CN113253611A - Method for realizing consistency of multi-agent system with interference and time lag - Google Patents
Method for realizing consistency of multi-agent system with interference and time lag Download PDFInfo
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Abstract
A method for achieving consistency in a multi-agent system with interference and time-lag. The present invention solves the problem of state consistency in discrete-time multi-agent systems with external interference and communication time lag. The influence of communication time lag and external interference on the multi-agent system in cooperative control is overcome. A networked predictive control method is utilized to actively make up for communication time lag, a distributed state observer is used for estimating state and disturbance, and a consistency control protocol with state feedback and static output feedback forms is designed, so that the state consistency of the discrete multi-agent system with external interference and communication time lag is realized.
Description
Technical Field
The invention relates to a method for solving the problem of state consistency of a discrete multi-agent system with external interference and communication time lag, and belongs to the technical field of networked multi-agent systems.
Background
At present, the discussion of the consistency of a multi-agent system is mostly under an ideal condition, that is, the mutual information exchange among agents is carried out while the influence of external uncertain factors is avoided.
However, in practical engineering applications, the information exchange and mutual coupling process between the agents are affected by various uncertain factors from the outside.
Disclosure of Invention
The invention solves the problem of state consistency of a discrete time multi-agent system with external interference and communication time lag, and designs a consistency control protocol for compensating the communication time lag by utilizing networked predictive control.
The invention relates to a method for realizing consistency of a multi-agent system with interference and time lag, which is realized by the following technical scheme:
the method comprises the following steps: establishing a discrete time dynamic model with time lag and disturbance of the multi-agent system;
step two: constructing a state observer aiming at a discrete time dynamic model of a multi-agent system with time lag and disturbance, and predicting the state;
step three: designing a distributed consistency control protocol according to the state prediction of the discrete time dynamic model of the two pairs of multi-agent systems with time lag and interference;
step four: obtaining a compact expression form of a grouping state error equation and an estimation error equation according to the distributed consistency control protocol designed in the third step;
step five: obtaining a state estimation gain matrix K based on a linear matrix inequality by using a compact expression form of a state error equation and an estimation error equation;
step six: and substituting the feedback gain moment K obtained in the fifth step into the consistency protocol in the third step for simulation verification, and realizing the state consistency of the discrete multi-agent system with time lag and disturbance.
As a further explanation of the above steps, the first step is specifically:
establishing a multi-agent system consisting of N agents, wherein the dynamic model of the ith agent with external interference is as follows:
wherein x isi(t)∈RnIs the ith agent state, ui(t)∈RqFor control input, di(t)∈RqFor external interference, yi(t)∈RrFor measuring the output, a, B, C are matrices with appropriate dimensions.
Further, the specific process of performing the state prediction in the step two includes:
introducing exogenous variables:
wherein, wi(t)∈RqIs an external disturbance.
Defining a new variable
The kinetic equation for the augmented system is:
wherein:
i＝1,2,…,N。
predicting the state of the multi-agent system to obtain a corresponding prediction equation as follows:
the time lag upper bound is tau, the formula shows that aiming at the ith follower agent, a state observer is utilized to obtain information of the next moment based on the information of the t-tau moment; li denotes the ith observer gain matrix.
The distributed consistency control protocol in the third step is as follows:
wherein the content of the first and second substances,
is the state estimate of the ith agent,
is a disturbance estimate of the ith agent, aijIs a contiguous matrix of the system.
The compact expression form of the state error equation and the estimation error equation in the fourth step is as follows:
for a discrete-time multi-agent system (1) with disturbance, the essential condition that the consistency control protocol designed by us can realize the consistency of the state of the discrete multi-agent system with external disturbance and communication time lag is that the T is Schur stable, i.e. the characteristic roots are all positioned in a unit circle.
The fifth step specifically comprises the following steps:
and obtaining a state estimation gain matrix K based on the linear matrix inequality by using a compact expression form of the state error equation and the estimation error equation.
The sixth step specifically comprises the following steps:
substituting the obtained feedback gain matrix K into the consistency protocol of the invention, carrying out simulation verification and obtaining a conclusion, wherein the designed consistency control protocol can realize the consistency of the state of the discrete multi-agent system with external interference and communication time lag.
The most prominent characteristics and remarkable beneficial effects of the invention are as follows:
the invention solves the problem of state consistency of a discrete time multi-agent system with external interference and communication time lag, and designs a consistency control protocol for compensating the communication time lag by utilizing networked predictive control. Compared with the prior art that the consistency of the multi-agent system is researched only under the ideal condition, the invention fully considers the influence of external interference and communication time lag on information exchange between the agents in the actual engineering environment, overcomes the influence, and finally realizes the consistency of the multi-agent system, and has the characteristics of easy operation and realization.
Drawings
In order to solve the technical problem, the invention will be explained with reference to the accompanying drawings. The following drawings are only some examples of the invention; other similar figures may be obtained by the user from this figure. Wherein:
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of a networked multi-agent system communication topology;
FIG. 3 is a state component x of agent ii1(t),i＝0,1,2,3,4；
FIG. 4 is a state component x of agent ii2(t),i＝0,1,2,3,4；
FIG. 5 is an error component e of agent ii1(t),i＝0,1,2,3,4；
FIG. 6 is an error component e of agent ii2(t),i＝0,1,2,3,4。
Detailed Description
The first embodiment is as follows: the embodiment is described with reference to the first drawing, and the method for implementing consistency of the discrete multi-agent system with external disturbance and communication time lag in the embodiment specifically comprises the following steps:
the method comprises the following steps: establishing a discrete time dynamic model with time lag and disturbance of the multi-agent system;
step two: constructing a state observer aiming at a discrete time dynamic model of a multi-agent system with time lag and disturbance, and predicting the state;
step three: designing a distributed consistency control protocol according to the state prediction of the discrete time dynamic model of the two pairs of multi-agent systems with time lag and interference;
step four: obtaining a compact expression form of a grouping state error equation and an estimation error equation according to the distributed consistency control protocol designed in the third step;
step five: obtaining a state estimation gain matrix K based on a linear matrix inequality by using a compact expression form of a state error equation and an estimation error equation;
step six: and substituting the feedback gain moment K obtained in the fifth step into the consistency protocol in the third step for simulation verification, and realizing the state consistency of the discrete multi-agent system with time lag and disturbance.
The second embodiment is as follows: the difference between this embodiment and the first embodiment is that the first step specifically is:
establishing a multi-agent system consisting of N agents, wherein the dynamic model of the ith agent with external interference is as follows:
wherein x isi(t)∈RnIs the ith agent state, ui(t)∈RqFor control input, di(t)∈RqFor external interference, yi(t)∈RrFor measuring the output, a, B, C are matrices with appropriate dimensions.
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment is different from the second embodiment in that the specific process of performing the state prediction in the second step includes:
introducing exogenous variables:
wherein, wi(t)∈RqIs an external disturbance.
Defining a new variable
The kinetic equation for the augmented system is:
wherein the content of the first and second substances,
i＝1,2,…,N。
predicting the state of the multi-agent system to obtain a corresponding prediction equation as follows:
the time lag upper bound is tau, the formula shows that aiming at the ith follower agent, a state observer is utilized to obtain information of the next moment based on the information of the t-tau moment; li denotes the ith observer gain matrix.
Other steps and parameters are the same as those in the second embodiment.
The fourth concrete implementation mode: the third difference between this embodiment and the third embodiment is that, in the third step, the distributed consistency protocol is:
wherein the content of the first and second substances,
is the state estimate of the ith agent,
is a disturbance estimate of the ith agent, aijIs a contiguous matrix of the system.
Other steps and parameters are the same as those in the third embodiment.
The fifth concrete implementation mode: the fourth difference between this embodiment and the specific embodiment is that the compact expression form of the state error equation and the estimation error equation in step four is:
for a discrete-time multi-agent system (1) with disturbance, the essential condition that the consistency control protocol designed by us can realize the consistency of the state of the discrete multi-agent system with external disturbance and communication time lag is that the T is Schur stable, i.e. the characteristic roots are all positioned in a unit circle.
The other steps and parameters are the same as those in the fourth embodiment.
The sixth specific implementation mode: the difference between this embodiment and the fifth embodiment is that step five includes the following steps:
and obtaining a state estimation gain matrix K based on the linear matrix inequality by using a compact expression form of the state error equation and the estimation error equation.
The other steps and parameters are the same as those in the fifth embodiment.
Examples
The following examples were used to demonstrate the beneficial effects of the present invention:
as shown in the communication topology of fig. 2, the discrete multi-agent system with external interference is composed of 4 agents, which are denoted by 1, 2, 3, 4, respectively.
System parameters:
the system laplacian matrix is:
the adjacency matrix of the system is:
Mi Nirespectively as follows:
let 2 be the upper bound τ of the skew that exists when an agent transmits data over a network. By using a pole allocation technology, an observer gain matrix L is obtained as follows:
calculating a control gain K:
K＝[0.6082 0.4387]
the initial state of the system is:
the characteristic value lambda can be obtained by calculationiAre all within the unit circle, therefore, our invented protocol can solve the consistency problem of multi-agent systems with external interference and communication skew.
Fig. 3 is the state component xi1(t) of agent i, fig. 4 is the state component xi2(t) of agent i, fig. 5 is the error component ei1(t) of agent i, and fig. 6 is the error component ei2(t) of agent i.
As can be seen from fig. 3-6, the inventive coherency control protocol is effectively consistent for multi-agent systems with external disturbances and communication skew.
Claims (7)
1. A method for achieving consistency in a multi-agent system with perturbation and time-lag, comprising the steps of:
the method comprises the following steps: establishing a discrete time dynamic model with time lag and disturbance of the multi-agent system;
step two: constructing a state observer aiming at a discrete time dynamic model of a multi-agent system with time lag and disturbance, and predicting the state;
step three: designing a distributed consistency control protocol according to the state prediction of the discrete time dynamic model of the two pairs of multi-agent systems with time lag and interference;
step four: obtaining a compact expression form of a grouping state error equation and an estimation error equation according to the distributed consistency control protocol designed in the third step;
step five: obtaining a state estimation gain matrix K based on a linear matrix inequality by using a compact expression form of a state error equation and an estimation error equation;
step six: and substituting the feedback gain moment K obtained in the fifth step into the consistency protocol in the third step for simulation verification, and realizing the state consistency of the discrete multi-agent system with time lag and disturbance.
2. The method for achieving consistency in a multi-agent system with perturbation and time lag as claimed in claim 1, said step one being specifically:
establishing a multi-agent system consisting of N agents, wherein the dynamic model of the ith agent with external interference is as follows:
wherein x isi(t)∈RnIs the ith agent state, ui(t)∈RqFor control input, di(t)∈RqFor external interference, yi(t)∈RrFor measuring the output, a, B, C are matrices with appropriate dimensions.
3. The method for achieving consistency of the discrete multi-agent system with external disturbance and communication time lag as recited in claim 2, wherein the second step is specifically as follows:
introducing exogenous variables:
wherein, wi(t)∈RqIs an external disturbance;
defining a new variable
The kinetic equation for the augmented system is:
wherein the content of the first and second substances,
i＝1,2,…,N。
predicting the state of the multi-agent system to obtain a corresponding prediction equation as follows:
the time lag upper bound is tau, the formula shows that aiming at the ith follower agent, a state observer is utilized to obtain information of the next moment based on the information of the t-tau moment; li denotes the ith observer gain matrix.
4. The method for achieving consistency in a discrete multi-agent system with external disturbances and communication skews as recited in claim 3, wherein the consistency control protocol in step three is as follows:
wherein the content of the first and second substances,
is the state estimate of the ith agent,
is a disturbance estimate of the ith agent, aijIs a contiguous matrix of the system.
5. The method for achieving consistency in a discrete multi-agent system with external disturbances and communication skews as recited in claim 4, wherein the compact representation of the state error equations and estimation error equations in step four is as follows:
L1＝diag(L11,L21,…,LN1)
N＝diag(N1,N2,…,NN)
M＝diag(M1,M2,…,MN)
for a discrete-time multi-agent system (1) with perturbations, the essential condition that our designed coherence control protocol can achieve state coherence of the discrete multi-agent system with external disturbances and communication time-lags is that Γ is Schur stable, i.e. their characteristic roots are all located within a unit circle.
6. The method for achieving consistency in a discrete multi-agent system with external disturbances and communication skews as recited in claim 5, wherein step five comprises the following process:
and obtaining a state estimation gain matrix K based on the linear matrix inequality by using a compact expression form of the state error equation and the estimation error equation.
7. The method for achieving consistency in a discrete multi-agent system with external disturbances and communication skews as recited in claim 6, wherein step six comprises the following process:
substituting the obtained feedback gain matrix K into a designed consistency protocol for simulation verification; and the conclusion is drawn that the consistency control protocol designed by the user can realize the state consistency of the discrete multi-agent system with external interference and communication time lag.
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