Multi-agent Set-Time Consensus Control Method Based on a Time Base Generator

Abstract

The present invention discloses a multi-agent set-time consensus control method based on a time-base generator. By only using the output information of adjacent agents and itself, through designing a dynamic observer containing a time reference generator and combining state transformation techniques, a collaborative framework of a distributed output feedback controller and a leader controller is constructed, realizing the set-time tracking consensus of a multi-agent system, significantly saving communication bandwidth while reducing the amount of information transmission; the constructed set-time control strategy based on TBG effectively avoids saturation and saves energy by reducing the number of initial control inputs; the unsigned function TBG control method is innovatively proposed, ensuring the dynamic performance of the system while eliminating high-frequency oscillations; this strategy has a fixed-time convergence characteristic, which can ensure that all followers accurately track the leader state within a preset time, and the upper bound of its convergence time is strictly decoupled from the initial state of the system, significantly optimizing the balance problem of dynamic quality and convergence speed.

Description

Technical Field

[0001] The present invention belongs to the field of distributed cooperative control, and particularly relates to a multi-agent set-time consensus control method based on a time-base generator. Background Technique

[0002] The cooperative control of multi-agent systems has shown important application value in the distributed task execution in complex dynamic environments. Its typical scenarios include: cooperative operation of networked mobile robots (such as formation of disaster rescue robots); state fusion of distributed sensor networks (realizing spatio-temporal consistency of environmental monitoring data); intelligent drone swarm systems, etc. The core of the consensus cooperative goal is to design a distributed control protocol with local information interaction ability, so that the agent group can achieve quantitative constraints on the state convergence domain and convergence speed within a finite time / fixed time. According to the system structure characteristics, the consensus problem can be divided into leaderless consensus and leader-follower consensus. The purpose of this problem is to design a distributed consensus protocol for each multi-agent based on the local information of adjacent nodes to achieve the collaborative convergence of the group at the target state within the set time.

[0003] As the core performance index of the cooperative control of multi-agent systems, finite-time convergence has significant advantages in improving the dynamic performance of the system and achieving precise time-domain constraints. However, the upper bound of the convergence time of the finite-time consensus algorithm is strongly related to the initial state of the system, which makes it difficult to predict the convergence time in advance in practical engineering. Compared with finite-time consensus, fixed-time consensus introduces a non-linear function to make the upper bound of the convergence time can be preset independently of the initial state, effectively solving the fundamental defect of the finite-time control method. However, the mainstream fixed-time consensus control method has a structural defect, that is, when the initial state deviation is large, its power-law term non-linear feedback mechanism will cause the control input to increase exponentially with the error, and finally trigger actuator saturation.

[0004] The core advantage of set-time consensus is to decouple the time constraint from the control parameters, endowing the user with the ability to directly program the convergence time, and at the same time enhancing the system robustness through a time-varying gain mechanism. It is irreplaceable in scenarios with extremely high time sensitivity requirements such as drone swarms, intelligent manufacturing, and distributed energy management. Under the set-time framework, the current research on leader-follower consensus control of multi-agent systems generally starts from the idealized assumption that the leader control input is strictly constrained to zero. This premise simplifies the problem analysis but may ignore the common situation where the leader has a non-zero control input in the actual system. How to independently design a control law for each follower when the leader control input is non-zero and construct an observer for each follower based on a time-base generator that only depends on the local and its neighbor output information, overcoming the dependence on the full state of the traditional method, and achieving the set-time consensus of non-linear multi-agents is the key technical problem that needs to be focused on and broken through in this field. Summary of the Invention

[0005] The present invention aims to solve at least one of the technical problems existing in the related art to some extent.

[0006] An object of the present invention is to provide a multi-agent set-time consensus control method based on a time-base generator. For the set-time consensus control problem of non-linear multi-agents, in the complex scenario considering that the leader has a continuous non-zero control input, a time-base-driven distributed control law is constructed for each follower; at the same time, an observer network that only depends on local output information and neighbor interaction topology is designed to break through the traditional full-dimensional state observation paradigm to meet engineering applications.

[0007] To achieve the above object, on the one hand, the present invention provides a multi-agent set-time consensus control method based on a time-base generator, including:

[0008] S100. Obtain the communication topology structure and dynamic model of the multi-agent system, where the multi-agent system includes one leader agent and multiple follower agents;

[0009] S200. Construct a time-base generator according to the communication topology structure and dynamic model, where the time-base generator is used to generate a time-varying gain within a set time;

[0010] S300. Generate a dynamic observer for each follower agent through the time-base generator, where the dynamic observer is based on the output information of the follower and its neighbor agents;

[0011] S400. Construct a distributed output feedback controller according to the dynamic observer, where the distributed output feedback controller is used to control the state of each follower agent;

[0012] S500. Achieve the consensus tracking of the multi-agent system within a set time through the distributed output feedback controller and the control input of the leader agent.

[0013] A further preferred technical solution of the present invention is that the multi-agent system is a feedforward non-linear system composed of one leader agent and N follower agents. For each agent in the multi-agent system, obtain its state, output, and control input, where the state represents the dynamic characteristics of the agent, the output represents the measurement information of the agent, and the control input represents the control signal of the agent;

[0014] According to the state, output, and control input, represent the dynamic equation of the th agent as:

[0015] ;

[0016] In the formula, is the state vector of the th agent. The state vector of the th agent has a total of components, , where, represents the th component of the state vector of the th agent, represents the th component of the state vector of the th agent; represents the measurement output of the th agent; and represent the control input, is the non - linear function of the th agent; represents time, and N represents the number of agents.

[0017] Preferably, in step S100, a directed topological graph structure is constructed for the multi - agent system , which is used to represent the communication relationship between agents;

[0018] Among them, represents a non - empty vertex set; represents the edge set that characterizes the binary association characteristics between agents, represents that there is an edge from node to node ; is the adjacency matrix, which represents the connection relationship between agents. When and only when then ;

[0019] According to the directed topological graph structure, a Laplacian matrix and a pinning matrix are generated. Among them, the Laplacian matrix represents the in - degree characteristics of the communication topology and is expressed as , where represents the in - degree matrix, represents the sum of the in - degrees of node ;

[0020] The leader node is labeled 0, is defined as the pinning matrix of graph . If there is a connection edge from the leader node to the th follower node, then , otherwise ; Denote .

[0021] Preferably, the time reference generator constructed in step S200 is expressed as:

[0022] ;

[0023] wherein represents the state of the dynamic system, is the initial state, is a real constant;

[0024] TBG gain , where , satisfies: from the initial value to the terminal value is continuous and non-decreasing, and the right derivative satisfies ; when , and ; for , according to the property, the state approaches the value at ; represents being twice differentiable in the interval , and the first derivative and the second derivative are continuous in the interval .

[0025] Preferably, for the communication constraint condition that N follower agents only output state observations through network interaction with the leader in step S300, the set-time consistency cooperation problem is transformed into a preset-time tracking problem under the leader-follower framework. By combining the time scaling characteristics of the time reference generator with a distributed observer, the output consistency error is introduced into the observer; wherein represents the set of neighbor nodes of node , represents the output of the m-th follower agent, represents the output of the leader agent;

[0026] Only using the output information of the followers and their neighbor agents, for each follower agent , a dynamic observer driven by the time reference generator is designed, expressed as:

[0027] ;

[0028] wherein represents the TBG gain parameter, represents the control input, satisfies the Hurwit memory polynomial: ; represents a complex variable with a negative real part;

[0029] Based on the TBG gain, the state variables of the observer are subjected to a state transformation to obtain , where represents a positive integer; represents the -th component of the state vector of the -th dynamic observer after the state transformation, represents the -th component of the state of the -th dynamic observer;

[0030] Define the state of the -th agent, the state of the leader, and the state error of the observer:

[0031] , and the error variable is subjected to a state transformation to .

[0032] Preferably, the distributed output feedback controller constructed in step S400 is expressed as:

[0033] ;

[0034] ;

[0035] In the formula are the coefficients of the Hurwitz polynomial , is a control parameter;

[0036] are the control parameters for designing the controller. Taking the time derivatives of the above-defined respectively, we can obtain

[0037] ;

[0038] where represents the vector composed of the states of the N observers after the state transformation, represents the state of each observer, which is an n-dimensional vector; , ; represents the transpose of the vector;

[0039] ;

[0040] represent the coefficients of the hurwitz polynomial, satisfying the Hurwitz polynomial: , is the column vector composed of these coefficients; is a Hurwitz polynomial coefficients; consists of parameters that satisfy the Hurwitz polynomial and ;

[0041] ;

[0042] represents the th component of the nonlinear function of the th follower agent; represents the th component of the nonlinear function of the leader agent; represents the control parameter; , where represents the composite error, that is, the follower state and the desired reference trajectory.

[0043] Preferably, in step S500, the leader agent control input is first designed. Under the condition of non-zero excitation of the leader agent control input, a leader agent control protocol with preset convergence characteristics is constructed to ensure global state synchronization of the system within a finite time domain. The leader agent controller is designed as:

[0044] ;

[0045] .

[0046] Preferably, in step S500, the constructed leader agent controller is combined with a distributed output feedback controller to convert the set-time tracking error between the leader agent and each follower agent into a dynamic system, expressed as:

[0047] ;

[0048] where , and

[0049] ;

[0050] , represents the state of each observer; represents an n-by-n matrix; , respectively represent the th component corresponding to the nonlinear function of the th agent; , respectively represent control parameters;

[0051] Based on the finite-time stability of the dynamic system, various tracking error states finally tend to zero in finite time, that is, the finite-time consensus cooperation goal among multi-agents is achieved.

[0052] Beneficial effects: The finite-time consensus tracking control strategy based on TBG proposed in the present invention realizes the optimization of the control structure by innovatively introducing a dynamic gain adjustment mechanism while ensuring the convergence performance of the system. It can make the number of initial control inputs less than that of the traditional finite-time consensus tracking control strategy. This structural simplification not only reduces the computational complexity but also effectively prevents the actuator saturation phenomenon, significantly saving the communication bandwidth while reducing the amount of information transmission.

[0053] In view of the chattering problem caused by the sign function in the traditional finite-time tracking control, the present invention proposes a sign-function-free control method based on TBG, and realizes the finite-time cooperative tracking of multi-agents by constructing a new consensus control strategy, ensuring the dynamic performance of the system while eliminating high-frequency oscillations.

[0054] The control method based on TBG proposed in the present invention has the characteristic of fixed-time convergence, which can ensure that all follower states track the leader state within the finite time, and the upper bound of its convergence time is strictly decoupled from the initial state of the system, and effectively reduces the amplitude of the initial control input, effectively solving the trade-off problem between the dynamic quality and the convergence speed in the traditional finite-time control. Description of the Drawings

[0055] Figure 1 is the block diagram of the finite-time cooperative control system of the multi-agent system of the present invention;

[0056] Figure 2 is the communication topology structure diagram of the multi-agent system of the present invention;

[0057] Figure 3 is the curve diagram of the finite-time tracking error state between the follower and the leader in the embodiment of the present invention;

[0058] Figure 4 is the transformation curve diagram of the observer in the embodiment of the present invention;

[0059] Figure 5 is the curve diagram of the control input change of the follower in the embodiment of the present invention. Detailed Embodiments

[0060] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions in the present invention in conjunction with the accompanying drawings in the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention, and they should not be construed as limitations on the present invention. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms used are only for the purpose of description and cannot be construed as indicating or implying relative importance.

[0061] The following combines Figures 1 - 5 to describe the multi-agent set-time consensus control method based on a time-based generator provided by the present invention.

[0062] Embodiment: This embodiment provides a multi-agent set-time consensus control method based on a time-based generator. Based on the multi-agent control architecture as Figure 1 shown, the non-linear preset-time tracking control problem between each follower agent and the leader is reconstructed into a linear time-varying dynamic system. Through the evolution of the error dynamics, it is ensured that all tracking error states asymptotically converge to zero within the preset time, thereby achieving the preset-time consensus control objective of the multi-agent system.

[0063] To solve the preset-time cooperative control problem of heterogeneous feedforward non-linear multi-agent systems, the general idea of this embodiment includes: 1) Design of a dynamic observer based on neighbor output information fusion: Each follower only needs to obtain the local output information of adjacent nodes and its own output signal, and a distributed state observer with time-varying characteristics is constructed by introducing the TBG gain; 2) Construction of a composite control architecture: Combining the diffeomorphic state transformation method, a distributed output feedback controller containing the TBG is designed for the follower, and a dynamic control input is constructed for the leader at the same time; 3) Guarantee of preset-time stability: The proposed TBG control protocol can ensure that the system achieves consensus tracking within the set time, and the upper bound of its convergence time is independent of the initial state and is only determined by the TBG parameters.

[0064] The specific steps of this embodiment are as follows:

[0065] S100. Obtain the communication topology structure and dynamic model of the multi-agent system. In this embodiment, taking a multi-agent system composed of 4 follower agents and 1 leader agent as an example, the dynamic model of the multi-agent system is expressed as:

[0066]

[0067] where represents the state of the th follower agent, represents the input of the th follower agent, represents the output of the th follower agent, and the state initial condition is:

[0068] ,

[0069] ,

[0070] ,

[0071] ,

[0072] .

[0073] In this embodiment, as Figure 2 shown, a directed topological structure diagram is given for 5 multi - agents , which is used to represent the communication relationship between agents, where represents the set of follower nodes, represents the edge set. If there is an edge between agents, they are regarded as neighbor agents: represents the adjacency matrix. If , then , otherwise . The leader node is marked with 0, is defined as the pinning matrix. If there is an edge from the leader node to the th follower node, then , otherwise . The adjacency matrix .

[0074] S200. According to the communication topology structure and the dynamic model, construct a time - based generator (TBQ), where the time - based generator is used to generate a time - varying gain within a set time.

[0075] The time - varying function TBG with strong constraint characteristics designed in this embodiment is:

[0076]

[0077] In the formula, ; By taking the derivative of the TBG gain , combined with the general properties of TBG, when , increases from to reach the maximum value, and then decreases to zero at , is the set time. When After the value is selected, When the maximum and minimum values of the TBGs gain are respectively recorded as and . In this embodiment .

[0078] S300. Generate a dynamic observer for each follower agent through the time-based generator (TBQ).

[0079] Introduce the output consistency error into the observer. Only using the output information of the follower and its neighbor agents, design the TBG-driven dynamic observers for 4 follower agents as follows:

[0080]

[0081] where , the state variable represents the observer state, .

[0082] S400. Construct a distributed output feedback controller according to the dynamic observer.

[0083] In this example, to achieve the leader-follower state consistency at the set time, the distributed output feedback controllers of 4 followers all adopt the information of the same observer and design the following controllers:

[0084] .

[0085] S500. Achieve the consistency tracking of the multi-agent system within the set time through the distributed output feedback controller and the control input of the leader agent.

[0086] Design the leader agent controller:

[0087]

[0088] where, , , , , .

[0089] Combine the constructed leader agent controller with the distributed output feedback controller, and transform the set-time tracking error between the leader agent and each follower agent into a dynamic system, expressed as:

[0090]

[0091] where, , and

[0092] ;

[0093] Based on the finite-time stability of the dynamic system, various tracking error states finally tend to zero in finite time, that is, the finite-time consensus cooperation goal among multi-agents is achieved.

[0094] In the finite-time consensus control method for multi-agents based on a time-based generator described in this embodiment, the non-linear tracking error system between the leader and each follower will be converted into a linear system. Further, through state transformation and combined with the non-zero control input of the leader, finally, each tracking error tends to zero within finite time, that is, the finite-time consensus of the feedforward multi-agent system is achieved. The finite-time tracking error between the follower and the leader is as Figure 3 shown. It can be seen from Figure 3 that under the action of the designed controller, the tracking error state between the leader and the follower tends to zero within finite time. The transformation curve of the observer is as Figure 4 shown. Figure 4 shows the evolution process of the observer, where the initial value is 0 and the final observed value also becomes 0, indicating that the leader and the follower reach an agreement. The change curve of the control input of the follower is as Figure 5 shown. Figure 5 shows the change trend of the control input. It can be seen that the control input value gradually decreases before the fixed time , and the control input becomes 0 when . This indicates that the controller of the present invention is not only effective but also can save control costs.

[0095] The finite-time consensus control method for multi-agents based on a time-based generator in this embodiment simultaneously considers the finite-time consensus problem of different feedforward non-linear multi-agent systems. Each follower only needs the relevant output information of adjacent agents and its own output information. A dynamic observer with TBG gain is designed, and combined with the state transformation method, a distributed output feedback controller with TBG and a leader controller are constructed for each follower. The proposed TBG control protocol can ensure that all follower states track the leader state within finite time, and the convergence time is independent of the initial conditions. The TBG protocol effectively reduces the amplitude of the initial control input and plays an important role in improving the convergence speed and transient performance. It can be applied to industrial automation fields such as industrial robot cooperative assembly.

[0096] 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 described in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-agent set-time consensus control method based on a time-base generator, characterized in that Including: S100. Obtain the communication topology structure and dynamic model of the multi-agent system, where the multi-agent system includes a leader agent and multiple follower agents; assume that the multi-agent system is a feedforward nonlinear system composed of 1 leader agent and N follower agents. For each agent in the multi-agent system, obtain its state, output, and control input, where the state represents the dynamic characteristics of the agent, the output represents the measurement information of the agent, and the control input represents the control signal of the agent. According to the state, output, and control input, the dynamic equation of the -th agent is expressed as: ； wherein is the state vector of the -th agent. The state vector of the -th agent has a total of components, , where represents the -th component of the state vector of the -th agent, and represents the -th component of the state vector of the -th agent; represents the measurement output of the -th agent; and represent the control inputs, is the non - linear function of the -th agent; represents time, and N represents the number of agents; S200. Construct a time-based generator according to the communication topology structure and dynamic model, where the time-based generator is used to generate a time-varying gain within a set time. S300. Generate a dynamic observer for each follower agent through the time-based generator, where the dynamic observer is based on the output information of the follower agent and its neighbor agents. S400. Construct a distributed output feedback controller according to the dynamic observer, where the distributed output feedback controller is used to control the state of each follower agent. S500. Achieve the consensus tracking of the multi-agent system within a set time through the distributed output feedback controller and the control input of the leader agent.

2. The multi-agent set time consistency control method based on a time base generator according to claim 1, characterized in that In step S100, a directed topological graph structure is constructed for the multi-agent system , which is used to represent the communication relationship between agents; Among them, represents a non-empty vertex set; represents that the edge set depicts the binary association characteristics among agents, represents starting from node to node there is an edge; is the adjacency matrix, representing the connection relationship among agents, if and only if when ; Generate a Laplacian matrix and a pinning matrix according to the directed topological graph structure, where the Laplacian matrix represents the in-degree characteristics of the communication topology and is expressed as , where represents the in-degree matrix, represents the node sum of in-degrees; The leader agent node is marked as 0, defined as the figure of the pinning matrix. If there is a connection edge from the leader agent node to the th follower agent node, then , otherwise ; Denote .

3. The multi-agent set time consistency control method based on a time base generator according to claim 1, characterized in that The time-based generator constructed in step S200 is expressed as: ； wherein, represents the state of the dynamic system, is the initial state, is a real constant; TBG gain , where , satisfies: from the initial value to the terminal value is continuous and non-decreasing, and the right derivative satisfies ; when , and ; for , from the property, it can be known that the state is close to the value at ; means that it is twice differentiable in the interval , and the first derivative and the second derivative are continuous in the interval .

4. The multi-agent set time consistency control method based on a time base generator according to claim 3, wherein In step S300, for the N follower agents, only through the communication constraint condition of the leader agent outputting the state observation value via network interaction, the set-time consistency coordination problem is transformed into a preset-time tracking problem under the leader-follower framework. By combining the time scaling characteristic of the time reference generator with the distributed observer, the output consistency error is introduced into the observer; where represents the set of neighbor nodes of node , represents the output of the m-th follower agent, represents the output of the leader agent; Only using the output information of the follower agent and its neighbor agents, for each follower agent Design a dynamic observer driven by a time reference generator, expressed as: ； wherein represents the TBG gain parameter, represents the control input, satisfies the Hurwit polynomial: ; represents a complex variable with a negative real part; Based on the TBG gain, the state variables of the observer are subjected to a state transformation to obtain , where represents a positive integer; represents the -th component of the state vector of the -th dynamic observer after the state transformation, represents the -th component of the state of the -th dynamic observer; Define the state of the th follower agent, the state of the leader, and the observer state error: , and transform the error variable state into .

5. The multi-agent set time consistency control method based on a time base generator according to claim 4, characterized in that The distributed output feedback controller constructed in step S400 is expressed as: ； ； wherein is a Hurwitz polynomial are the coefficients of is the control parameter; To design the control parameters of the controller, for the above-defined Taking the time derivatives respectively, we can obtain ； Among them, represents the vector composed of the states of N observers after state transformation, represents the state of each observer, which is an n-dimensional vector; , ; represents the transpose of the vector; ； Denote the coefficients of the Hurwitz polynomial, satisfying the Hurwitz polynomial: , is the column vector formed by these coefficients; is the coefficient of the Hurwitz polynomial ; is composed of the parameters and that satisfy the Hurwitz polynomial; ； The -th component of the non - linear function of the -th follower agent; The -th component of the non - linear function representing the leader agent; Denotes the control parameter; , where, Denotes the composite error, i.e., the follower state and the desired reference trajectory.

6. The multi-agent set time consistency control method based on a time base generator according to claim 5, characterized in that In step S500, first design the control input of the leader agent. Under the condition of non-zero excitation of the control input of the leader agent, construct a control protocol of the leader agent with preset convergence characteristics to ensure that the global state synchronization is achieved within a finite time domain. The leader agent controller is designed as: ； 。 7. The multi-agent set time consistency control method based on a time base generator according to claim 6, characterized in that, In step S500, combine the constructed leader agent controller with the distributed output feedback controller, and transform the set-time tracking error between the leader agent and each follower agent into a dynamic system, which is expressed as: ； Among them, , and ； , represents the state of each observer; represents an n-by-n matrix; , respectively represent the components corresponding to the non-linear functions of the th agent; represents a diagonal matrix, i.e., , respectively represent the control parameters; Based on the set-time stability of the dynamic system, finally achieve that various tracking error states tend to zero within the set time, that is, achieve the set-time consensus cooperation goal among multi-agents.

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