CN112486114A - Prediction-based actuator saturation multi-agent global consistency method - Google Patents

Prediction-based actuator saturation multi-agent global consistency method Download PDF

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CN112486114A
CN112486114A CN202011318273.2A CN202011318273A CN112486114A CN 112486114 A CN112486114 A CN 112486114A CN 202011318273 A CN202011318273 A CN 202011318273A CN 112486114 A CN112486114 A CN 112486114A
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agent
matrix
global consistency
actuator
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崔胤
谭冲
宋承霖
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Harbin University of Science and Technology
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Abstract

A prediction-based actuator saturation multi-agent global consistency method. The invention designs the field of global consistency of actuator saturation multi-agent based on prediction, and particularly relates to a method for realizing the global consistency of an actuator saturation system by actively compensating time lag by utilizing networked prediction control, dividing a matrix A of a critical stable system into an orthogonal matrix and a Schur matrix by utilizing the idea of matrix division, and designing a brand-new consistency control protocol based on prediction in an undirected graph. The invention solves the problem that the states of a multi-agent system can be consistent by using a designed predictive control protocol when an actuator is full due to excessive information exchange among agents.

Description

Prediction-based actuator saturation multi-agent global consistency method
Technical Field
The invention relates to the technical field of multi-agent global consistency, in particular to a method for analyzing global consistency of a multi-agent system based on predicted actuator saturation critical stability.
Background
The research of the consistency theory of the multi-agent system tends to be perfect in twenty years, the main purpose is to complete complex tasks through the mutual coordination and cooperation of a plurality of agents with simple functions, and the multi-agent system is widely applied to various fields due to the characteristics of low cost, strong reliability, strong stability and the like.
In an actual multi-agent system or a relatively large multi-agent network, it is possible for each agent to receive coupling information sent by adjacent agents. Then, feedback of these relatively large amounts of information may saturate the actuators of the agent. At this time, how to limit the excessive information amount should be considered, so as to ensure that the actuator is not saturated as much as possible, which is the problem of input saturation limitation to be considered. It is clear that input saturation limits can slow the time for the system actuator to reach saturation and do not completely eliminate the saturation. Meanwhile, in a networked multi-agent system, information exchange between agents is realized through a network. Due to the limited bandwidth of the communication channel, the occurrence of network time lag is inevitable, which causes new problems, such as network packet loss, time lag, and multi-packet transmission. The principle of the networked forecasting control method comprises the following steps: in the aspect of a sensor, a sequence of an output end is packaged and sent to one end of a controller through a feedback channel; at the controller side, the predictive control sequence at time t is sent to the system via forward path packing.
Disclosure of Invention
The method provides a control protocol based on prediction, and solves the problem of global consistency of a critically stable multi-agent system saturated by an actuator.
The method aims to realize the following steps:
step 1, establishing a discrete time state equation of a multi-agent system with saturated actuators;
step 2, designing a control protocol based on networked predictive control to enable the system to achieve global consistency;
step 3, dividing the critical stable matrix into a stable matrix and a neutral matrix, namely dividing the system matrix A into an orthogonal matrix and a Schur matrix;
and 4, designing a Lyapunov function to prove global consistency.
The state equation of the multi-agent system with the saturated actuators in the step 1 is as follows:
xi(t+1)＝Axi(t)+BΔ(ui(t))
wherein xi(t)，ui(t) represents the state and control inputs of agent i, respectively, A ∈ Rn×n,B∈Rn×m，Rn×nRepresenting the set of all n x n matrices in the number domain R, and Δ representingStandard saturation function:
Figure BDA0002791986810000011
the step 2 specifically comprises the following steps: for agent i, in order to be able to obtain its state, a state observer is designed:
Figure BDA0002791986810000012
wherein
Figure BDA0002791986810000021
yi(t) represents the state prediction and measurement output, respectively, for the previous step, because of the time lag τ in the reception of the information by the agent, in order to solve this problem, the states from time t- τ to time t are constructed based on agent i as:
Figure BDA0002791986810000022
the state of agent i at time t may be represented as:
Figure BDA0002791986810000023
the following results are obtained by calculation:
Figure BDA0002791986810000024
wherein
Figure BDA0002791986810000025
For a multi-agent system with constant communication time lag due to estimation error at the moment t, a consistency protocol based on networked predictive control is designed:
Figure BDA0002791986810000026
the closed loop control system can be expressed as:
Figure BDA0002791986810000027
Figure BDA0002791986810000028
where L is the laplacian matrix L ═ D-E, D is the in-degree matrix of the undirected graph, E is the adjacency matrix of the undirected graph, aijAs a weight, c is a design parameter and has a value range of
Figure BDA0002791986810000029
Figure BDA00027919868100000210
Expressing the kronecker product, in order to realize global consistency, the following requirements are satisfied under the action of a control protocol u (t):
Figure BDA00027919868100000211
Figure BDA00027919868100000212
the step 3 specifically comprises the following steps: a matrix segmentation method is used for segmenting a critical stable matrix into an orthogonal matrix and a Schur matrix, and the specific form is as follows:
Figure BDA00027919868100000213
where T is a nonsingular matrix, AcAnd BcIs an orthogonal matrix, i.e. Ac×Bc＝I，BcAnd BsAs a Schur matrix (eigenvalues)All within the unit circle).
The step 4 is specifically as follows: the Lyapunov function is constructed to prove that the global consistency can be achieved under the control protocol, and the designed Lyapunov function is as follows:
Figure BDA0002791986810000031
defining a fluid model:
Figure BDA0002791986810000032
if and only if x e M,
Figure BDA0002791986810000033
and
Figure BDA0002791986810000034
further proves that
Figure BDA0002791986810000035
Drawings
FIG. 1 is a block diagram of an actuator saturation configuration;
FIG. 2 is a block diagram of an undirected graph constructed using seven agents;
FIG. 3 is a diagram of critically stable multi-agent global coherency achieved with actuator saturation.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings and the detailed description.
The state equation of the multi-agent system with saturated actuators is constructed according to fig. 1:
xi(t+1)＝Axi(t)+BΔ(ui(t))
to get the state of agent i, a state observer is constructed:
Figure BDA0002791986810000036
the state of agent i can be derived by iteration:
Figure BDA0002791986810000037
the following results are obtained by calculation:
Figure BDA0002791986810000038
wherein
Figure BDA0002791986810000039
For a multi-agent system with constant communication time lag due to estimation error at the moment t, a consistency protocol based on networked predictive control is designed:
Figure BDA00027919868100000310
the closed loop control system can be expressed as:
Figure BDA00027919868100000311
Figure BDA0002791986810000041
constructing a prediction-based Lyapunov function:
Figure BDA0002791986810000042
defining a fluid model:
Figure BDA0002791986810000043
if and only if x e M,
Figure BDA0002791986810000044
and
Figure BDA0002791986810000045
further proves that:
Figure BDA0002791986810000046
Figure BDA0002791986810000047
Figure BDA0002791986810000048
when c is 0.0957, Δ V is less than or equal to 0 only when x is equal to M, which proves that the states of the agents tend to be consistent under the saturation of the actuator, i.e. global consistency is achieved.
With reference to fig. 2, a network topology with 7 agents yields a laplacian matrix L:
Figure BDA0002791986810000049
and (3) obtaining a simulation diagram of the critical stable multi-agent global consistency of the actuator saturation.
The above description is only one embodiment of the present invention, and is not intended to limit the present invention, and it is apparent to those skilled in the art that various modifications and variations can be made in the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. A prediction-based actuator-saturated multi-agent global coherence method, said method comprising that it is a critically-stabilized multi-agent system based on networked predictive control, and that the network topology is an undirected graph, an un-piloted agent, characterized in that it comprises the steps of:
step 1: establishing a discrete time state equation of the multi-agent system with saturated actuators;
step 2: designing a control protocol based on networked predictive control to enable the system to achieve global consistency;
and step 3: dividing a critical stable matrix into a stable matrix and a neutral matrix, namely dividing a system matrix A into an orthogonal matrix and a Schur matrix;
and 4, step 4: the Lyapunov function was designed to demonstrate global consistency.
2. The actuator-saturated critically-stabilized multi-agent global consistency method as claimed in claim 1, wherein the state equation of said step 1 actuator-saturated multi-agent system is:
xi(t+1)＝Axi(t)+BΔ(ui(t))
wherein xi(t)，ui(t) represents the state and control inputs of agent i, respectively, A ∈ Rn×n,B∈Rn×m，Rn×nRepresents the set of all n × n matrices in the number domain R, Δ represents the standard saturation function:
Figure FDA0002791986800000011
3. the method for critically-stabilized multi-agent global consistency of actuator saturation as claimed in claim 1, wherein said step 2 is specifically:
for agent i, in order to be able to obtain its state, a state observer is designed:
Figure FDA0002791986800000012
wherein
Figure FDA0002791986800000013
yi(t) represents the state prediction and measurement output, respectively, for the previous step, because of the time lag τ in the reception of the information by the agent, in order to solve this problem, the states from time t- τ to time t are constructed based on agent i as:
Figure FDA0002791986800000014
the state of agent i at time t may be represented as:
Figure FDA0002791986800000015
the following results are obtained by calculation:
Figure FDA0002791986800000016
wherein
Figure FDA0002791986800000017
For a multi-agent system with constant communication time lag due to estimation error at the moment t, a consistency protocol based on networked predictive control is designed:
Figure FDA0002791986800000021
the closed loop control system can be expressed as:
Figure FDA0002791986800000022
Figure FDA0002791986800000023
where L is the laplacian matrix L ═ D-E, D is the in-degree matrix of the undirected graph, E is the adjacency matrix of the undirected graph, aijAs a weight, c is a design parameter and has a value range of
Figure FDA0002791986800000024
Figure FDA0002791986800000025
Expressing the kronecker product, in order to realize global consistency, the following requirements are satisfied under the action of a control protocol u (t):
Figure FDA0002791986800000026
Figure FDA0002791986800000027
4. the method for critically-stabilized multi-agent global consistency of actuator saturation as claimed in claim 1, wherein said step 3 is specifically:
Figure FDA0002791986800000028
where T is a nonsingular matrix, AcAnd BcBeing an orthogonal matrix, BcAnd BsA Schur matrix (eigenvalues are all within the unit circle).
5. The method for critically-stabilized multi-agent global consistency of actuator saturation as claimed in claim 1, wherein said step 4 is specifically:
constructing a lyapunov function:
Figure FDA0002791986800000029
further evidence is needed
Figure FDA00027919868000000210
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CN113485101A (en) * 2021-06-10 2021-10-08 杭州电子科技大学 Gain scheduling control method for actuator saturated multi-agent system

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