Research on non-smooth consistency protocol and anti-interference performance based on leader-free multi-agent system

Abstract

The invention discloses a method for constructing a non-smooth consistency protocol based on a leader-free multi-agent system and improving the anti-interference performance of the non-smooth consistency protocol. The method comprises the following steps: firstly, establishing a dynamic model based on a leader-free agent system, introducing mismatching disturbance and matching disturbance, establishing a Laplacian matrix between agent formations according to a communication topological graph, and determining the coupling strength between agents and whether the agents are intercommunicated or not; designing a virtual speed based on a backstepping method to enable the states of the multiple agents to be consistent in a fixed time, and designing a control law according to a fixed time control method to enable the actual speed of the multiple agents to track the virtual speed in the fixed time in the presence of composite interference; as not all states can be directly obtained by measurement in practical application, an observer needs to be designed to reconstruct the system state. Therefore, a finite-time multi-dimensional state reconstructor is designed and is used for simultaneously estimating the unknown state and interference of the system. The control purpose of stabilizing the second-order multi-agent disturbed system in the global finite time is achieved.

Description

Technical Field

[0001] The present invention relates to a multi-agent consensus protocol, and specifically to a study on a non-smooth consensus protocol and anti-interference performance based on a leaderless multi-agent system Background Art

[0002] With the development of modern control theory and distributed systems, multi-agent systems have gradually become a research hotspot. Such systems are composed of multiple interacting agents and are widely applied in fields such as robot swarms, unmanned aerial vehicle formations, sensor networks, and autonomous driving. The key challenge in multi-agent systems is how to achieve global coordination among agents through local communication and information interaction, so as to accomplish goals such as consensus, cooperation, and optimization. In this context, the consensus problem, as a fundamental problem in multi-agent systems, has received extensive attention The consensus problem aims to design a control protocol such that the states of all agents tend to be consistent based on local information interaction, that is, to achieve a globally coordinated state. Traditional consensus protocols are mostly based on the assumption of smooth dynamical systems, while in practical applications, the dynamics of agents often exhibit non-smooth characteristics. For example, due to factors such as friction, hard collisions, or discontinuous control, the motion or behavior of agents may be discontinuous. This makes it difficult to directly apply traditional control methods based on smooth conditions, thus giving rise to the research on consensus control protocols for non-smooth systems

[0003] Non-smooth consensus protocols focus on solving the consensus problem in non-smooth dynamical systems, and their core lies in dealing with the discontinuity and local non-smoothness of the system. As a typical method of non-smooth consensus protocols, sliding mode control uses the design of a sliding surface to make the states of agents slide on the sliding surface, thereby effectively dealing with non-smoothness problems. In addition, switching control strategies further improve the consensus performance of the system under non-smooth conditions by switching between different dynamical models

[0004] In practical applications, non-smooth consensus protocols and anti-interference technologies often need to be co-designed. On the one hand, non-smooth consensus protocols deal with discontinuous dynamics problems in agent systems; on the other hand, anti-interference technologies enhance the robustness of the system in complex environments Summary of the Invention

[0005] The purpose of the present invention is to propose a study on a non-smooth consensus protocol and anti-interference performance based on a leaderless multi-agent system, which can effectively address discontinuous problems such as friction, collisions, switch control, or discontinuous communication existing in agent dynamics

[0006] The specific technical solution of the present invention is as follows: A study on a non-smooth consensus protocol and anti-interference performance based on multi-agents includes the following steps:

[0007] According to the given communication topology graph \(G\), represent it with the adjacency matrix \(A\), where \(A\) ij represents the edge weight between vertices \(i\) and \(j\). If there is no edge between vertices \(i\) and \(j\), then \(A\) ij is \(0\).

[0008]

[0009] Calculate the degree matrix \(D\). The elements on the diagonal of the degree matrix \(D\) ij represent the degree of the vertex.

[0010]

[0011] Calculate the Laplacian matrix, \(L = D - A\).

[0012]

[0013] Based on the leaderless multi-agent system, establish the following dynamic model:

[0014]

[0015] where \(i\in V=\{1,\ldots,n\}\) represents the number of agents, \(n\) represents the number of agents, \(x\) i \(=[x\) i，1 , \(x\) i，2 \) T is the system state, \(u\) i is the control input, and \(y\) i is the output.

[0016] To study the robustness and adaptability of the multi-agent system more comprehensively, introduce the matching perturbation and mismatching perturbation into the dynamic model

[0017]

[0018] where \(i\in V=\{1,\ldots,n\}\) represents the number of agents, \(n\) represents the number of agents, \(x\) i \(=[x\) i,1 , \(x\) i，2 \) T is the system state, \(u\) i is the control input, and \(y\) i is the output. \(d\) i,1 , \(d\) i，2 represent the mismatching perturbation and matching perturbation respectively

[0019] Design a virtual velocity so that the states of the multi-agents reach consensus within a fixed time.

[0020] First, define the virtual velocity \(x\) * i，2is the reference value of x i，2 ;

[0021] According to the distributed control objective, the error term f is defined as: i :

[0022]

[0023] where f i is the position error between node i and its neighbors, and a ij > 0 is the connection weight.

[0024] The virtual velocity x * i，2 is the reference value of x i，2 used to guide x i，1 to achieve the goal.

[0025] Secondly, according to the objective f i → 0, the virtual velocity can be designed as:

[0026]

[0027] where f i is the position error, is a function with non-linear characteristics that can improve the robustness of the system, and α 1 , α 2 > 0 are non-linear adjustment parameters, and k 1 , k 2 > 0 are gain coefficients.

[0028] Substitute into x * i，2 ;

[0029]

[0030] where a ij is an element of the adjacency matrix A of the multi-agent communication topology graph G, k 1 , k 2 are positive numbers, α 1 ∈(0, 1), α 2 > 1 sig(x) = sign(x)|x|, x > 0, x ∈ R, and sign(x) is the sign function.

[0031] Define the velocity error e i :

[0032]

[0033] Take the derivative of the velocity error for calculation

[0034]

[0035] Calculate the control law u i :

[0036]

[0037] where u i represents the control law, e i represents the velocity error, sig() is a function with non-linear characteristics, N i is the set of neighbor nodes of node i, k 1 , k 2 , k 3 , k 4 are control parameters, p 1 ∈(0, 1), P 2 > 1, D i is the upper bound of the disturbance.

[0038] Since not all states can be directly obtained by measurement in practical applications, an observer needs to be designed to reconstruct the system state. For this purpose, a finite-time extended state observer for simultaneously estimating the unknown states and disturbances of the system is designed.

[0039] Consider the second-order perturbed system:

[0040]

[0041] where, x 1 , x 2 are the system states, u is the control input, and d(t) is the external disturbance

[0042] If the disturbance in the system is first-order differentiable and is Lipschitz continuous with the Lipschitz constant L known, then the following non-linear reconstructor is designed for the system:

[0043]

[0044] where, the weights μ 0 , μ 1 , μ 2 > 0, are the estimated values of x 1 , x 2 , d respectively, then this reconstructor is finite-time convergent.

[0045] Define the reconstruction error The reconstruction error system can be obtained:

[0046]

[0047] Because there exists a gain μ greater than zero0 , μ 1 , μ 2 , so the observation error system is finite-time stable.

[0048] Consider a second-order system with mismatched disturbances:

[0049]

[0050] Let the disturbance d in the system i，1 be twice differentiable, and d i，2 be once differentiable and be Lipschitz continuous, and their Lipschitz constants be L 1 , L 2

[0051] Let The system can be transformed as follows:

[0052]

[0053] According to the transformed system, set up the following observer:

[0054]

[0055] is the value reconstructed after passing through the reconstructor

[0056] Define the virtual velocity

[0057]

[0058] where a ij is an element of the adjacency matrix A of the multi-agent communication topology graph G, k 1 , k 2 is a positive number, β 1 ∈(0, 1), β 2 > 1. sig(x) = sign(x)|x|, x > 0, x ∈ R, and sign(x) is the sign function.

[0059] Define the velocity error e i * :

[0060]

[0061] Take the derivative of the velocity error

[0062]

[0063] Calculate the control law u i* is:

[0064]

[0065] where \(u\) * i represents the control law, \(e\) * i represents the velocity error, sig() is a function with non-linear characteristics, \(N\) i is the set of neighbor nodes of node \(i\), \(l\) 1 , \(l\) 2 , \(l\) 3 , \(l\) 4 are control parameters, \(q\) 1 \(\in(0, 1)\), \(q\) 2 \(> 1\), \(D\) i is the upper bound of the disturbance. Advantageous Effects

[0066] Compared with the prior art, the advantages of the present invention are as follows: The present invention designs a non-smooth consensus protocol based on a leaderless multi-agent system, and by introducing a reconstructor, the protocol can achieve consensus by using partial available data without directly obtaining the complete system state information, making up for the deficiencies of unobservable partial states or inaccurate measurement data. Compared with traditional consensus protocols, it has better steady-state performance when subject to external disturbances and better accuracy when facing unobservable partial states. Brief Description of the Drawings

[0066] Figure 1 is the flow chart of the present invention;

[0066] Figure 2 is the communication topology diagram adopted by the present invention;

[0067] Figure 3 is the speed response curve of the system under the method proposed by the present invention;

[0068] Figure 4 is the position response curve of the system under the method proposed by the present invention; Detailed Embodiments

[0069] The following further clarifies the present invention in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art fall within the scope defined by the appended claims of this application.

[0070] As Figure 1 shown, a study on a non-smooth consensus protocol and anti-interference performance based on a leaderless multi-agent system includes the following steps:

[0071] Step 1: Calculate the Laplacian matrix according to the communication topology diagram;

[0072] Step 2: Establish a dynamic model;

[0073] Step 3: Design the virtual velocity \(x\) * i，2 , define the velocity error \(e\) i ;

[0074] Step 4: Derive the control law \(u\) by differentiating the velocity error i ;

[0075] Step 5: Introduce a reconstructor to convert \(x\) i,2 , \(d\) into

[0076] Step 6: According to the reconstructed Substitute and recalculate the control law \(u\) * i ;

[0077] The following introduces an embodiment of the present invention:

[0078] Consider a leaderless multi-agent system, whose corresponding dynamic model is:

[0079]

[0080] Design the control law:

[0081]

[0083] Figure 1 is the method flow chart of the embodiment of the present invention; applying the proposed method, the communication topology diagram of this multi-agent is as Figure 2 shown, the velocity response curve of the system is as Figure 3 shown, and the position response curve is as Figure 4 shown. It can be seen from this that for the finite-time stabilization problem of a mismatched and disturbed multi-agent system, in order to simultaneously estimate the unmeasurable states and disturbances of the system, a multi-dimensional state reconstructor with finite-time convergence is designed. Based on the backstepping method and the homogeneity theory, a fixed-time composite controller is designed to achieve the control purpose of globally stabilizing the disturbed system in finite time.

Claims

1. A study on non-smooth consensus protocol and anti-interference performance based on leaderless multi-agent system, characterized in that: The following steps are involved: Step 1: Based on the communication topology diagram, establish the Laplacian matrix between the agent formations to determine the coupling strength between the agents and whether they are interoperable; Step 2: Establish a dynamic model based on the leaderless intelligent agent system and introduce mismatched disturbances and matched disturbances; Step 3: Design a virtual speed based on the backstepping method so that the states of multiple agents reach consistency within a fixed time; Step 4: Based on the fixed-time control method, the control rate is designed so that the actual speed of the multi-agent system can track the virtual speed within a fixed time in the presence of complex interference.

2. The research on non-smooth consensus protocol and anti-interference performance based on leaderless multi-agent according to claim 1 is characterized in that: In step 1, based on the communication topology diagram, the Laplacian matrix between the agent formations is established to determine the coupling strength between the agents and whether they are interoperable. The specific steps are as follows: First, based on the given communication topology graph G, it is represented by the adjacency matrix A, where A ij represents the edge weight between vertices i and j. If there is no edge between vertices i and j, then A ij is 0. Next, calculate the degree matrix D, where D is the diagonal element of the matrix D ij Indicates the degree of the vertex. Finally, the Laplacian matrix is ​​calculated. L = DA 。 3. The research on the non-smooth consensus protocol and anti-interference performance based on multi-agent according to claim 2 is characterized in that: In step 2, a dynamic model is established based on the leaderless intelligent agent system, and mismatched disturbances and matched disturbances are introduced. The specific steps are as follows: Where i∈V={1,…,n} represents the number of agents, n represents the number of agents, x i =[x i,1 , x i，2 ] T is the system status, u i is the control input, y i is the output, d i，1 , d i，2 represent mismatched interference and matched interference respectively.

4. The research on the non-smooth consensus protocol and anti-interference performance based on multi-agent according to claim 3 is characterized in that: Based on the backstepping method, a virtual speed is designed so that the states of multiple agents can reach consistency within a fixed time. The specific steps are as follows: First, define a virtual speed x * i，2 For x i，2 Reference value of Secondly, the error term is defined according to the distributed control objective Among them f i is the position error between node i and its neighbors, a ij >0 is the connection weight; Finally, according to the target f i →0, virtual speed can be designed Among them, e i is the position error, It is a function with nonlinear characteristics, which can improve the robustness of the system. α1, α2>0 are nonlinear adjustment parameters, and k1, k2>0 are gain coefficients. The error term will be Bring in x * i，2 , the virtual speed can be defined as x * i，2 : Among them, a ij is the element of the adjacency matrix A of the multi-agent communication topology structure graph G, k1, k2 are positive numbers, ɑ1∈(0, 1), α2>1. sig(x)=sign(x)|x|, x>0, x∈R.

5. The research on the non-smooth consensus protocol and anti-interference performance based on multi-agent according to claim 4 is characterized in that: Based on the fixed time control method, the control rate is designed so that the actual speed of the multi-agent can track the virtual speed within a fixed time in the presence of compound interference. The specific steps are as follows: B001: Based on the backstepping method, the speed error e can be defined i : B002: Derivative of speed error: B002: Calculate the control law u i : Where u i represents the control law, e i Represents the speed error, sig() is a function with nonlinear characteristics, N i is the set of neighbor nodes of node i, k1, k2, k3, k4 are control parameters, p i ∈(0,1),p2>1,D i is the perturbation upper bound. B003: Assume that in the system, the interference d i，1 Second order differentiable, d i，2 First-order differentiable and are Lipschitz continuous, and their Lipschitz constants are L1 and L2 respectively. Let The system can be transformed into the following: B004: Set up the following reconstructor according to the converted system: in is the value observed after passing through the observer, L i is the Lipschitz constant, μ i，0 , μ i，1 , μ i，2 >0 is the reconstructor weight. B005: Redefine virtual speed based on observed values B006: Define speed error e i * : B007: Calculate control law u i * : Where u * i represents the control law, e * i Represents the speed error, sig() is a function with nonlinear characteristics, N i is the set of neighbor nodes of node i, l1, l2, l3, l4 are control parameters, q1∈(0,1), q2>1, D i is the perturbation upper bound.

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