Multi-agent system finite pulse control method with packet loss and parameter mismatching

Abstract

The invention provides a finite pulse control method for a multi-agent system with packet loss and parameter mismatching, and relates to the field of agent control, and the method comprises the steps: setting a precondition of a time-delay multi-agent system with packet loss and parameter mismatching; establishing a dynamic model of the time-delay multi-agent system; and designing a finite pulse control protocol and an auxiliary function for simulating a packet loss process, and realizing finite pulse control on the multi-agent system with packet loss and parameter mismatching in combination with a precondition and a dynamic model. The problem of leader-follower consistency of a non-linear time-delay multi-agent system with pulse control under the conditions of data packet loss and parameter mismatching is solved.

Description

Technical Field

[0001] The present application relates to the field of intelligent agent control, and in particular to a finite pulse control method for a multi-agent system with packet loss and parameter mismatch. Background Art

[0002] In the wide application of modern complex network systems, the coordination and consistency of multi-agent systems has become an important research topic. By rationally designing control strategies, multiple agents can achieve consistent goals in a distributed environment, which is of great significance for practical applications in the fields of drone formations, distributed sensor networks, and autonomous driving systems. However, in practical applications, multi-agent systems are often interfered by various unforeseen factors, among which communication packet loss and parameter mismatch are the two most challenging problems.

[0003] Communication packet loss refers to the situation in which information transmission between agents in a multi-agent system cannot be timely or completely delivered due to network delays, bandwidth limitations, or signal interference. This phenomenon not only leads to incomplete or delayed information, but also has a significant impact on the consistency control of the system and may even undermine the stability of the system. In addition, the time lag problem is another challenge that cannot be ignored. The existence of time lag makes the information exchange between agents more complicated and may cause oscillation or instability. Therefore, how to design an effective control strategy in the presence of communication packet loss, parameter mismatch, and time lag to ensure that the multi-agent system can achieve consistency is a difficult problem that needs to be solved urgently.

[0004] In practical systems, network communication is subject to different degrees of bandwidth and capacity constraints. In order to solve this communication constraint problem, many researchers have proposed many meaningful consensus control protocols for multi-agent systems by combining different models and conditions. For example, the paper “Network-based practical set consensus of multi-agent systems subject to input saturation” studies the consensus problem of multi-agent systems with input saturation. “Distributed edge event-triggered control of nonlinear fuzzy multiagent systems with saturation constraint hybrid impulsive protocols” uses the consensus control protocol proposed in “Exponential synchronisation of nonlinear multi-agent systems via distributed self-triggered hybrid control with virtual linked agents” to study the global consensus problem of multi-agent systems under the leader-follower framework when the actuators are saturated and the adjacent inputs are saturated. Therefore, the communication constraint problem in multi-agent systems is still a hot topic in current research and a problem that needs to be solved urgently. Summary of the invention

[0005] The purpose of the present invention is to provide a finite pulse control method for a multi-agent system with packet loss and parameter mismatch in order to solve the problem that the existing multi-agent control method cannot achieve consistency in the case of communication packet loss, parameter mismatch and time lag.

[0006] The above-mentioned purpose of the present application is achieved through the following technical solutions:

[0007] S1: Preconditions for setting up a time-delay multi-agent system with packet loss and parameter mismatch; the time-delay multi-agent system includes: UAV formation system and distributed sensing system;

[0008] S2: Establish a dynamic model of a multi-agent system with time delays;

[0009] S3: Design a finite impulse control protocol and auxiliary functions to simulate the packet loss process, combined with the premise and dynamic model, to achieve finite impulse control of multi-agent systems with packet loss and parameter mismatch.

[0010] Optionally, step S1 includes:

[0011] Setting prerequisite 1: For the nonlinear function g γ (·): R→R satisfies the Lipschitz continuity condition,

[0012] |g γ (s1)-g γ (s2)|≤l η |s1-s2|,η=1,2

[0013] Among them, l η >0 is the Lipschitz constant; R→R represents the function g γ (·) is continuous in the real number domain; s1, s2 represent the function g γ The two variable values ​​in (·) correspond to the follower s i and the state of leader s0;

[0014] Set prerequisite 2: All topologies are connected, and when a leader exists, at least one follower communicates with the leader.

[0015] Optionally, step S1 further includes:

[0016] Lemma 1: Let matrices U, V∈R n , And V=(v1,v2,…,v n ) T And n∈N + , let K be an n-dimensional diagonal matrix K i The collection of K i The elements in are 1 or 0; U represents the target vector subject to saturation constraint; V is a given n-dimensional vector, whose vector elements are all less than 1;

[0017] definition Obviously Ki- belongs to the set K; when |v i |≤1, i=1,…,n, we get Where co{·} represents the convex hull of a set of vectors; sat represents the saturation function;

[0018] For Lemma 1, when n = 2,

[0019] For matrices U, V∈R n ,gather The elements in are composed of the elements in matrices U and V;

[0020] If s∈R n And G,H∈R n×n , when ||Hs|| ∞ ≤1, so we have G and H represent control matrices;

[0021] Existence constant α i Satisfy 0≤α i ≤1 and Make Established;

[0022] Lemma 2: Let the matrices Φ, Ψ∈R n×n , and the matrices Φ and Ψ are both positive definite and symmetric, then λ min (Φ -1 Ψ)Ω T ΦΩ≤Ω T ΨΩ≤λ max (Φ -1 Ψ)Ω T ΦΩ; Φ and Ψ represent positive definite symmetric matrices;

[0023] For Lemma 2, if the matrix Φ is the identity matrix, then

[0024] λ min (Ψ)Ω T Ω≤Ω T ΨΩ≤λ max (Ψ)Ω T Ω

[0025] Lemma 3: Let the matrices Υ, Θ∈R n×n , and there exists a positive constant ρ, then

[0026]

[0027] Optionally, step S1 further includes:

[0028] Definition 1: If It always holds true, indicating that the leader and followers of the multi-agent system have reached a consensus, where i = 1, 2, ..., n, s0 is the state of the leader in the time-delay multi-agent system, s i is the state of the follower in the time-delay multi-agent system;

[0029] Definition 2: Let Q(t,γ) and represents the number of valid pulses and the total number of pulses in the control process of the time-delay multi-agent system, and the pulse data packet loss rate is defined as

[0030]

[0031] If there exists a positive integer Q0 and a positive Make

[0032]

[0033] Then the pulse time series t k ,k∈Z+ The reverse average residence time is Where t≥γ≥0, Q0 is the jitter boundary.

[0034] Optionally, step S2 includes:

[0035] Let s0 be the state of the leader in the time-delay multi-agent system, s i is the state of the follower in the time-delay multi-agent system, i = 1, 2, ..., n, and the dynamic model of n followers is as follows:

[0036]

[0037] The dynamic model of a leader is:

[0038]

[0039] in, represents the state of the follower at the next moment; g1(·) represents a continuous nonlinear function; g2(·) represents a continuous nonlinear function; s i (t)∈R n and s0(t)∈R n represents the state of agent i and the leader; a0, a i ,b0,b i ,c0,c i is the system parameter, τ is the delay parameter, p i (t) is the finite pulse control protocol to be designed.

[0040] Optionally, step S3 includes:

[0041] Define auxiliary functions to simulate the packet loss process as follows:

[0042]

[0043] The finite pulse control protocol is designed as follows:

[0044]

[0045] Where m(t k ) represents the packet loss function at the pulse time, d i and represents the pulse intensity, δ(·) is the Dirac function; a ij represents the information interaction relationship between followers i and j, which is closely related to the topological structure of the time-delay multi-agent system; s i (t k ) and s j (t k ) represent followers i and j at pulse time t k status.

[0046] Optionally, step S3 further includes:

[0047] Assuming that the time-delay multi-agent system is continuous, the dynamic model of the time-delay multi-agent system can be written as:

[0048]

[0049] where Δs i (t k ) represents the state tracking error at the pulse time under the saturation constraint;

[0050] Define the state tracking error between the follower and the leader as φ i (t) = s i (t)-s0(t);

[0051] According to φ i (t), the impulse error of the time-delay multi-agent system is derived as

[0052]

[0053] Where φ(t)=[φ1(t),φ2(t),…,φ n (t)] T ;G1(t,φ(t))=[g(s1(t))-g(s0(t)),g(s2(t))-g(s0(t)),…,g(s n (t))-g(s0(t))] T ;G2(t,φ(g-τ))=[g(s1(g-τ))-g(s0(t-τ)),g(s2(t-τ))-g(s0(t-τ)),…,g(s n (g-τ))-g(s0(t-τ))] T ; Z = is a diagonal matrix with diagonal elements A=diag[a i ],B=diag[b i ],C=diag[c i ],D=diag[d i ]; are all diagonal matrices and their diagonal elements are (a i -a0), (b i -b0) and (c i -c0);

[0054] make There exists a constant Make F(t,s0(t)) represents a composite function, where F is a function of s0, and s0 is a function of time t.

[0055] Optionally, Theorem 1: Under the control of the finite impulse control protocol, if all conditions in equation (7) are satisfied, the leader and followers of the time-delay multi-agent system can eventually reach a consensus:

[0056]

[0057] Where λ4 represents the matrix I n - the smallest eigenvalue of Z; It is a decomposition item containing packet loss information; Represents the number of pulses from t0 to time t; represents the average ratio coefficient of Q pulses; represents the ratio coefficient of the ιth pulse; Indicates the packet loss rate; represents the average residence time of the pulse in the reverse direction; ζ1, ζ2 and ζ3 are parameters in solving ordinary differential equations, ζ is another parameter used when scaling the solution of ordinary differential equations; sup represents the supremum; V(ρ) is the Lyapunov equation; χ represents the initial value of V(ρ) at t0;

[0058] Proof: Construct the Lyapunov function V(t) as

[0059] V(t)=φ T (t)φ(t) (8)

[0060] When t≠t k When , the derivative of the Lyapunov function is derived as

[0061]

[0062] From Premise 1, Lemma 2 and Lemma 3, we get

[0063]

[0064] where λ1=λ max (B) For the term with delayed information and the term with F(t,s0(t)), we derive

[0065]

[0066] as well as

[0067]

[0068] where λ2=λ max (C), further deduced from equations (9) to (12)

[0069]

[0070] in and

[0071] When t = t k When , the Lyapunov function becomes

[0072]

[0073] Packet loss only occurs at the pulse time, so when packet loss occurs, Δφ i (t k )=0

[0074] Suppose that among the Q pulses, Q1 pulses have no packet loss, and the remaining Q-Q1 pulses have packet loss. When k∈[1,Q1], we have

[0075]

[0076] where λ4=λ min (I n -Z);

[0077] By condition A in Theorem 1, we can get

[0078]

[0079] Therefore, when t∈[t0,t1], from equations (13) and (16) we can obtain

[0080]

[0081] Similarly, when t∈(t1,t2], we get

[0082]

[0083] Therefore, after repeated iterations, when t∈(t k ,t k+1 ], we further get

[0084]

[0085] Let each term in V(t) be V1(t), V2(t), ..., V k+1 (t);

[0086] Based on condition B in Theorem 1 and considering the packet loss rate V1(t) is further derived as

[0087]

[0088] in represents the ratio coefficient of the Qth pulse. According to condition C, we have

[0089]

[0090] Therefore, V1(t) is exponentially decaying, and the second term V2(t) in V(t) is processed as follows:

[0091]

[0092] According to condition C, V2(t) shows exponential decay; by deduction, the other items in V(t) also show exponential decay;

[0093] It is concluded that when t→∞, V(t)→0, the states of the leader and the follower can eventually reach a consensus, that is, finite impulse control of the multi-agent system with packet loss and parameter mismatch is achieved.

[0094] The beneficial effects of the technical solution provided by this application are:

[0095] The leader-follower consistency problem of a nonlinear time-delay multi-agent system is considered. Through theoretical analysis, sufficient conditions to ensure that the nonlinear time-delay multi-agent system reaches a consensus are derived. In order to make the system model more suitable for practical problems, on the basis of the traditional leader-follower nonlinear time-delay model, the mismatch problem of system parameters is considered more deeply, and a more complex dynamic model is constructed for analysis. In order to reduce the communication frequency, the present invention proposes a saturation constrained pulse control strategy. At the same time, in order to further fit the actual communication situation, the packet loss situation is considered during the communication process, and an auxiliary function is defined to describe the process. This application considers the system parameter mismatch problem between the leader and follower dynamics; considers the packet loss situation during the communication process, and defines an auxiliary function to describe the communication process of packet loss. Setting a new pulse control protocol with limited pulses can effectively reduce the pulse control amount, avoid system disorder caused by excessive control amount, and further improve control accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] The present application will be further described below with reference to the accompanying drawings and embodiments, in which:

[0097] Figure 1 is a control framework diagram in an embodiment of the present application;

[0098] Figure 2 is a leader-follower system topology diagram in an embodiment of the present application;

[0099] Figure 3 is a first state diagram of each intelligent agent of pure impulse control in the embodiment of the present application;

[0100] Figure 4 is the first error graph of each intelligent agent of pure impulse control in the embodiment of the present application;

[0101] Figure 5 is a second state diagram of each intelligent agent of finite impulse control in an embodiment of the present application;

[0102] Figure 6 It is the second error graph of each intelligent agent in the finite impulse control in the embodiment of the present application. DETAILED DESCRIPTION

[0103] In order to have a clearer understanding of the technical features, purposes and effects of the present application, the specific implementation methods of the present application are now described in detail with reference to the accompanying drawings.

[0104] An embodiment of the present application provides a finite impulse control method for a multi-agent system with packet loss and parameter mismatch.

[0105] Please refer to Figure 1 , Figure 1 : is a control framework diagram of a finite impulse control method for a multi-agent system with packet loss and parameter mismatch in an embodiment of the present application, including:

[0106] S1: Preconditions for setting up a time-delay multi-agent system with packet loss and parameter mismatch; the time-delay multi-agent system includes: UAV formation system and distributed sensing system;

[0107] Step S1 includes:

[0108] Setting prerequisite 1: For the nonlinear function g γ (·): R→R satisfies the Lipschitz continuity condition,

[0109] |g γ (s1)-g γ (s2)|≤l η |s1-s2|,η=1,2

[0110] Among them, l η >0 is the Lipschitz constant; R→R represents the function g γ (·) is continuous in the real number domain; s1, s2 represent the function g γ The two variable values ​​in (·) correspond to the follower s i and the state of leader s0;

[0111] Set prerequisite 2: All topologies are connected, and when a leader exists, at least one follower communicates with the leader.

[0112] Step S1 also includes:

[0113] Lemma 1: Let matrices U, V∈R n , And V=(v1,v2,…,v n ) T And n∈N + , let K be an n-dimensional diagonal matrix K i The collection of K i The elements in are 1 or 0; U represents the target vector subject to saturation constraint; V is a given n-dimensional vector, whose vector elements are all less than 1;

[0114] Specifically, U represents the target vector subject to saturation constraint; V is a given n-dimensional vector whose vector elements are all less than 1, that is, |v i |≤1, and infinite norm The meanings are the same; U is known and generally represents the control quantity, while Indicates which elements in U and V can be represented by K i and This is a commonly used saturation constraint method.

[0115] definition Apparently belongs to the set K; when |v i |≤1, i=1,…,n, we get Where co{·} represents the convex hull of a set of vectors; sat represents the saturation function;

[0116] For Lemma 1, when n = 2,

[0117] For matrices U, V∈R n ,gather The elements in are composed of the elements in matrices U and V;

[0118] If s∈R n And G,H∈R n×n , when ||Hs|| ∞ ≤1, so we have G and H represent control matrices;

[0119] Specifically, let s represent the control quantity, which is an n-dimensional vector, and G represents the control matrix, which is used to perform a linear transformation on s. Then Gs corresponds to U above, and similarly Hs corresponds to V above.

[0120] Existence constant α i Satisfy 0≤α i ≤1 and Make Established;

[0121] Specifically, the saturation constraint Denotes sat(Gs) by the set The elements in the formula are composed of a certain proportion, and the total proportion is 1, which is the existence constant α described in the lemma. i Satisfy 0≤α i ≤1 and Make Established, so far the control amount is constrained within -1 to 1.

[0122] Lemma 2: Let the matrices Φ, Ψ∈R n×n , and the matrices Φ and Ψ are both positive definite and symmetric, then λ min (Φ -1 Ψ)Ω T ΦΩ≤Ω T ΨΩ≤λ max (Φ -1 Ψ)Ω T ΦΩ; Φ and Ψ represent positive definite symmetric matrices;

[0123] For Lemma 2, if the matrix Φ is the identity matrix, then

[0124] λ min (Ψ)Ω T Ω≤Ω T ΨΩ≤λ max (Ψ)Ω T Ω

[0125] Lemma 3: Let the matrices Υ, Θ∈R n×n , and there exists a positive constant ρ, then

[0126]

[0127] Step S1 also includes:

[0128] Definition 1: If It always holds true, indicating that the leader and followers of the multi-agent system have reached a consensus, where i = 1, 2, ..., n, s0 is the state of the leader in the time-delay multi-agent system, s i is the state of the follower in the time-delay multi-agent system;

[0129] Definition 2: Let Q(t,γ) and represents the number of valid pulses and the total number of pulses in the control process of the time-delay multi-agent system, and the pulse data packet loss rate is defined as

[0130]

[0131] If there exists a positive integer Q0 and a positive Make

[0132]

[0133] Then the pulse time series t k ,k∈Z + The reverse average residence time is Where t≥γ≥0, Q0 is the jitter boundary.

[0134] S2: Establish a dynamic model of a multi-agent system with time delays;

[0135] Step S2 includes:

[0136] Specifically, the present invention mainly discusses the leader-follower problem of multiple agents. In the system, the follower receives information directly from the leader and designates agent s0 as the leader.

[0137] Let s0 be the state of the leader in the time-delay multi-agent system, s i is the state of the follower in the time-delay multi-agent system, i = 1, 2, ..., n, and the dynamic model of n followers is as follows:

[0138]

[0139] The dynamic model of a leader is:

[0140]

[0141] in, represents the state of the follower at the next moment; g1(·) represents a continuous nonlinear function; g2(·) represents a continuous nonlinear function; s i (t)∈R n and s0(t)∈R n represents the state of agent i and the leader; a0, a i ,b0,b i ,c0,c i is the system parameter, τ is the delay parameter, p i (t) is the finite pulse control protocol to be designed.

[0142] S3: Design a finite impulse control protocol and auxiliary functions to simulate the packet loss process, combined with the premise and dynamic model, to achieve finite impulse control of multi-agent systems with packet loss and parameter mismatch.

[0143] Step S3 includes:

[0144] Specifically, in the actual communication process of intelligent agents, due to the increasingly complex communication environment, communication data often cannot be transmitted to the correct location due to various reasons, resulting in data packet loss, communication information loss, and actual control loss of the multi-agent system.

[0145] Define auxiliary functions to simulate the packet loss process as follows:

[0146]

[0147] The finite pulse control protocol is designed as follows:

[0148]

[0149] Where m(t k ) represents the packet loss function at the pulse time, d i and represents the pulse intensity, δ(·) is the Dirac function; a ij represents the information interaction relationship between followers i and j, which is closely related to the topological structure of the time-delay multi-agent system; s i (t k ) and s j (t k ) represent followers i and j at pulse time t k status.

[0150] Step S3 also includes:

[0151] Assuming that the time-delay multi-agent system is continuous, the dynamic model of the time-delay multi-agent system can be written as:

[0152]

[0153] where Δs i (t k ) represents the state tracking error at the pulse time under the saturation constraint;

[0154] Define the state tracking error between the follower and the leader as φ i (t) = s i (t)-s0(t);

[0155] According to φ i (t), the impulse error of the time-delay multi-agent system is derived as

[0156]

[0157] Where φ(t)=[φ1(t),φ2(t),…,φ n (t)] T ;G1(t,φ(t))=[g(s1(t))-g(s0(t)),g(s2(t))-g(s0(t)),…,g(s n (t))-g(s0(t))] T;G2(t,φ(g-τ))=[g(s1(g-τ))-g(s0(t-τ)),g(s2(t-τ))-g(s0(t-τ)),…,g(s n (g-τ))-g(s0(t-τ))] T ; Z = is a diagonal matrix with diagonal elements A=diag[a i ],B=diag[b i ],C=diag[c i ],D=diag[d i ]; are all diagonal matrices and their diagonal elements are (a i -a0), (b i -b0) and (c i -c0);

[0158] make There exists a constant Make F(t,s0(t)) represents a composite function, where F is a function of s0, and s0 is a function of time t.

[0159] Step S3 also includes:

[0160] Theorem 1: Under the control of the finite impulse control protocol, if all the conditions in equation (7) are satisfied, the leader and followers of the time-delay multi-agent system can eventually reach a consensus:

[0161]

[0162] Where λ4 represents the matrix I n - the smallest eigenvalue of Z; It is a decomposition item containing packet loss information; Represents the number of pulses from t0 to time t; represents the average ratio coefficient of Q pulses; represents the ratio coefficient of the ιth pulse; Indicates the packet loss rate; represents the average residence time of the pulse in the reverse direction; ζ1, ζ2 and ζ3 are parameters in solving ordinary differential equations, ζ is another parameter used when scaling the solution of ordinary differential equations; sup represents the supremum; V(ρ) is the Lyapunov equation; χ represents the initial value of V(ρ) at t0;

[0163] Proof: Construct the Lyapunov function V(t) as

[0164] V(t)=φ T (t)φ(t) (8)

[0165] When t≠t k When , the derivative of the Lyapunov function is derived as

[0166]

[0167] From Premise 1, Lemma 2 and Lemma 3, we get

[0168]

[0169] where λ1=λ max (B) For the term with delayed information and the term with F(t,s0(t)), we derive

[0170]

[0171] as well as

[0172]

[0173] where λ2=λ max (C), further deduced from equations (9) to (12)

[0174]

[0175] in and

[0176] When t = t k When , the Lyapunov function becomes

[0177]

[0178] Packet loss only occurs at the pulse time, so when packet loss occurs, Δφ i (t k )=0

[0179] Suppose that among the Q pulses, Q1 pulses have no packet loss, and the remaining Q-Q1 pulses have packet loss. When k∈[1,Q1], we have

[0180]

[0181] where λ4=λ min (I n -Z);

[0182] By condition A in Theorem 1, we can get

[0183]

[0184] Therefore, when t∈[t0,t1], from equations (13) and (16) we can obtain

[0185]

[0186] Similarly, when t∈(t1,t2], we get

[0187]

[0188] Therefore, after repeated iterations, when t∈(t k ,t k+1 ], we further get

[0189]

[0190] Let each term in V(t) be V1(t), V2(t), ..., V k+1 (t);

[0191] Based on condition B in Theorem 1 and considering the packet loss rate V1(t) is further derived as

[0192]

[0193] in represents the ratio coefficient of the Qth pulse. According to condition C, we have

[0194]

[0195] Therefore, V1(t) is exponentially decaying, and the second term V2(t) in V(t) is processed as follows:

[0196]

[0197] According to condition C, V2(t) shows exponential decay; by deduction, the other items in V(t) also show exponential decay;

[0198] It is concluded that when t→∞, V(t)→0, the states of the leader and the follower can eventually reach a consensus, that is, finite impulse control of the multi-agent system with packet loss and parameter mismatch is achieved.

[0199] Simulation Analysis: A multi-agent system with 1 leader and 8 followers is established to verify the validity of Theorem 1. The topology of the system is as follows Figure 2 shown.

[0200] Specifically, multi-agent systems include: drone formation systems and distributed sensor systems. The leaders and followers of agents can be any entities with perception, decision-making and execution capabilities. Entities include: robots, automated equipment, software agents or other intelligent systems that can independently or collaboratively complete specific tasks.

[0201] The state of the agent is:

[0202]

[0203] Among them, the selection functions g1(·) and g2(·) are

[0204] g1(·)=cos(·)sin(·),g2(·)=cot(·)

[0205] The control parameter is set to t k -t k-1 =0.3, other parameters are selected as follows

[0206] ε=0.25,d i =0.25, ζ=3.9,χ=0.66

[0207] Since the finite pulse control proposed in the present invention is designed based on the traditional pure pulse control, the pure pulse control and the finite pulse control use the same topological structure and the same system parameters, which is convenient for comparison.

[0208] contrast Figure 3 and Figure 5 , when the saturation constraint is not considered, the state of the agent changes relatively greatly at the pulse time. For agent 8, when the first pulse time is 0.3 seconds, the state mutation value of the unconstrained pulse control protocol is significantly greater than 1; Figure 5 In the error simulation, the saturation constraint is considered and the upper and lower bounds of the constraint are ±1; therefore, the mutation value of agent 8 at time 0.3 does not exceed 1, which verifies the correspondence between the simulation and the theoretical proof. Figure 4 and Figure 6 The same situation also exists in . Comparing the control effects of the two control protocols, the finite impulse control can achieve more precise control, avoid large fluctuations in the state of the intelligent agent, and make the goal reach a stable state smoothly.

[0209] The above are only exemplary embodiments of the present disclosure and cannot be used to limit the scope of the present disclosure. That is, any equivalent changes and modifications made according to the teachings of the present disclosure are still within the scope of the present disclosure. After considering the disclosure of the specification and the truth of practice, those skilled in the art will easily think of other embodiments of the present disclosure.

[0210] This application is intended to cover any variation, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary technical means in the art not described in the present disclosure. The description and examples are to be regarded as exemplary only, and the scope and spirit of the present disclosure are defined by the claims.

Claims

1. A finite impulse control method for a multi-agent system with packet loss and parameter mismatch, characterized in that: The method comprises the following steps: S1: Setting the prerequisites for a time-delayed multi-agent system with packet loss and parameter mismatch; The time-delay multi-agent system includes: UAV formation system and distributed sensor system; S2: Establish a dynamic model of a multi-agent system with time delays; S3: Design a finite impulse control protocol and auxiliary functions to simulate the packet loss process, combined with the premise and dynamic model, to achieve finite impulse control of multi-agent systems with packet loss and parameter mismatch.

2. A finite impulse control method for a multi-agent system with packet loss and parameter mismatch as claimed in claim 1, characterized in that: Step S1 includes: Setting prerequisite 1: For the nonlinear function g γ (·): R→R satisfies the Lipschitz continuity condition, |g γ (s1)-g γ (s2)|≤l η |s1-s2|,η=1,2 Among them, l η >0 is the Lipschitz constant; R→R represents the function g γ (·) is continuous in the real number domain; s1, s2 represent the function g γ The two variable values ​​in (·) correspond to the follower s i and the state of leader s0; Set prerequisite 2: All topologies are connected, and when a leader exists, at least one follower communicates with the leader.

3. A finite impulse control method for a multi-agent system with packet loss and parameter mismatch as claimed in claim 2, characterized in that: Step S1 also includes: Lemma 1: Let matrices U, V∈R n , U=(u1,u2,…,u n ) T And V=(v1,v2,…,v n ) T And n∈N + , let K be an n-dimensional diagonal matrix K i The collection of K i The elements in are 1 or 0; U represents the target vector subject to saturation constraint; V is a given n-dimensional vector, whose vector elements are all less than 1; definition Apparently belongs to the set K; when |v i |≤1, i=1,...,n, we get Where co{·} represents the convex hull of a set of vectors; sat represents the saturation function; For Lemma 1, when n = 2, For matrices U, V∈Rn ， gather The elements in are composed of the elements in matrices U and V; If s∈R n And G, H∈R n×n , when ||Hs|| ∞ ≤1, so we have G and H represent control matrices; Existence constant α i Satisfy 0≤α i ≤1 and Make Established; Lemma 2: Let the matrices Φ, Ψ∈R n×n , and the matrices Φ and Ψ are both positive definite and symmetric, then λ min (Φ -1 Ψ)Ω T ΨΩ≤Ω T ΨΩ≤λ max (Φ -1 Ψ)Ω T ΦΩ; Φ and Ψ represent positive definite symmetric matrices; For Lemma 2, if the matrix Φ is the identity matrix, then l min (W)O T Ω≤Ω T PsO≤l max (W)O T Oh Lemma 3: Let the matrices γ, Θ∈R n×n , and there exists a positive constant ρ, then 4. A finite impulse control method for a multi-agent system with packet loss and parameter mismatch as claimed in claim 3, characterized in that: Step S1 also includes: Definition 1: If It always holds true, indicating that the leader and followers of the multi-agent system have reached a consensus, where i = 1, 2, ..., n, s0 is the state of the leader in the time-delay multi-agent system, s i is the state of the follower in the time-delay multi-agent system; Definition 2: Let Q(t,γ) and represents the number of valid pulses and the total number of pulses in the control process of the time-delay multi-agent system, and the pulse data packet loss rate is defined as If there exists a positive integer Q0 and a positive Make Then the pulse time series t k , k∈Z + The reverse average residence time is Where t≥γ≥0, Q0 is the jitter boundary.

5. A finite impulse control method for a multi-agent system with packet loss and parameter mismatch as claimed in claim 4, characterized in that: Step S2 includes: Let s0 be the state of the leader in the time-delay multi-agent system, s i is the state of the follower in the time-delay multi-agent system, i = 1, 2, ..., n, and the dynamic model of n followers is as follows: The dynamic model of a leader is: in, represents the state of the follower at the next moment; g1(·) represents a continuous nonlinear function; g2(·) represents a continuous nonlinear function; s i (t)∈R n and s0(t)∈R n represents the state of agent i and the leader; a0, a i , b0, b i , c0, c i is the system parameter, τ is the delay parameter, p i (t) is the finite pulse control protocol to be designed.

6. A finite impulse control method for a multi-agent system with packet loss and parameter mismatch as claimed in claim 5, characterized in that: Step S3 includes: Define auxiliary functions to simulate the packet loss process as follows: The finite pulse control protocol is designed as follows: Where m(t k ) represents the packet loss function at the pulse time, d i and represents the pulse intensity, δ(·) is the Dirac function; a ij represents the information interaction relationship between followers i and j, which is closely related to the topological structure of the time-delay multi-agent system; s i (t k ) and s j (t k ) represent followers i and j at pulse time t k status.

7. A finite impulse control method for a multi-agent system with packet loss and parameter mismatch as claimed in claim 6, characterized in that: Step S3 also includes: Assuming that the time-delay multi-agent system is continuous, the dynamic model of the time-delay multi-agent system can be written as: where Δs i (t k ) represents the state tracking error at the pulse time under the saturation constraint; Define the state tracking error between the follower and the leader as φ i (t) = s i (t)-s0(t); According to φ i (t), the impulse error of the time-delay multi-agent system is derived as Where φ(t)=[φ1(t), φ2(t),...,φ n (t)] T ;G1(t,φ(t))=[g(s1(t))-g(s0(t)), g(s2(t))-g(s0(t)),..., g(s n (t))-g(s0(t))] T ;G2(t,φ(t-τ))=[g(s1(t-τ))-g(s0(t-τ)), g(s2(t-τ))-g(s0(t-τ)),..., g(s n (t-τ))-g(s0(t-τ))] T ; is a diagonal matrix with diagonal elements A=diag[a i ],B=diag[b i ],C=diag[c i ],D=diag[d i ]; and are all diagonal matrices and their diagonal elements are (a i -a0), (b i -b0) and (c i -c0); make Then there is a constant Make F(t, s0(t)) represents a composite function, where F is a function of s0, and s0 is a function of time t.

8. A finite impulse control method for a multi-agent system with packet loss and parameter mismatch as claimed in claim 7, characterized in that: Step S3 also includes: Theorem 1: Under the control of the finite impulse control protocol, if all the conditions in equation (7) are satisfied, the leader and followers of the time-delay multi-agent system can eventually reach a consensus: Where λ4 represents the matrix I n - the smallest eigenvalue of Z; It is a decomposition item containing packet loss information; Represents the number of pulses from t0 to time t; represents the average ratio coefficient of Q pulses; represents the ratio coefficient of the ιth pulse; Indicates the packet loss rate; represents the average residence time of the pulse in the reverse direction; ζ1, ζ2 and ζ3 are parameters in solving ordinary differential equations, ζ is another parameter used when scaling the solution of ordinary differential equations; sup represents the supremum; V(ρ) is the Lyapunov equation; χ represents the initial value of V(ρ) at t0; Proof: Construct the Lyapunov function V(t) as V(t)=φ T (t)φ(t) (8) When t≠t k When , the derivative of the Lyapunov function is derived as From Premise 1, Lemma 2 and Lemma 3, we get where λ1=λ max (B) For the term with time-delay information and the term with F(t, s0(t)), we derive as well as where λ2=λ max (C), further deduced from equations (9) to (12) in and When t = t k When , the Lyapunov function becomes Packet loss only occurs at the pulse time, so when packet loss occurs, △φ i (t k )=0 Suppose that among the Q pulses, Q1 pulses have no packet loss, and the remaining Q-Q1 pulses have packet loss. When k∈[1,Q1], we have Whereλ4=λ min (I n -Z); According to condition A in Theorem 1, we can get Therefore, when t∈[t0, t1], we can obtain from equations (13) and (16) Similarly, when t∈(t1, t2], we get Therefore, after repeated iterations, when t∈(t k , t k+1 ], we further get Let each term in V(t) be V1(t), V2(t), ..., V k+1 (t); Based on condition B in Theorem 1 and considering the packet loss rate V1(t) is further derived as in represents the ratio coefficient of the Qth pulse. According to condition C, we have Therefore, V1(t) is exponentially decaying, and the second term V2(t) in V(t) is processed as follows: According to condition C, V2(t) shows exponential decay; by deduction, the other items in V(t) also show exponential decay; It is concluded that when t→∞, V(t)→0, the states of the leader and the follower can eventually reach a consensus, that is, finite impulse control of the multi-agent system with packet loss and parameter mismatch is achieved.

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