CN114690634A - Nonlinear multi-agent system finite time consistency control method based on state constraint pulse control strategy - Google Patents

Nonlinear multi-agent system finite time consistency control method based on state constraint pulse control strategy Download PDF

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CN114690634A
CN114690634A CN202210270331.1A CN202210270331A CN114690634A CN 114690634 A CN114690634 A CN 114690634A CN 202210270331 A CN202210270331 A CN 202210270331A CN 114690634 A CN114690634 A CN 114690634A
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王洁
杨莎莎
王茜竹
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Chongqing University of Post and Telecommunications
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Abstract

The invention belongs to the field of intelligent information processing, and particularly relates to a finite time consistency method of a nonlinear multi-agent system based on a state constraint pulse control strategy, which comprises the following steps: constructing a switching topological structure of a nonlinear multi-agent system and a dynamic model of an agent; designing a state constraint pulse control strategy and a finite time continuous control strategy; the intelligent agent receives state information of a neighbor intelligent agent at a pulse time or a non-pulse time; updating the state information of each intelligent agent at the pulse time by adopting a state constraint pulse control strategy, or updating the state information of each intelligent agent at the non-pulse time by adopting a finite time continuous control strategy, and finishing the finite time consistency; the invention provides a state constraint pulse control strategy and a finite time continuous control strategy, which can save communication resources, improve the stability of the system and reduce the convergence time of the system.

Description

Nonlinear multi-agent system finite time consistency control method based on state constraint pulse control strategy
Technical Field
The invention belongs to the field of intelligent information processing, and particularly relates to a finite time consistency control method of a nonlinear multi-agent system based on a state constraint pulse control strategy.
Background
In recent years, the distributed cooperative control problem of the multi-agent system has wide application in the fields of robot formation control, sensor networks, neural networks, traffic vehicle control and the like. In the control system, the state of the control system is suddenly changed in the control process under the influence of external environmental factors, so that the control effect is poor; while the perturbation of the continuous control strategy is not only not instantaneous but also increases the consumption of system resources. Due to the characteristic that the pulse signals are suddenly changed at certain specific moments, the discontinuous pulse control mechanism can only transmit information with each node at the pulse moment, and the communication frequency and the energy consumption of the system can be reduced. Although the discontinuous control protocol of the traditional pulse theory can reduce the communication resources of the system to a certain extent, the theoretical value and the actual value of the pulse intensity have deviation; for example, due to practical limitations, the upper limit of the actual control strength is lower than the theoretical impulse strength, resulting in insufficient system control and irreversible effects on information transfer between agents. Therefore, it is necessary to limit and constrain the intensity of the pulses in the control strategy.
Based on the above studies, state-constrained pulses have become an important issue in the design of control protocols. The state constraint pulse control strategy can constrain the pulse jump value in a safe range through a saturation function, thereby improving the system stability and preventing the system from generating large fluctuation. At present, the most widely applied method is a constraint control method using a saturation function theory, and the method adds an auxiliary matrix H in system analysis by using a combined convex method and then converts input saturation pulses into convex polyhedrons to simplify the calculation process. In addition, the trainees also obtain variable pulse intervals based on constrained pulse control strategies, and propose constrained pulse time windows and multi-agent consistency to increase system flexibility. Although the state constraint pulse control strategy in the method can limit the intensity of the pulse within the range required by the system to process a plurality of consistency problems, the stable convergence time of the system is not considered, the non-limited time consistency in the multi-agent system is low in efficiency, and the robustness of the system is poor. In addition, the ideal environment without considering input delay and fixed topology is not favorable for improving the reliability and complexity of the system.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a nonlinear multi-agent system finite time consistency control method based on a state constraint pulse control strategy, which comprises the following steps:
s1: constructing a switching topology structure of the nonlinear multi-agent system, wherein the switching topology structure comprises a leaderless switching topology structure and a leadership switching topology structure;
s2: building a dynamic model of an agent in the system according to algebraic graph theory, and initializing the system;
s3: designing a state constraint pulse control strategy and a finite time continuous control strategy; the state constraint pulse control strategy comprises a state constraint pulse control protocol with a leader and a state constraint pulse control protocol without the leader, and the finite time continuous control strategy comprises a finite time continuous control protocol with the leader and a finite time continuous control protocol without the leader;
s4: judging whether a leader exists in the multi-agent system with the input time delay; if the leader does not exist, executing step S5, and if the leader exists, executing step S6;
s5: the intelligent agent receives state information of a neighbor intelligent agent at a pulse time or a non-pulse time; updating the state information of each intelligent agent at the pulse time by adopting a state constraint pulse control protocol without a leader, or updating the state information of each intelligent agent at the non-pulse time by adopting a finite time continuous control protocol with the leader, so as to finish the finite time consistency;
s6: the intelligent agent receives state information of the neighbor intelligent agent and the leader intelligent agent at a pulse time or a non-pulse time; and updating the state information of each intelligent body at the pulse time by adopting a state constraint pulse control protocol with a leader, or updating the state information of each intelligent body at the non-pulse time by adopting a finite time continuous control protocol with the leader to finish the finite time consistency.
Preferably, the constructing of the switching topology of the nonlinear multi-agent system comprises: taking each agent in the nonlinear multi-agent system as a node, and gathering all the nodes; acquiring the edge of an intelligent system; and constructing a topological structure chart according to the set of the intelligent agent points and the set of the intelligent agent edges, taking each edge in the chart as information interaction between adjacent nodes, and switching the communication topological structure of the multi-intelligent-agent system continuously along with time.
Preferably, a dynamic model of the agent in the system is constructed, and the expression of the dynamic model is as follows:
Figure BDA0003554418070000031
wherein the content of the first and second substances,
Figure BDA0003554418070000032
the derivative representing the i-th agent state, f (.) representing a non-linear function, xi(t) indicates the status of the ith agent,
Figure BDA0003554418070000033
derivative, x, representing the state of leader node 00(t) represents the state of leader node 0, t represents the system occurrence time, uiRepresenting the controller, h represents the input delay, and M represents a positive integer.
Preferably, the formula for updating the state information of each agent at the pulse time by using a state constraint pulse control protocol without a leader, or the formula for updating the state information of each agent at the non-pulse time by using a finite time continuous control protocol with a leader is as follows:
Figure BDA0003554418070000034
Figure BDA0003554418070000035
wherein u isi(t) denotes a controller function, α denotes a constant greater than zero, niPresentation intelligenceThe set of the number of the energy bodies,
Figure BDA0003554418070000036
representing the adjacency matrix, sigma (t) the switching signal of the system topology, sign (. -) the sign function, χj(t) represents a delayed agent state, m represents a positive number less than one,
Figure BDA0003554418070000037
representing finite time control gain, t representing time, tkIndicating the time of occurrence of the pulse, dkDenotes pulse gain, sat (. eta.) denotes saturation function, δ (. delta.). denotes pulse function, xi(t) represents the state of the ith agent, h represents the delay time, u represents the delay timei(T) denotes the controller function at time T, T denotes time T.
Preferably, the formula for updating the state information of each agent at the pulse time by using the state constraint pulse control protocol with the leader, or the formula for updating the state information of each agent at the non-pulse time by using the finite time continuous control protocol with the leader is as follows:
Figure BDA0003554418070000041
Figure BDA0003554418070000042
wherein u isi(t) denotes a controller function, β denotes a constant greater than zero, niA set of numbers of agents is represented,
Figure BDA0003554418070000043
representing an adjacency matrix, sign (.)ηRepresenting a symbolic function, η representing a positive number less than one, yj(t) indicates the state of the agent after the delay, biRepresenting the connection weight between the agent node and the leader node, y0(t) represents a delayed leader agent state,
Figure BDA0003554418070000048
denotes a finite time control gain, t denotes time, tkIndicating the time of occurrence of the pulse, dkDenotes pulse gain, sat (. eta.) denotes saturation function, δ (. delta.). denotes pulse function, xi(t) represents the state of the ith agent, h represents the delay time, u represents the delay timei(T) denotes the controller function at time T, T denotes time T.
Preferably, the conditions for achieving finite time consistency for each agent are: if there is a continuous function V (t) satisfying
Figure BDA0003554418070000044
V (t) satisfies the finite time consistency condition, i.e.:
V1-β(t)≤V1-β(t0)-α(1-β)(t-t0),t0t < T and
Figure BDA0003554418070000045
the system settling time is
Figure BDA0003554418070000046
Where α represents a constant greater than zero, β represents a positive number less than one, V (t) represents a continuous function,
Figure BDA0003554418070000047
representing the derivative of a continuous function, t0Represents the initial time of the system, TsRepresents the system stationary convergence time, TmaxRepresenting the maximum system convergence time.
The invention has the beneficial effects that:
the invention provides a state constraint pulse control strategy, which can not only save communication resources, but also dynamically limit the pulse intensity within a certain range according to the actual requirements of a system; the fluctuation of the system is avoided by using a saturation function theory in the formulated state constraint pulse control strategy, and the stability of the system is improved; the invention adopts an exponential convergence measure to control the priority time in a finite time control strategy, shortens the convergence time of the system and ensures that the system has better robust performance and anti-interference performance than a non-finite time control system; in addition, the invention also analyzes the consistency problem of the multi-agent system with input delay under the switching topology so as to improve the accuracy and the reliability of the system.
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FIG. 1 is a flow chart of a method of finite time consistency control of a nonlinear multi-agent system based on a state-constrained pulse control strategy of the present invention;
FIG. 2 is a schematic of the leaderless topology of the present invention;
FIG. 3 is a comparison of state values of six agents without leaders in a handoff topology of the present invention;
FIG. 4 is a comparison of error values for six agents without a leader in a handoff topology of the present invention;
FIG. 5 is a schematic diagram of a different topology of the leader of the present invention;
FIG. 6 is a state value comparison graph of six agents with a leader and the leader in a switching topology of the present invention;
FIG. 7 is a comparison graph of error values for six agents with a leader and the leader in a handoff topology of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
An embodiment of a finite time consistency control method of a nonlinear multi-agent system based on a state constraint pulse control strategy is shown in fig. 1, and the method comprises the following steps:
s1: constructing a switching topology of the nonlinear multi-agent system, wherein the switching topology comprises a leaderless switching topology and a leadership switching topology;
s2: building a dynamic model of an agent in the system according to an algebraic graph theory, and initializing the system;
s3: designing a state constraint pulse control strategy and a finite time continuous control strategy; the state constraint pulse control strategy comprises a state constraint pulse control protocol with a leader and a state constraint pulse control protocol without the leader, and the finite time continuous control strategy comprises a finite time continuous control protocol with the leader and a finite time continuous control protocol without the leader;
s4: judging whether a leader exists in the multi-agent system with the input time delay; if the leader does not exist, executing step S5, and if the leader exists, executing step S6; the input delay multi-agent system means that input delay is added into the system, namely, a time delay factor is considered in the system;
s5: the intelligent agent receives state information of a neighbor intelligent agent at a pulse time or a non-pulse time; updating the state information of each intelligent agent at the pulse time by adopting a state constraint pulse control protocol without a leader, or updating the state information of each intelligent agent at the non-pulse time by adopting a finite time continuous control protocol with the leader, so as to finish the finite time consistency;
s6: the intelligent agent receives state information of the neighbor intelligent agent and the leader intelligent agent at a pulse time or a non-pulse time; and updating the state information of each intelligent agent at the pulse time by adopting a state constraint pulse control protocol with a leader, or updating the state information of each intelligent agent at the non-pulse time by adopting a finite time continuous control protocol with the leader, so as to finish the finite time consistency.
The topological structure for constructing the nonlinear multi-agent system comprises the following steps: taking each agent in the nonlinear multi-agent system as a node, and gathering all the nodes; acquiring the edge of an intelligent system; according to the point of the agentThe set of the intelligent agent edges and the set of the intelligent agent edges construct a topological structure chart, each edge in the graph is used as information interaction between adjacent nodes, and the communication topological graph of the multi-intelligent agent system is switched continuously along with time. The specific process comprises the following steps: consider an undirected graph
Figure BDA0003554418070000063
Wherein
Figure BDA0003554418070000064
Is a set of agent points, vnRepresenting the nth agent in the set of agents,
Figure BDA0003554418070000061
representing a set of edges, each edge in the set of points corresponding to two agent nodes, Λ ═ aij)N×NAn adjacency matrix representing a topological graph, if agent node i can receive information from agent node j, then agent node i is called agent node j's neighbor agent and aij> 0, otherwise aij0. When the topological graph is an undirected graph and the adjacency matrix is positive, then aij＝aji. In the topological graph, a degree matrix is defined as
Figure BDA0003554418070000062
And the laplacian matrix L is defined as L ═ D- Λ, where D is the diagonal matrix and D ═ diag (D)1,d2,…dM),di＝deg(vi) Wherein N represents a positive integer N, M represents a positive integer M, diRepresenting the ith element in the diagonal matrix.
Communication topological graph of multi-agent system in a topological set G (G) along with time1,G2,…,GgG is more than or equal to 1, wherein G is switched randomlygRepresenting the g-th topological graph in the topological set. t is t0＝＜t1＜t2＜…＜tnIs the switching time of the system communication topology, and τk＝tk-tk-1Wherein, tnDenotes time n, τkIndicating the switching time at time kDifference, tkIndicating time k, k is 1, and 2 … ∞ represents the time that a communication topology stays. σ (t) < t0, + ∞) is the switching signal of the system topology, and σ (t) is used to represent the communication topology at time t. Thus, the Laplace matrix of the multi-agent system is L at time tσ(t)＝Dσ(t)-Λσ(t)Wherein, Lσ(t)Laplace matrix, D, representing the switching topologyσ(t)Diagonal matrix, Λ, representing the switching topologyσ(t)An adjacency matrix representing a switching topology.
Adopting a saturation function to constrain the state of an agent in the nonlinear multi-agent system; the system can be divided into local input constraints and global state constraints according to a saturation function. Local constraints refer to constraints between an agent and its neighboring agents, while global constraints refer to constraints of the leader agent and its neighboring agents as a whole. The saturation function may be defined as follows:
Figure BDA0003554418070000071
wherein the upper and lower bounds of the u ∈ R saturation function are +1 and-1, respectively.
A typical multi-agent system model is composed of M agents, and the dynamic model of each agent is expressed as
Figure BDA0003554418070000072
Wherein x isi(t)∈RmIndicating the status of the ith agent, f (x)i(t), t) is a continuous nonlinear derivative function, h is the known input delay, ui(t) is the control protocol of the multi-agent system, t represents the system occurrence time, uiRepresenting the controller function, h the input delay, and M a positive integer.
The average consistency of a leaderless non-linear multi-agent system can be achieved in a limited time under any initial condition if the following expression is satisfied:
Figure BDA0003554418070000073
wherein
Figure BDA0003554418070000081
Representing the average state of n agents.
Non-linear multi-agent system consistency with one leader can be achieved in any initial condition for a limited time if the following expression is satisfied:
Figure BDA0003554418070000082
wherein x is0(t) represents the status of the leader in the multi-agent system.
The conditions for achieving finite time consistency for each agent are: if there are continuous functions V (t) satisfying
Figure BDA0003554418070000083
V (t) satisfies the finite time consistency condition, i.e.:
V1-β(t)≤V1-β(t0)-α(1-β)(t-t0),t0t < T and
Figure BDA0003554418070000084
the system settling time is
Figure BDA0003554418070000085
Where α represents a constant greater than zero, β represents a positive number less than one, V (t) represents a continuous function,
Figure BDA0003554418070000086
representing the derivative of a continuous function, t0Represents the initial time of the system, TsRepresents the system stationary convergence time, TmaxMaximum system convergence time.
A specific implementation mode of a nonlinear multi-agent system finite time consistency control method based on a state constraint pulse control strategy is characterized in that the process of updating the received state information of neighbor agents through a leaderless state constraint control protocol comprises the following steps: the convergence of the multi-agent in the limited time is realized by adopting a control protocol combining the state constraint pulse and the limited time, and the leaderless state constraint pulse mainly constrains the states of the agent and the neighbors thereof so as to achieve the purpose of state constraint. The formula for updating the received state information of the neighbor agents by adopting the state constraint control protocol without leaders is as follows:
Figure BDA0003554418070000087
Figure BDA0003554418070000088
wherein u isi(t) denotes a controller function, α denotes a constant greater than zero, niA set of numbers of agents is represented,
Figure BDA0003554418070000091
representing the adjacency matrix, sigma (t) the switching signal of the system topology, sign (. -) the sign function, χj(t) represents a delayed agent state, m represents a positive number less than one,
Figure BDA0003554418070000099
representing finite time control gain, t representing time, tkIndicating the time of occurrence of the pulse, dkDenotes pulse gain, sat (. eta.) denotes saturation function, δ (. delta.). denotes pulse function, xi(t) represents the state of the ith agent, h represents the delay time, ui(T) denotes the controller function at time T, T denotes time T.
Calculating a kinetic equation of the ith intelligent agent by using a Newton-Lebulinitz equation and a leaderless state constraint control protocol, wherein the expression is as follows:
Figure BDA0003554418070000092
Figure BDA0003554418070000093
wherein the content of the first and second substances,
Figure BDA0003554418070000094
representing a kinetic model of the agent with input delay at non-pulse instants, phi (t) representing a finite time controller, delta chii(tk) Dynamic model representing the pulse time, dkIndicating the pulse gain.
Definition of
Figure BDA0003554418070000095
For the error state of the ith agent, the error of the system is:
Figure BDA0003554418070000096
ζ(t)＝(ζi(t),ζi(t),…,ζn(t))T
wherein the content of the first and second substances,
Figure BDA0003554418070000097
an error controller indicating a time instant of non-pulse,
Figure BDA0003554418070000098
indicating the average state of the agent, Δ ζi(tk) Error controller indicating the pulse time, InRepresenting an identity matrix of order n, 11TA diagonal matrix representing the unit 1, n representing the number of pulses, Lσ(t)A laplacian matrix representing a switching topology,
Figure BDA00035544180700000910
to represent
Figure BDA00035544180700000911
The error in the time of day is,
Figure BDA00035544180700000912
to represent
Figure BDA00035544180700000913
The time of day.
λ2(Lσ(t)) Is a Laplace matrix Lσ(t)Of the second minimum eigenvalue. One matrix H satisfies | | Hx | | non-calculation∞Is less than or equal to 1 and gamma is less than 1 when the gamma is more than 0. Under the state constraint control protocol without a leader, if the following equality and inequality are established, the system can reach the finite time consistency within the finite time T; the conditions that hold are:
Figure BDA0003554418070000101
wherein α represents a constant greater than zero, α1Denotes the variable after transformation by alpha, kappa1Denotes a non-negative constant, n1-m1-m powers, lambda, representing n agents2The second smallest eigenvalue of the laplacian matrix,
Figure BDA0003554418070000102
of Laplace matrices representing switching topologies
Figure BDA0003554418070000103
To the power, I denotes the identity matrix, DiRepresents the set D, Lσ(t)A laplacian matrix representing a switching topology,
Figure BDA0003554418070000104
each element i in D is represented, H represents a set of H matrices, and γ represents a constant less than one.
The expression for the finite time T is:
Figure BDA0003554418070000105
a specific implementation method of a nonlinear multi-agent system finite time consistency control method based on a state constraint pulse control strategy adopts a state constraint control protocol with a leader to update received state information of neighbor agents; the specific process comprises the following steps: the state-constrained pulse control protocol with leader primarily constrains the global state, i.e., the pulses are controlled by constraining the states of the agent and its neighboring agents, agents and the leader agent, and then the multi-agent system stabilizes for a limited time. Thus, the dynamics of the leader agent node 0 are as follows:
Figure BDA0003554418070000106
wherein x0(t),f(x0(t, t) represents the state of the leader of the Multi agent and with respect to x0(t) is a non-linear function.
The formula for updating the received state information of the neighbor agents by adopting the state constraint control protocol with the leader is as follows:
Figure BDA0003554418070000111
Figure BDA0003554418070000112
wherein u isi(t) denotes a controller function, β denotes a constant greater than zero, niA set of numbers of agents is represented,
Figure BDA0003554418070000113
representing an adjacency matrix, sign (.)ηExpression symbolNumber function, η represents a positive number less than one, yj(t) indicates the state of the agent after the delay, biRepresenting the connection weight between the agent node and the leader node, y0(t) represents a delayed leader agent state,
Figure BDA0003554418070000118
denotes a finite time control gain, t denotes time, tkRepresenting the pulse generation time, dkDenotes pulse gain, sat (. eta.) denotes saturation function, δ (. delta.). denotes pulse function, xi(t) represents the state of the ith agent, h represents the delay time, u represents the delay timei(T) denotes the controller function at time T, T denotes time T.
Unlike the leaderless case, the multi-agent system consistency problem with a leader is primarily related to communication between the follower agent and the leader agent. Eventually, all agents reach the same state as the leader agent. Further, an exchange interaction topology with leader agents is described
Figure BDA0003554418070000114
The system control protocol parameters may vary depending on the actual situation.
Calculating a kinetic equation of the ith intelligent agent by using a Newton-Lebulinitz equation and a state constraint control protocol with a leader, wherein the expression is as follows:
Figure BDA0003554418070000115
Figure BDA0003554418070000116
definition xii(t)＝yi(t)-y0(t) is the state error of the ith agent. Thus, the error of the system is expressed as:
Figure BDA0003554418070000117
wherein
Figure BDA0003554418070000121
Respectively diagonal matrix and topological graph
Figure BDA0003554418070000122
The laplacian matrix of.
Figure BDA0003554418070000123
Is defined as a Laplace matrix
Figure BDA0003554418070000124
Of the second minimum eigenvalue. In addition, there is one matrix H satisfying | | Hx | | luminance∞Not more than 1 and theta is more than 0 and less than 1. Under the state constraint control protocol with the leader, if the following equation or inequality holds, the system can reach the finite time consistency in the finite time T; the conditions are as follows:
Figure BDA0003554418070000125
Figure BDA0003554418070000126
wherein β represents a constant greater than zero, β1Representing a variable transformed by beta, lambda2The second smallest eigenvalue of the laplacian matrix,
Figure BDA0003554418070000127
representing Laplace matrices
Figure BDA0003554418070000128
To the power, η represents a positive number less than one.
Nonlinear multi-agent system finite time consistency based on state constraint pulse control strategyThe specific implementation mode of the sex control method provides three undirected interactive topologies G with six nodes for the consistency problem of a leaderless delay multi-agent system1,G2,G3As shown in fig. 2, the laplace matrix can thus be expressed as:
Figure BDA0003554418070000129
Figure BDA00035544180700001210
Figure BDA0003554418070000131
the parameters are respectively set to be alpha-2, m-0.4,
Figure BDA0003554418070000136
γ is 0.9, pulse intensity d is-0.4, κ1＝κ20.2; the kinetic system of each agent is f (x)i(t),t)＝0.3xi(t)+sin(xi(t), t), i ═ 1,2, …, 6; and has an initial value x (0) {5,1, -4,4, -3,3 }; selecting
Figure BDA0003554418070000132
And h is 0.03. sigma (t) ═ mod (n,3) +1, sigma (t): t0, + ∞) a switching signal representing a switching topology; by calculation, one can obtain:
Figure BDA0003554418070000133
similarly, the values for the second and third topologies are 0.4809 < γ and 0.6488 < γ, then the settling time for the system is T (χ). ltoreq.Tmax1.8694, and thus a final time t (x) 1.8994, the simulation results for the agent states and agent error values under the leader-free state constraint control protocol are shown in fig. 3 andas shown in fig. 4, it can be obtained that the error value converges to 0 at T ═ 0.38 s.
For the leaders delayed multi-agent system consistency, three undirected interaction topologies with six following nodes and one agent node are selected
Figure BDA0003554418070000134
As shown in fig. 5, the laplace matrix can be expressed as:
Figure BDA0003554418070000135
Figure BDA0003554418070000141
Figure BDA0003554418070000142
the parameter is set to β 3 η, which is,
Figure BDA0003554418070000143
theta is 0.9, h is 0.03, and is selected
Figure BDA0003554418070000144
dk-0.4; each following kinetic system is f (x)i(t),t)＝0.2sin(xi(t, t) with an initial value of xi(0)＝{5,2,4,-2,-3,-5}TThe leader's kinetic system is f (x)0(t),t)＝3sin(x0(t, t), and an initial value x0(0) 1 is ═ 1; by calculation it is possible to obtain:
Figure BDA0003554418070000145
similarly, the values for the second and third topologies are 0.8700 < θ and0.7046 < θ; the convergence time of the system is T (y) less than or equal to Tmax2.9625s, final time T (x) ≦ timeTmax2.9925 s. Simulation results of the agent states and agent error values under the state constraint control protocol with leader as shown in fig. 6 and 7, it can be obtained that the error value converges to 0 at T-0.75 s.
It can be known from numerical simulation that the finite time control parameters affect the convergence speed of the multi-agent, and the finite time control parameters are adjusted
Figure BDA0003554418070000146
The value of (c) may change the convergence speed of the system. Furthermore, the convergence time of a time-delayed system is longer than if there were no time delay, so the presence of an input time delay will also determine the convergence time of the system. Finally, b isiDecides the connection between the leader and the agent with assurance bi> 0, the system can reach leader consistency.
The above-mentioned embodiments, which further illustrate the objects, technical solutions and advantages of the present invention, should be understood that the above-mentioned embodiments are only preferred embodiments of the present invention, and should not be construed as limiting the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A nonlinear multi-agent system finite time consistency control method based on a state constraint pulse control strategy is characterized by comprising the following steps:
s1: constructing a switching topology of the nonlinear multi-agent system, wherein the switching topology comprises a leaderless switching topology and a leadership switching topology;
s2: building a dynamic model of an agent in the system according to an algebraic graph theory, and initializing the system;
s3: designing a state constraint pulse control strategy and a finite time continuous control strategy; the state constraint pulse control strategy comprises a state constraint pulse control protocol with a leader and a state constraint pulse control protocol without the leader, and the finite time continuous control strategy comprises a finite time continuous control protocol with the leader and a finite time continuous control protocol without the leader;
s4: judging whether a leader exists in the multi-agent system with the input time delay; if the leader does not exist, executing step S5, and if the leader exists, executing step S6;
s5: the intelligent agent receives state information of a neighbor intelligent agent at a pulse time or a non-pulse time; updating the state information of each intelligent agent at the pulse time by adopting a leaderless state constraint pulse control protocol, or updating the state information of each intelligent agent at the non-pulse time by adopting a leaderless finite time continuous control protocol, so as to finish the finite time consistency;
s6: the intelligent agent receives state information of the neighbor intelligent agent and the leader intelligent agent at a pulse time or a non-pulse time; and updating the state information of each intelligent agent at the pulse time by adopting a state constraint pulse control protocol with a leader, or updating the state information of each intelligent agent at the non-pulse time by adopting a finite time continuous control protocol with the leader, so as to finish the finite time consistency.
2. The method of claim 1, wherein constructing a switching topology of the nonlinear multi-agent system comprises: taking each agent in the nonlinear multi-agent system as a node, and gathering all the nodes; acquiring the edge of an intelligent system; and constructing a topological structure chart according to the set of the intelligent agent points and the set of the intelligent agent edges, taking each edge in the chart as information interaction between adjacent nodes, and switching the communication topological structure of the multi-intelligent agent system continuously along with time.
3. The finite time consistency control method of the nonlinear multi-agent system based on the state-constrained pulse control strategy as claimed in claim 1, characterized in that a dynamical model of the agents in the system is constructed, and the expression of the dynamical model is as follows:
Figure FDA0003554418060000021
wherein the content of the first and second substances,
Figure FDA0003554418060000022
the derivative representing the state of the i-th agent, f (. -) represents a non-linear function, xi(t) indicates the status of the ith agent,
Figure FDA0003554418060000023
derivative, x, representing the state of leader node 00(t) represents the state of leader node 0, t represents the system occurrence time, uiDenotes the controller function, h denotes the input delay, and M denotes a positive integer.
4. The finite time consistency control method of the nonlinear multi-agent system based on the state constraint pulse control strategy as claimed in claim 1, wherein the formula for updating the state information of each agent at the pulse time by using the leaderless state constraint pulse control protocol or updating the state information of each agent at the non-pulse time by using the leadership finite time continuous control protocol is as follows:
Figure FDA0003554418060000024
Figure FDA0003554418060000025
wherein u isi(t) denotes a controller function, α denotes a constant greater than zero, niA set of numbers of agents is represented,
Figure FDA0003554418060000026
denotes an adjacency matrix, σ (t) denotes a switching signal of the system topology, sign (. -) denotes a sign function, χj(t) represents the state of the agent after the delay, m represents a positive number less than one, θ represents the finite time control gain, t represents time, t represents the timekIndicating the time of occurrence of the pulse, dkDenotes pulse gain, sat (. eta.) denotes saturation function, δ (. delta.). denotes pulse function, xi(t) represents the state of the ith agent, h represents the delay time, u represents the delay timei(T) denotes the controller function at time T, T denotes time T.
5. The finite time consistency control method of the nonlinear multi-agent system based on the state constraint pulse control strategy as claimed in claim 1, wherein the formula for updating the state information of each agent at the pulse time by using the state constraint pulse control protocol with the leader or the formula for updating the state information of each agent at the non-pulse time by using the finite time continuous control protocol with the leader is as follows:
Figure FDA0003554418060000031
Figure FDA0003554418060000032
wherein u isi(t) denotes a controller function, β denotes a constant greater than zero, niA set of numbers of agents is represented,
Figure FDA0003554418060000033
representing an adjacency matrix, sign (.)ηRepresenting a symbolic function, η representing a positive number less than one, yj(t) indicates the state of the agent after the delay, biRepresenting the connection weight between the agent node and the leader node, y0(t) represents a delayed leader agent state,
Figure FDA0003554418060000034
representing finite time control gain, t representing time, tkRepresenting the pulse generation time, dkDenotes pulse gain, sat (. eta.) denotes saturation function, δ (. delta.). denotes pulse function, xi(t) represents the state of the ith agent, h represents the delay time, u represents the delay timei(T) represents the controller function at time T, T represents time T.
6. The finite time consistency control method of the nonlinear multi-agent system based on the state constraint pulse control strategy as claimed in claim 1, wherein the condition that each agent achieves the finite time consistency is as follows: if there is a continuous function V (t) satisfying
Figure FDA0003554418060000035
V (t) satisfies the finite time consistency condition, i.e.:
V1-β(t)≤V1-β(t0)-α(1-β)(t-t0),t0t < T and
Figure FDA0003554418060000036
the system settling time is
Figure FDA0003554418060000037
Where α represents a constant greater than zero, β represents a positive number less than one, V (t) represents a continuous function,
Figure FDA0003554418060000038
representing the derivative of a continuous function, t0Represents the initial time of the system, TsRepresents the system stationary convergence time, TmaxMaximum system convergence time.
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