 2 . Thus, the operations, features, and corresponding technical effects described above for the method also apply to

[0074] the various modules in

[0075] and will not be elaborated here.

[0076] Construct a second-order multi-leader-follower multi-agent system model;

[0077] Define the state tracking error according to the control objective and augment it into matrix form, and design an integral sliding mode surface to suppress disturbances;

[0078] Design a distributed fixed-time containment consensus protocol and a dynamic event-triggering mechanism based on position information and velocity information;

[0079] After controlling the multi-agent system model to reach the integral sliding mode surface according to the distributed fixed-time containment consensus protocol and the dynamic event-triggering mechanism, make it slide on the integral sliding mode surface, and control the state of the multi-agent system model to achieve containment consensus within a fixed time.

[0080] The computer-readable storage medium may include a storage program area and a storage data area. Among them, the storage program area can store an operating system and application programs required for at least one function; the storage data area can store data created according to the use of the fixed-time containment control system of the second-order nonlinear multi-agent system, etc. In addition, the computer-readable storage medium may include high-speed random access memory, and may also include memories, such as at least one magnetic disk storage device, a flash memory device, or other non-volatile solid-state storage devices. In some embodiments, the computer-readable storage medium may optionally include a memory remotely set relative to the processor, and these remote memories can be connected to the fixed-time containment control system of the second-order nonlinear multi-agent system through a network. Examples of the above networks include, but are not limited to, the Internet, an enterprise intranet, a local area network, a mobile communication network, and combinations thereof.

[0081] Figure 3 is a schematic structural diagram of the electronic device provided by the embodiments of the present invention, as Figure 3As shown in the figure, the device includes a processor 310 and a memory 320. The electronic device may further 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 Taking the connection via the bus as an example. The memory 320 is the aforementioned 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, implementing the fixed-time containment control method for the second-order nonlinear multi-agent system in the above method embodiment. The input device 330 can receive input digital or character information, and generate key signal inputs related to the user settings and function control of the fixed-time containment control system of the second-order nonlinear multi-agent system. The output device 340 may include display devices such as a display screen.

[0082] The above electronic device can execute the method provided in the embodiment of the present invention, and has corresponding functional modules and beneficial effects for executing the method. For technical details not described in detail in this embodiment, reference can be made to the method provided in the embodiment of the present invention.

[0083] As an implementation manner, the above electronic device is applied to the fixed-time containment control system of the second-order nonlinear multi-agent system, and is used for the client, including: 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:

[0084] Construct a second-order multi-leader-follower multi-agent system model;

[0085] Define the state tracking error according to the control objective and augment it into matrix form, and design an integral sliding mode surface to suppress disturbances;

[0086] Design a distributed fixed-time containment consensus protocol and a dynamic event-triggering mechanism based on position information and velocity information;

[0087] After controlling the multi-agent system model to reach the integral sliding mode surface according to the distributed fixed-time containment consensus protocol and the dynamic event-triggering mechanism, and sliding on the integral sliding mode surface, control the state of the multi-agent system model to achieve containment consensus within a fixed time.

[0088] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the essence of the above technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions for causing 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 embodiments.

[0089] 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 them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of each embodiment 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 an integral sliding surface for suppressing disturbance is designed. 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; 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 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, .

5. 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.

6. 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; The first design module is configured to define the state tracking error according to the control target and expand it into a matrix form, and design an integral sliding surface for suppressing disturbance, wherein 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; 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.

7. 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 execute the method described in any one of claims 1 to 5.

8. 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 5 is implemented.

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