Method and device for consistent control of multi-agent system with asymmetric constraints on communication channels

Abstract

The present invention discloses a method and device for consistent control of a multi-agent system with asymmetric constraints on communication channels, including: obtaining a multi-agent system containing n agents, constructing the dynamic equations of each agent therein; constructing an undirected connected network of the multi-agent system; constructing a hybrid pulse control protocol through the dynamic equations and the undirected connected network, and combining an asymmetric input saturation constraint pulse control method with an event triggering method; and performing consistent control of the multi-agent system through the hybrid pulse control protocol. The present invention combines asymmetric saturation constraint pulse control with event triggering control, inherits the advantage of pulse control that does not require secondary sampling, and combines time triggering control to avoid invalid communication; estimates the attraction domain of asymmetric saturation constraints and error systems to reduce the conservatism of the control protocol.

Description

Technical Field

[0001] The present invention relates to the field of multi-agent control, and in particular to a method and device for consistent control of a multi-agent system with asymmetric communication channel constraints. Background Art

[0002] The paper [Event-Based Consensus Control of Multi-Agent Systems with InputSaturation Constraint] studied the event-triggered consistency problem of linear multi-agent systems with input saturation. It first analyzed the convergence regulation of the control protocol based on the trigger function under the condition of input saturation, and then considered the limitations of input saturation and input delay, designed the corresponding control protocol, realized the consistency control, and excluded the Zeno behavior for the trigger time series. However, this paper is aimed at linear multi-agent systems. In practice, nonlinear multi-agent systems are more widely used.

[0003] The paper [Leader-Following Consensus of Multi-Agent Systems via AdaptiveEvent-Based Control] applies the adaptive control method to the study of the consistency of linear multi-agent systems with leaders. Based on algebraic graph theory, matrix theory, stability theory and inequality technology, the leader-following consistency problem of multi-agent systems based on adaptive event control is studied. The adaptive function only depends on the local information of each agent at the time of the event. Under the designed event-based adaptive controller, leader-following consistency can be achieved by using only local information, and Zeno behavior is excluded. However, the case of channel restriction is not considered, which has limitations in practical applications. Summary of the invention

[0004] The technical problem solved by the present invention is that the prior art usually targets linear multi-agent systems and ignores the situation of channel limitation. Therefore, the present invention discloses a control method and device combining asymmetric input saturation constrained pulse control with event triggering method to solve the consistency problem of nonlinear multi-agent systems.

[0005] According to one aspect of the present invention, the present invention provides a method for consistent control of a multi-agent system with asymmetric constraints on communication channels, comprising the following steps:

[0006] Obtain a multi-agent system containing n agents and construct the dynamic equations of each agent;

[0007] Constructing an undirected connected network of the multi-agent system;

[0008] A hybrid pulse control protocol is constructed by using the dynamic equation and the undirected connected network and combining an asymmetric input saturation constrained pulse control method with an event triggering method;

[0009] Consistency control of multi-agent systems via a hybrid impulse control protocol.

[0010] Preferably, in the multi-agent system, the dynamic equation of each agent is:

[0011]

[0012] Among them, s i (t) represents the state value of the ith agent at the non-pulse moment, represents the derivative of the state value, s o (t) represents the state value of the leader in the multi-agent system at time t, represents the derivative of the leader state value, U i (t) is the control input of the multi-agent system, h(t, s i (t)) is a nonlinear function, and α is a preset constant.

[0013] Preferably, the step of constructing an undirected connected network of the multi-agent system comprises:

[0014] The multi-agent system communicates through an undirected connected network. The topology of the undirected connected network is defined as G = (v, ε), where v = {1, 2, ..., n} is a node set, each node represents an agent, and ε ∈ v × v represents a directed edge set;

[0015] Define A = [a ij ] is the weighted adjacency matrix, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix, is the degree matrix, b ij is the element in the i-th row and j-th column of the degree matrix. If for any two nodes v i ,v j If there is a path, then the undirected graph is connected, and the topology graph G contains m edges, and the m edges are marked as e g , where g∈[1,m], define L=DA as a Laplace matrix;

[0016] The incidence matrix is ​​defined as D = [d ij ],but

[0017] Preferably, the step of constructing a hybrid pulse control protocol by using the kinetic equation and the undirected connected network and combining an asymmetric input saturation constrained pulse control method with an event triggering method comprises:

[0018] Define δ(t) as an impulse function and define ψ(t) as an asymmetric saturation function that satisfies: in, They are all normal numbers;

[0019] Define a multi-agent system as left continuous, that is, let s i (t k )=s i (t k - ), s i (t k ) represents the i-th agent at t k The state value at the moment, s i (t k - ) represents the i-th agent at the pulse time t k The state value at the left limit value, and there is a constant ω greater than 0 so that the pulse time series {t k} satisfies the following inequality: 0<t0<t1<t2<...<t k <t k+1 And t k+1 -t k ≥ω, k is the pulse count;

[0020] According to the event triggering strategy: the edge marked is e m =(v i ,v j ), where m∈[1,g], g represents the number of edges in the graph, then the rules are as follows:

[0021]

[0022] in u m ,σ m is the preset constant, It represents the standard judgment state quantity of the mth edge at the kth pulse time, represents the actual decision state of the mth edge, φ m (t k ) represents the standard judgment state of the mth edge;

[0023] The hybrid pulse control protocol is constructed according to the inequality and the rule:

[0024]

[0025] Where k is the number of pulses, δ(t) represents the impulse function, and b i is the protocol gain, c i , f i is a preset constant, u i (t) is an intermediate variable, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix, s i (t k ) represents the i-th agent at t k The state value at the moment, s j (t k ) represents the jth agent at t k The state value at the moment, s o (t k ) indicates t k Status value of the moment leader, definition in It indicates the triggering time of the mth edge at the kth pulse time, and defines the event triggering time at the pulse time.

[0026] Preferably, in the process of performing consistency control on the multi-agent system by the hybrid pulse control protocol, the multi-agent system needs to meet the following conditions to achieve consistency:

[0027]

[0028] Among them, θ k ,γ k ,η is a constant, satisfying 0<θ k <1,η>0,λ1=λ min (M1M2),λ2=λ max (M1M2),θ k =λ min (2λ1Γ-λ 2 2Λ),λ3=λ max [(P T ) -1 FM1], λ4=λ max (I n -M1),λ5=λ max (I n -M1M2Γ),λ6=λ min [M1(I n -M1)], Γ, Λ are the designed system parameters, and P is defined as [p1, p2, …, p n ] T ,u=[u i ] T , Q = diag[q i], where ∈ i and is a positive constant, i = 1, 2, ... n, P, u are both vector matrices, M1 = QM, M2 = BL + C, B = diag[b1, b2, ..., b n ],C=[c1,c2,…,c n ], b i 、c i These are the designed system parameters. K i is an n-dimensional diagonal matrix, K - i =IK i , H is a diagonal matrix, |vx|≤1 is a constant.

[0029] According to a second aspect of the present invention, the present invention provides a multi-agent system consensus control device with asymmetric constraints on communication channels, comprising the following modules:

[0030] The dynamics equation construction module is used to obtain a multi-agent system containing n agents and construct the dynamics equations of each agent;

[0031] An undirected connected network construction module, used to construct an undirected connected network of the multi-agent system;

[0032] A hybrid pulse control protocol building module, used to build a hybrid pulse control protocol by using the dynamic equation and the undirected connected network, and combining an asymmetric input saturation constrained pulse control method with an event triggering method;

[0033] The consistency control module is used to perform consistency control on the multi-agent system through a hybrid pulse control protocol.

[0034] The beneficial effects brought by the technical solution provided by the present invention are:

[0035] (1) It combines asymmetric saturation constrained pulse control with event-triggered control, inheriting the advantage of pulse control that does not require secondary sampling, and combined with time-triggered control to avoid invalid communication.

[0036] (2) The attraction domain of the asymmetric saturation constraint and the error system is estimated to reduce the conservatism of the control protocol. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 This is a flow chart of a method according to an embodiment of the present invention;

[0038] Figure 2 It is the topological graph of an undirected connected network;

[0039] Figure 3is the error graph of the multi-agent system;

[0040] Figure 4 It is the state diagram of the multi-agent system;

[0041] Figure 5 A triggering timing diagram of a method according to an embodiment of the present invention;

[0042] Figure 6 This is a structural diagram of an embodiment of the present invention;

[0043] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0044] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0045] refer to Figure 1 This embodiment provides a method for consistent control of a multi-agent system with asymmetric communication channel constraints, including the following steps:

[0046] S1: Obtain a multi-agent system containing n agents, and construct a dynamic equation for each agent. In this embodiment, the dynamic equation for each agent is:

[0047]

[0048] Among them, s i (t) represents the state value of the ith agent at the non-pulse moment, represents the derivative of the state value, s o (t) represents the state value of the leader in the multi-agent system at time t, represents the derivative of the leader state value, U i (t) is the control input of the multi-agent system, h(t, s i (t)) is a nonlinear function, and α is a preset constant.

[0049] Define sign(.) as the sign function, sat(.) as the unit symmetric saturation function, when c∈R,

[0050]

[0051] S2: constructing an undirected connected network of the multi-agent system;

[0052] In this embodiment, step S2 includes:

[0053] S21: The multi-agent system communicates through an undirected connected network. The topology of the undirected connected network is defined as G = (v, ε), where v = {1, 2, ..., n} is a node set, each node represents an agent, and ε ∈ v × v represents a directed edge set;

[0054] S22: Define A = [a ij ] is the weighted adjacency matrix, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix, is the degree matrix, b ij is the element in the i-th row and j-th column of the degree matrix. If for any two nodes v i ,v j If there is a path, then the undirected graph is connected, and the topology graph G contains m edges, and the m edges are marked as e g , where g∈[1,m];

[0055] S23: Defined as the correlation matrix D = [d ij ],but

[0056] S3: constructing a hybrid pulse control protocol by using the dynamic equation and the undirected connected network, and combining an asymmetric input saturation constrained pulse control method with an event triggering method;

[0057] In this embodiment, step S3 includes:

[0058] S31: Define δ(t) as an impulse function and define ψ(t) as an asymmetric saturation function that satisfies: in, They are all normal numbers;

[0059] S32: Define the multi-agent system as left continuous, that is, let s i (t k )=s i (t k - ), s i (t k ) represents the i-th agent at t k The state value at the moment, s i (t k - ) represents the i-th agent at the pulse time t k The state value at the left limit value, and there is a constant ω greater than 0 so that the pulse time series {t k} satisfies the following inequality: 0<t0<t1<t2<...<t k <t k+1 And t k+1 -t k ≥ω, k is the pulse count;

[0060] S33: According to the event trigger strategy: the marked edge is e m =(v i ,v j ), where m∈[1,g], g represents the number of edges in the graph, then the rules are as follows:

[0061]

[0062] in u m ,σ m is the preset constant, It represents the standard judgment state quantity of the mth edge at the kth pulse time, represents the actual decision state of the mth edge, φ m (t k ) represents the standard judgment state of the mth edge;

[0063] S34: Construct the hybrid pulse control protocol according to the inequality and the rule:

[0064]

[0065] Where k is the number of pulses, δ(t) represents the impulse function, and b i is the protocol gain, c i , f i is a preset constant, u i (t) is an intermediate variable, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix, s i (t k ) represents the i-th agent at t k The state value at the moment, s j (t k ) represents the jth agent at t k The state value at the moment, s o (t k ) indicates t k Status value of the moment leader, definition in It indicates the triggering time of the mth edge at the kth pulse time, and defines the event triggering time at the pulse time.

[0066] S4: Consistency control of multi-agent systems via a hybrid impulse control protocol.

[0067] Lemma 1: Define u,v∈R n ,K=[K i ] is an n-dimensional diagonal matrix, K i +Ki - =I, obviously K i - ∈K, therefore, if |v i |≤1, then sat(u)∈co{K i u+K i - v:i={1,2,…,2 n}}.

[0068] Assumption 1: v i ,v j ∈R, and t>0, assuming that for any nonlinear function h(…), there exists a constant η greater than 0 that satisfies: |h(t,s j (t))-h(t,s j (t))|≤η|s j (t)-s i (t)|.

[0069] To facilitate derivation, the following identity transformation is performed to reduce the asymmetric saturation function ψ(u i ) is the symmetric saturation function sat(u i ):

[0070] make Q = diag[q i ], where ∈ i and is a positive constant, define P = [p1, p2, ..., p n ] T ,u=[u i ] T , P, u are all vector matrices. Obviously ψ(u i )=q i sat(u i -p i )+p i . Its matrix form is: ψ(u)=Qsat(uP)+P.

[0071] In this embodiment, the error is defined as:

[0072] Apparently it's easy to get

[0073]

[0074] in, represents the state value of the ith agent at the pulse time, and satisfies t≠t k hour And t = t k If the event is triggered, If the event does not trigger, s0(t) represents the state value of the leader, and α is a preset constant. e(t)=[e1(t),e2(t),…,e n (t)] T ,H(t,e(t))=(h(t,e1(t)),h(t,e2(t)),…,h(t,e n (t)) T , B=diag[b1,b2,…,b n ],C=[c1,c2,…,c n ],F=diag[f1,f2,…,f n ], H is a diagonal matrix.

[0075] Under the premise that assumption 1 is true, if there exists a constant 0<θ k <1, according to the hybrid pulse control protocol (2), the multi-agent system (1) needs to meet the following conditions in order to achieve consistency:

[0076]

[0077] The proof process is as follows: Construct a Lyapunov function as follows:

[0078]

[0079] At the non-pulse moment (t≠t k ), we can get:

[0080]

[0081] At the pulse time, let e(t k ) = e, M1=QM,M2=BL+C,we can get:

[0082]

[0083]

[0084] in:

[0085]

[0086]

[0087] definition:

[0088] λ1=λ min (M1M2),λ2=λ max (M1M2),θk =λ min (2λ1Γ-λ 2 2Λ),λ3=λ max [(P T ) -1 FM1],

[0089] λ4=λ max (I n -M1), λ5=λ max (I n -M1M2Γ), λ6=λ min [M1(I n -M1)], Γ, Λ are the designed system parameters.

[0090] Simplified:

[0091]

[0092]

[0093]

[0094] From (4)(5)(6)(7), we can get: V(t k + )≤(1-θ k )V(t k - )≤γ k V(t k - ) (8)

[0095] From (3) and (8), we can get:

[0096]

[0097] Through iterative calculation, we can get:

[0098]

[0099] Based on the following conditions:

[0100] ln(γ k )+η(t k -t k-1 )≤0 and γ k ∈(0, 1)

[0101] Available Then the multi-agent system (1) reaches consensus and the proof is complete.

[0102] The effectiveness of the consistency control of the present invention is demonstrated in combination with specific experiments below:

[0103] Experimental data and conclusions:

[0104] Consider the following system: Its topology diagram is as follows Figure 2 As shown,

[0105] The unknown quantities set in it are set in reasonable ranges, and the multi-agent system after setting the values ​​is:

[0106]

[0107] Where i=1,2,3,4,5,6,7,8,9.

[0108] Let b i =0.25, f i =0.01,η=5.8,θ k =0.75,

[0109] C = diag[0.84, 0.69, 0.87, 0.62, 0.67, 0.65, 0.73, 0.82, 0.93], let the step size in Theorem 1 be 0.001. After calculation, all the cases are in compliance, so the error diagram of the system is obtained (such as Figure 3 ) and state diagrams (as shown in Figure 4 shown), Figure 5 Given the triggering method of the system, it is not difficult to see from the simulation diagram that the system eventually converges to a consistent state.

[0110] The present invention proposes a control protocol that combines asymmetric saturation constrained pulse control with an event triggering method, and sets the event determination time at the pulse time. The key points are as follows:

[0111] (1) Protocol gain b i , the designed constant c i , f i All should be controlled within a reasonable range.

[0112] (2) Setting the event judgment time at the time when the pulse occurs reduces the communication frequency and energy consumption, avoiding the "Zeno" phenomenon and ineffective consumption.

[0113] (3) The nonlinear dynamic model with a leader is discussed, which is more in line with some practical situations.

[0114] Please refer to Figure 6 This embodiment provides a multi-agent system consensus control device with asymmetric communication channel constraints, including the following modules:

[0115] The dynamics equation construction module 1 is used to obtain a multi-agent system containing n agents and construct the dynamics equation of each agent therein;

[0116] An undirected connected network construction module 2, used to construct an undirected connected network of the multi-agent system;

[0117] A hybrid pulse control protocol construction module 3 is used to construct a hybrid pulse control protocol by using the dynamic equation and the undirected connected network, and combining an asymmetric input saturation constrained pulse control method and an event triggering method;

[0118] The consistency control module 4 is used to perform consistency control on the multi-agent system through a hybrid pulse control protocol.

[0119] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or system. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or system including the element.

[0120] The serial numbers of the embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. In a unit claim that lists several means, several of these means may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order and these words may be interpreted as identifiers.

[0121] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A consensus control method for a multi-agent system with asymmetric communication channel constraints, characterized in that: The following steps are involved: Obtain a multi-agent system containing n agents and construct the dynamic equations of each agent; Constructing an undirected connected network of the multi-agent system; A hybrid pulse control protocol is constructed by using the dynamic equation and the undirected connected network and combining an asymmetric input saturation constrained pulse control method with an event triggering method; Performing consistency control on a multi-agent system through the hybrid pulse control protocol; In the multi-agent system, the dynamic equation of each agent is: Among them, s i (t) represents the state value of the ith agent at the non-pulse moment, represents the derivative of the state value, s o (t) represents the state value of the leader in the multi-agent system at time t, represents the derivative of the leader state value, U i (t) is the control input of the multi-agent system, h(t, s i (t)) is a nonlinear function, α is a preset constant; The step of constructing an undirected connected network of the multi-agent system comprises: The multi-agent system communicates through an undirected connected network, and the topology of the undirected connected network is defined as G = (ν, ε), where ν = {1, 2, ..., n} is a node set, each node represents an agent, and ε∈ν×ν represents a directed edge set; Define A = [a ij ] is the weighted adjacency matrix, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix, is the degree matrix, b ij is the element in the i-th row and j-th column of the degree matrix. If for any two nodes ν i ,ν j If there is a path, then the undirected graph is connected, and the topology graph G contains m edges, and the m edges are marked as e g , where g∈[1,m], define L=DA as a Laplace matrix; The incidence matrix is ​​defined as D = [d ij ],but The step of constructing a hybrid pulse control protocol by using the dynamic equation and the undirected connected network and combining an asymmetric input saturation constrained pulse control method and an event triggering method comprises: Define δ(t) as an impulse function and define ψ(t) as an asymmetric saturation function that satisfies: Among them, ∈ i , They are all normal numbers; Define a multi-agent system as left continuous, that is, let s i (t k )=s i (t k - ), s i (t k ) represents the i-th agent at t k The state value at the moment, s i (t k - ) represents the i-th agent at the pulse time t k The state value at the left limit value, and there is a constant ω greater than 0 so that the pulse time series {t k } satisfies the following inequality: 0 <t0<t1<t2<...<t k <t k+1 And t k+1 -t k ≥ω,lim k→∞ t k =+∞, k is the pulse count; According to the event triggering strategy: the edge marked is e m =(v i ,v j ), where m∈[1,g], g represents the number of edges in the graph, then the rules are as follows: in u m ,σ m is the preset constant, It represents the standard judgment state quantity of the mth edge at the kth pulse time, represents the actual decision state of the mth edge, φ m (t k ) represents the standard judgment state of the mth edge; The hybrid pulse control protocol is constructed according to the inequality and the rule: Where k is the number of pulses, δ(t) represents the impulse function, and b i is the protocol gain, c i , f i is a preset constant, u i (t) is an intermediate variable, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix, s i (t k ) represents the i-th agent at t k The state value at the moment, s j (t k ) indicates that the jth agent is at t k The state value at the moment, s o (t k ) indicates t k Status value of the moment leader, definition in It indicates the triggering time of the mth edge at the kth pulse time, and defines the event triggering time at the pulse time; In the process of controlling the consistency of the multi-agent system through the hybrid pulse control protocol, the multi-agent system needs to meet the following conditions to achieve consistency: Among them, θ k ,γ k ,η is a constant, satisfying 0<θ k <1,η>0,λ1=λ min (M1M2),λ2=λ max (M1M2),θ k =λ min (2λ1Γ-λ 2 2Λ),λ3=λ max [(P T ) -1 FM1], λ4=λ max (I n -M1,λ5=λmaxIn-M1M2Γ,λ6=λminM1In-M1,Γ,Λ are the designed system parameters, and define P=[p1,p2,…,p n ] T ,u=[u i ] T , Q = diag[q i ], where ∈ i and is a positive constant, i = 1, 2, ... n, P, u are both vector matrices, M1 = QM, M2 = BL + C, B = diag[b1, b2, ..., b n ],C=[c1,c2,…,c n ], bi and ci are the designed system parameters, K i is an n-dimensional diagonal matrix, K - i =IK i , H is a diagonal matrix, |υ i |≤1 is a constant.

2. A consensus control device for a multi-agent system with asymmetric communication channel constraints, characterized in that: Includes the following modules: The dynamics equation construction module is used to obtain a multi-agent system containing n agents and construct the dynamics equations of each agent; An undirected connected network construction module, used to construct an undirected connected network of the multi-agent system; A hybrid pulse control protocol building module, used to build a hybrid pulse control protocol by using the dynamic equation and the undirected connected network, and combining an asymmetric input saturation constrained pulse control method with an event triggering method; A consistency control module, used for performing consistency control on the multi-agent system through the hybrid pulse control protocol; In the multi-agent system, the dynamic equation of each agent is: Among them, s i (t) represents the state value of the ith agent at the non-pulse moment, represents the derivative of the state value, s o (t) represents the state value of the leader in the multi-agent system at time t, represents the derivative of the leader state value, U i (t) is the control input of the multi-agent system, h(t, s i (t)) is a nonlinear function, α is a preset constant; The step of constructing an undirected connected network of the multi-agent system comprises: The multi-agent system communicates through an undirected connected network, and the topology of the undirected connected network is defined as G = (ν, ε), where ν = {1, 2, ..., n} is a node set, each node represents an agent, and ε∈ν×ν represents a directed edge set; Define A = [a ij ] is the weighted adjacency matrix, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix, is the degree matrix, b ij is the element in the i-th row and j-th column of the degree matrix. If for any two nodes ν i ,ν j If there is a path, then the undirected graph is connected, and the topology graph G contains m edges, and the m edges are marked as e g , where g∈[1,m], define L=DA as a Laplace matrix; The correlation matrix is ​​defined as D = [d ij ],but The step of constructing a hybrid pulse control protocol by using the dynamic equation and the undirected connected network and combining an asymmetric input saturation constrained pulse control method and an event triggering method comprises: Define δ(t) as an impulse function and define ψ(t) as an asymmetric saturation function that satisfies: Among them, ∈ i , They are all normal numbers; Define a multi-agent system as left continuous, that is, let s i (t k )=s i (t k - ), s i (t k ) represents the i-th agent at t k The state value at the moment, s i (t k - ) represents the i-th agent at the pulse time t k The state value at the left limit value, and there is a constant ω greater than 0 so that the pulse time series {t k } satisfies the following inequality: 0 <t0<t1<t2<...<t k <t k+1 And t k+1 -t k ≥ω,lim k→∞ t k =+∞, k is the pulse count; According to the event triggering strategy: the edge marked is e m =(v i ,v j ), where m∈[1,g], g represents the number of edges in the graph, then the rules are as follows: in u m ,σ m is the preset constant, It represents the standard judgment state quantity of the mth edge at the kth pulse time, represents the actual decision state of the mth edge, φ m (t k ) represents the standard judgment state of the mth edge; The hybrid pulse control protocol is constructed according to the inequality and the rule: Where k is the number of pulses, δ(t) represents the impulse function, and b i is the protocol gain, c i , f i is a preset constant, u i (t) is an intermediate variable, a ij is the element in the i-th row and j-th column of the weighted adjacency matrix, s i (t k ) represents the i-th agent at t k The state value at the moment, s j (t k ) indicates that the jth agent is at t k The state value at the moment, s o (t k ) indicates t k Status value of the moment leader, definition in It indicates the triggering time of the mth edge at the kth pulse time, and defines the event triggering time at the pulse time; In the process of controlling the consistency of the multi-agent system through the hybrid pulse control protocol, the multi-agent system needs to meet the following conditions to achieve consistency: Among them, θ k ,γ k ,η is a constant, satisfying 0<θ k <1,η>0,λ1=λ min (M1M2),λ2=λ max (M1M2),θ k =λ min (2λ1Γ-λ 2 2Λ),λ3=λ max [(P T ) -1 FM1], λ4=λ max (I n -M1,λ5=λmaxIn-M1M2Γ,λ6=λminM1In-M1,Γ,Λ are the designed system parameters, and define P=[p1,p2,…,p n ] T ,u=[u i ] T , Q = diag[q i ], where ∈ i and i is a positive constant, i = 1, 2, ... n, P, u are both vector matrices, M1 = QM, M2 = BL + C, B = diag[b1, b2, ..., b n ],C=[c1,c2,…,c n ], bi and ci are the designed system parameters, K i is an n-dimensional diagonal matrix, K - i =IK i , H is a diagonal matrix, |υ i |≤1 is a constant.

Images