CN110928185A - Quantitative control method of multi-agent system - Google Patents

Quantitative control method of multi-agent system Download PDF

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CN110928185A
CN110928185A CN201911159148.9A CN201911159148A CN110928185A CN 110928185 A CN110928185 A CN 110928185A CN 201911159148 A CN201911159148 A CN 201911159148A CN 110928185 A CN110928185 A CN 110928185A
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follower
order
ith
error
leader
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CN110928185B (en
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刘治
林壮壁
章云
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Guangdong University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
    • G05B13/027—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion using neural networks only

Abstract

The invention discloses a quantitative control method of a multi-agent system, wherein the multi-agent system comprises a leader and N followers; the control method comprises the following steps: establishing a system model of the multi-agent system, which comprises a system model of a follower and a system model of a leader; establishing an error system of the multi-agent system, wherein the error system comprises an error between the output of the ith follower and the leader and an error between the q-order state of the ith follower system and the virtual controller; a controller for a multi-agent system is designed, including designing first through qth virtual controllers for an ith follower, and then designing control inputs for the ith follower. The invention solves the problem that the system stability under the condition of limited bandwidth between the controller and the intelligent agent cannot be ensured in the prior art.

Description

Quantitative control method of multi-agent system
Technical Field
The application relates to the field of multi-agent consistency control, in particular to a quantitative control method for a single leader multi-agent of an uncertain system structure.
Background
People are inspired from the clustering behavior of living beings in nature, and a distributed idea is proposed. Distributed is more robust than centralized and can accomplish more complex tasks with less resource cost. To this end, multi-agent systems have been proposed. A multi-agent system refers to a system that is composed of a plurality of agents, where each agent can act on itself and the environment independently, but does not require global information resources.
The multi-agent technology of the multi-agent system is widely applied to intelligent robots, intelligent transportation, unmanned aerial vehicle formation control, distributed prediction, smart power grids and the like, and the most concerned is the problem of consistency control of the multi-agents. Consistency means that the state of all individuals in the multi-intelligent system tends to a same value with the increase of time; the consistency problem is a fundamental problem of multi-agent systems.
Many documents have been studied at home and abroad on the consistency control of the multi-agent, and the following of each follower to the leader under ideal conditions is realized. However, in many practical applications, the communication bandwidth between the intelligent agent and the controller is limited, which results in that the control signal received by the intelligent agent is not continuous and real-time, and the stability of the system is not guaranteed without proper adjustment and design.
Disclosure of Invention
The application aims to provide a quantitative control method of a multi-agent system, which is used for solving the problem that the stability of the system under the condition that the bandwidth between a controller and an agent is limited in the prior art cannot be ensured.
In order to realize the task, the following technical scheme is adopted in the application:
a method of quantitative control of a multi-agent system, said multi-agent system comprising a leader and N followers; the control method comprises the following steps:
establishing a system model of the multi-agent system, which comprises a system model of a follower and a system model of a leader;
establishing an error system of the multi-agent system, wherein the error system comprises an error between the output of the ith follower and the leader and an error between the q-order state of the ith follower and the virtual controller;
a controller for a multi-agent system is designed, including designing first through qth virtual controllers for an ith follower, and then designing control inputs for the ith follower.
Further, the system model of the follower is represented as:
for the ith follower, the following system model is established:
Figure BDA0002285592920000021
Figure BDA0002285592920000022
yi＝xi，1n formula 3, i ═ 1, 2
Wherein
Figure BDA0002285592920000023
xi，qAnd
Figure BDA0002285592920000024
representing the state variable of the system, wherein q is the order of the state variable of the system, niFor the total system order of the ith follower, the derivative of the parameter is represented by the dots above the parameter, fi，q() And
Figure BDA0002285592920000025
representing an unknown but smooth function, Δi，q(t) and
Figure BDA0002285592920000026
representing unknown time-varying interference, Qi(ui) Representing control input uiOutput after quantizer, ui＝ui(t) represents the true control input, yiRepresenting the output of each follower, and N representing the number of followers.
Further, the model of the quantizer is:
Figure BDA0002285592920000031
wherein the quantization levels of the quantizer are:
Figure BDA0002285592920000032
Figure BDA0002285592920000033
δi+，δi-e (0, 1) is a quantization density that can be selected,
Figure BDA0002285592920000034
and
Figure BDA0002285592920000035
as a dead zone parameter, ui(t-) Represents ui(t) the state at the previous time, p ═ 1, 2.
Further, the system model of the leader is represented as:
Figure BDA0002285592920000036
y0＝x0formula 8
y0An output representing the leader of the business is presented,
Figure BDA0002285592920000037
derivative of the output representing the leader, f0(x0T) is a known bounded function, i.e., the derivative function of the output of the leader that wants to track.
Further, the error between the ith follower and the leader output is expressed as:
Figure BDA0002285592920000038
where i and j denote the ith and jth followers, respectively, aijNot less than 0 is the information weight of jth follower received by ith follower, biThe information weight of the ith follower receiving the leader is more than or equal to 0, aijAnd biAre all non-negative constants.
Further, the error between the q-order state of the i followers and the virtual controller is represented as:
si，q＝xi，q-αi，q-1，q＝2，...，niformula 10
α thereini，q-1The q-1 th virtual controller of the ith follower.
Further, the first virtual controller of the ith follower is represented as:
Figure BDA0002285592920000041
wherein s isi，1Error between 1 st order state of ith follower system and virtual controller, Si，1Is a radial basis function vector, Si，1＝Si，1(Xi，1),Xi，1＝[xi，1，xj，1]T，xi，1Indicating the 1 st order state, x, of the ith followerj，1、xj，2Respectively representing the 1 st order state of the jth follower,
Figure BDA0002285592920000042
to the adaptation rate, ci，1And ai，1In order to be a positive adjustable parameter,
Figure BDA0002285592920000043
further, the second virtual controller of the ith follower is represented as:
Figure BDA0002285592920000044
wherein c isi，2And ai，2Is a positive adjustable parameter, si，2Error between 2 nd order state of ith follower system and virtual controller, Si，2Is a radial basis function vector, Si，2＝Si，2(Xi，2) And is
Figure BDA0002285592920000045
Figure BDA0002285592920000046
Figure BDA0002285592920000047
Is the adaptive rate;
the qth virtual controller for the ith follower is represented as:
Figure BDA0002285592920000048
wherein c isi，qAnd ai，qIs a positive adjustable parameter, wherein Si，qIs a radial basis function vector, Si，q＝Si，q(Xi，q) And is
Figure BDA0002285592920000049
Figure BDA00022855929200000410
In order to be able to adapt the rate,
Figure BDA00022855929200000411
Figure BDA00022855929200000412
xi，q、xj，qrespectively representing the q-order states of the ith follower and the jth follower systems.
Further, the ith follower designs a control input, represented as:
Figure BDA00022855929200000413
wherein:
Figure BDA0002285592920000051
Figure BDA0002285592920000052
Figure BDA0002285592920000053
wherein
Figure BDA0002285592920000054
ai，k,
Figure BDA0002285592920000055
ki，0，ki，1，gi，riIn order to be a positive adjustable parameter,
Figure BDA0002285592920000056
si，kn for the ith follower systemiThe states of the order and the k order,
Figure BDA0002285592920000057
is a radial basis function vector and
Figure BDA0002285592920000058
Figure BDA0002285592920000059
Figure BDA00022855929200000510
n representing the ith and jth follower systems, respectivelyiThe state of the step is that of the step,
Figure BDA00022855929200000511
is composed of
Figure BDA00022855929200000512
The derivative of (a) of (b),
Figure BDA00022855929200000513
to the adaptive rate
Figure BDA00022855929200000514
The derivative of (c).
Furthermore, the ith follower calculates the error between outputs by acquiring the information of the leader and other followers which can be acquired by the leader, the calculated first-order error establishes a first virtual controller, then the first controller is compared with the second-order state of the follower, the second-order error is calculated, a second virtual controller is established, then the second virtual controller is compared with the third-order state, the third-order error is calculated, and a third virtual controller is calculated; and so on until n is finally obtainediOrder error, then calculate the true input ui；uiThrough the quantizer model, a real quantized control signal Q is generatedi(ui) And the quantized signal is self-adapted by using the self-adapting rate, so that the ith follower can follow the output of the leader to realize quantization control.
Compared with the prior art, the method has the following technical characteristics:
1. the method for controlling the multi-agent system with the uncertain items and the interference signals has the advantages that the neural network is used for estimating the uncertain items and the interference signals contained in the system, so that the method for controlling the multi-agent system with the uncertain items and the interference signals is provided, compared with a common multi-agent system, the method has wider application and better practical effect, and the stability of the multi-agent system with the uncertain items under different communication speed requirements can be ensured.
2. The control input of the system is adjusted according to the quantization effect of the quantizer, so that a quantization control scheme is provided, the quantization grade of the quantizer can be automatically adjusted to meet different communication speed requirements, and the stability of the system can be always guaranteed no matter how coarse the quantizer is.
Drawings
FIG. 1 is a schematic flow diagram of the present application;
fig. 2 is a schematic diagram of a quantizer.
Detailed Description
The application discloses a quantitative control method of a multi-agent system, which is used for realizing consistency control of the multi-agent system under the limitation of different communication speed requirements. The method designs a corresponding controller for each follower multi-agent with a strict feedback structure; the method comprises the following steps:
step 1, establishing a system model of a multi-agent system, wherein the multi-agent system comprises a leader and N followers.
Step 1.1, establishing a system model of a follower
For the ith follower, the following system model is established:
Figure BDA0002285592920000061
Figure BDA0002285592920000062
yi＝xi，1n formula 3, i ═ 1, 2
Wherein
Figure BDA0002285592920000063
xi，qAnd
Figure BDA0002285592920000064
representing the state variable of the system, wherein q is the order of the state variable of the system, niIs the total system order of the ith follower. The dots above the parameter indicate the derivative of the parameter, the same applies below; f. ofi，q() And
Figure BDA0002285592920000065
representing an unknown but smooth function, Δi，q(t) and
Figure BDA0002285592920000066
representing unknown time-varying interference, Qi(ui) Representing control input uiOutput after quantizer, ui＝ui(t) represents the true control input, yiRepresenting the output of each follower, and N representing the number of followers.
The input is quantized by introducing the quantizer, so that control signals received by followers in the multi-agent system are not continuous any more, the communication rate is reduced, and different communication rate requirements can be met by adjusting quantization grade parameters in the quantizer.
The model of the quantizer is:
Figure BDA0002285592920000071
wherein the quantization levels of the quantizer are:
Figure BDA0002285592920000072
Figure BDA0002285592920000073
as shown in FIG. 2, δi+，δi-E (0, 1) is a quantization density that can be selected,
Figure BDA0002285592920000074
and
Figure BDA0002285592920000075
is a dead zone parameter.
Figure BDA0002285592920000076
Represents uiThe derivative of (c). u. ofi(t-) Represents ui(t) the state at the previous time, p ═ 1, 2.
Step 1.2, establishing a system model of the leader
The system model of the leader is represented as:
Figure BDA0002285592920000077
y0＝x0formula 8
y0Input representing leaderOut, the subscript 0 indicates that the leader, i.e., the leader's number in the multi-agent system, is 0.
Figure BDA0002285592920000078
Representing the derivative of the output, f0(x0T) is a known bounded function, i.e., the derivative function of the output of the leader that wants to track. In practice, this may be given according to any desired output trajectory, e.g. all follower outputs are intended to be a sine curve and the derivative is a cosine curve.
A system model of the multi-agent system is established through the step 1, and a foundation is provided for subsequent controller design.
And 2, establishing an error system of the multi-agent system.
In the scheme, in order to realize the synchronization of the output of the follower and the output of the leader, the problem is converted into the reduction of the error between the output of the follower and the output of the leader.
Step 2.1, firstly defining the error between the ith follower and the leader output:
Figure BDA0002285592920000081
where i and j denote the ith and jth followers, respectively, aijNot less than 0 is the information weight of jth follower received by ith follower, biThe information weight of the ith follower receiving the leader is more than or equal to 0, aijAnd biAre all non-negative constants.
And reducing the error, and converging the error to 0, so that the output of the follower can be finally followed to the leader. In practice, the follower may not receive the information of the leader, but only the information of other followers, so that in the defined error, the weight of the information of other followers is introduced, and the output of other followers can provide information for the current follower.
Step 2.2, defining the error between the q-order state of the ith follower and the virtual controller:
si，q＝xi，q-αi，q-1，q＝2，...，niformula 10
α thereini，q-1And (3) designing a q-1 th virtual controller of the ith follower through the step 3.
Because the output of the follower cannot be directly controlled, and only the output of the follower can be indirectly controlled through the design input, each stage state of the follower needs to be controlled, the states are made to follow the required states, and finally the control of the real output is realized.
Step 3, designing a controller of the multi-agent system
Step 3.1, design the first virtual controller for the ith follower, denoted as
Figure BDA0002285592920000082
Wherein Si，1Is a radial basis function vector, which is defined as:
s (x) is defined as a radial basis function vector, i.e., S (x) ═ S1(X)，S2(X)，...，Sl(X)]TAnd l is the dimension of the radial basis function vector and can be arbitrarily selected to be an integer greater than or equal to 2. X represents a variable of the function and,
Figure BDA0002285592920000091
wherein v iskThe radius of the radial basis function is represented,
Figure BDA0002285592920000092
the width of the radial basis function can be arbitrarily selected.
si，1Error between 1 st order state of ith follower system and virtual controller, Si，1＝Si，1(Xi，1),Xi，1＝[xi，1，xj，1]T，xi，1Indicating the 1 st order state, x, of the ith followerj，1、xj，2Respectively, representing the 1 st order state of the jth follower, wherein,
Figure BDA0002285592920000093
for the adaptation rate, this will be given at step 3.3. c. Ci，1And ai，1In order to be a positive adjustable parameter,
Figure BDA0002285592920000094
the first controller design uses the error defined in step 2, as well as the information available to other agents, including the leader and other followers.
If xi，2Is a directly designable input, say xi，2＝αi，1The design purpose can be achieved. But there is no way to design x directlyi，2Therefore, it is desirable to xi，2The first controller α capable of approaching designi，1. In step 2.2 s is definedi，2If this error also converges to 0, then xi，2＝αi，1The control objective can be achieved, with the follower output synchronized with the leader output.
The first virtual controller of the ith follower is used for controlling the output of the ith follower, however, the virtual controller does not exist in the actual system, so that the 2 nd order state of the ith follower needs to be controlled to approach the first virtual controller to achieve the control purpose.
Step 3.2, design the remaining virtual controllers for the ith follower
First, a second virtual controller is designed for the ith follower:
Figure BDA0002285592920000095
wherein c isi，2And ai，2Is a positive adjustable parameter, si，2Error between 2 nd order state of ith follower system and virtual controller, Si，2Is a radial basis function vector, Si，2＝Si，2(Xi，2) And is
Figure BDA0002285592920000096
Figure BDA0002285592920000097
Figure BDA0002285592920000098
Figure BDA0002285592920000099
Is the adaptation rate.
Then, a q-th virtual controller (q is more than or equal to 3 and less than or equal to n) is designed for the ith followeri-1)
Figure BDA00022855929200000910
Wherein c isi，qAnd ai，qIs a positive adjustable parameter. Wherein Si，qIs a radial basis function vector, Si，q＝Si，q(Xi，q) And is
Figure BDA00022855929200000911
Figure BDA00022855929200000912
In order to be able to adapt the rate,
Figure BDA00022855929200000913
Figure BDA00022855929200000914
xi，q、xj，qrespectively representing the q-order states of the ith follower and the jth follower systems.
Step 3.3, designing real control input for the ith follower:
Figure BDA0002285592920000101
wherein:
Figure BDA0002285592920000102
Figure BDA0002285592920000103
Figure BDA0002285592920000104
wherein
Figure BDA0002285592920000105
ai，k,
Figure BDA0002285592920000106
ki，0，ki，1，gi，riIn order to be a positive adjustable parameter,
Figure BDA0002285592920000107
si，kn for the ith follower systemiThe states of the order and the k order,
Figure BDA0002285592920000108
is a radial basis function vector and
Figure BDA0002285592920000109
Figure BDA00022855929200001010
Figure BDA00022855929200001011
n representing the ith and jth follower systems, respectivelyiA step state.
Figure BDA00022855929200001012
Is composed of
Figure BDA00022855929200001013
The derivative of (a) of (b),
Figure BDA00022855929200001014
to the adaptive rate
Figure BDA00022855929200001015
Given a derivative of
Figure BDA00022855929200001016
And
Figure BDA00022855929200001017
a positive initial value, their time-varying values can be calculated from their derivatives.
By increasing c, with other parameters unchangedi，k，ki，0，ki，1，ri，giEither or both, the error between the final follower output and the leader output may be reduced; by decreasing a with other parameters unchangedi，kThe error between the output of the final follower and the output of the leader can also be reduced. N, k 1, 2i。
The design of the virtual controller and control inputs in step 3 uses a neural network to estimate the unknown functions, thereby enabling the controller to adapt to the uncertainty contained in the multi-agent system. And 3, the controller is designed by using a Lyapunov stability method, so that the error system tends to be stable along with the time.
Considering that the signal of the control signal after passing through the quantizer, which is not the control signal, is input to the ith follower, the signal is discrete and distorted, an adaptive parameter is designed
Figure BDA00022855929200001018
To compensate for errors in the control signal generated by the quantizer.
The method comprises the following specific operations:
first, a control input signal u is designed for the ith followeri
The ith follower will output the information of the leader and other followers that it can acquireError is calculated using the first order error s calculated using equation 9i，1A first virtual controller is established by the formula 11, and then the second-order error s is calculated by comparing the first controller with the second-order state of the first controller by the formula 10i，2Using already obtained si，2Establishing a second virtual controller α by equation 12i，2To obtain αi，2Then, the error can be compared with the 3 rd order state of the ith follower, and the third order error s is calculated by the formula 10i，3Obtaining si，3A third virtual controller α can be calculated by equation 13i，3Then, the fourth order error s is calculated using equation 10i，4S for the passing formula 13i，4Computing the fourth virtual controller αi，4. From formula 13 to formula 10 to formula 13, this is repeated until finally n is obtained according to formula 10iOrder error
Figure BDA0002285592920000111
The true input u is then calculated by equation 14i. The scheme has no direct design input uiInstead, the design is completed by designing the virtual control rate step by step.
Then the designed uiThe generation applies to the ith follower:
designing control input u for ith follower by equation 14i，uiThrough quantizer formula 4, a true quantization control signal Q is generatedi(ui) At the input uiHas taken the quantization effect of the quantizer into account, using the adaptive rate
Figure BDA0002285592920000112
Equation 16 adapts the quantized signal, so uiControl signal Q generated by quantizationi(ui) The ith follower can be made to follow the output of the leader, implementing quantitative control.
As can be seen from equation 2, Qi(ui) Directly controlling the nth intelligent agentiDerivative of the order state, thereby controlling the nth of the ith agentiOrder status, according to equation 1, nth of ith followeriThe step state can control the nthiDerivatives of the order 1 states, and niThe derivative of the-1 st order state can control ni1 order state, niThe 1 st order state can control niThe derivatives of the-2 nd order state are analogized in turn, and finally can be controlled to the first order state of the ith follower, i.e., the output of the ith follower, so that the output of the ith follower follows the output of the leader.
This completes the design, and with the inventive controller, all of the follower outputs can be brought closer to the leader's output.

Claims (10)

1. A method of quantitative control of a multi-agent system, said multi-agent system comprising a leader and N followers; the control method is characterized by comprising the following steps:
establishing a system model of the multi-agent system, which comprises a system model of a follower and a system model of a leader;
establishing an error system of the multi-agent system, wherein the error system comprises an error between the output of the ith follower and the leader and an error between the q-order state of the ith follower and the virtual controller;
a controller for a multi-agent system is designed, including designing first through qth virtual controllers for an ith follower, and then designing control inputs for the ith follower.
2. A method of quantitative control of a multi-agent system according to claim 1, characterised in that the system model of the follower is represented as:
for the ith follower, the following system model is established:
Figure FDA0002285592910000011
Figure FDA0002285592910000012
yi＝xi，1n formula 3, i ═ 1, 2
Wherein
Figure FDA0002285592910000013
xi，qAnd xi，niRepresenting the state variable of the system, wherein q is the order of the state variable of the system, niFor the total system order of the ith follower, the derivative of the parameter is represented by the dots above the parameter, fi，q() And
Figure FDA0002285592910000014
representing an unknown but smooth function, Δi，q(t) and
Figure FDA0002285592910000015
representing unknown time-varying interference, Qi(ui) Representing control input uiOutput after quantizer, ui＝ui(t) represents the true control input, yiRepresenting the output of each follower, and N representing the number of followers.
3. A method of quantitative control of a multi-agent system according to claim 1, characterized in that the model of the quantizer is:
Figure FDA0002285592910000021
wherein the quantization levels of the quantizer are:
Figure FDA0002285592910000022
Figure FDA0002285592910000023
δi+，δi-e (0, 1) is selectableThe quantization density of (a) is determined,
Figure FDA0002285592910000024
and
Figure FDA0002285592910000025
as a dead zone parameter, ui(t-) Represents ui(t) the state at the previous time, p ═ 1, 2.
4. A method of quantitative control of a multi-agent system as claimed in claim 1, wherein the system model of the leader is represented as:
Figure FDA0002285592910000026
y0＝x0formula 8
y0An output representing the leader of the business is presented,
Figure FDA0002285592910000027
derivative of the output representing the leader, f0(x0T) is a known bounded function, i.e., the derivative function of the output of the leader that wants to track.
5. A method of quantitative control of a multi-agent system as claimed in claim 1, wherein the error between the ith follower and leader outputs is expressed as:
Figure FDA0002285592910000031
where i and j denote the ith and jth followers, respectively, aijNot less than 0 is the information weight of jth follower received by ith follower, biThe information weight of the ith follower receiving the leader is more than or equal to 0, aijAnd biAre all non-negative constants.
6. A method of quantitative control of a multi-agent system according to claim 1, wherein the error between the q-th order state of the i followers and the virtual controller is represented as:
si，q＝xi，q-αi，q-1，q＝2，...，niformula 10
α thereini，q-1The q-1 th virtual controller of the ith follower.
7. A method of quantitative control of a multi-agent system as claimed in claim 1, wherein the first virtual controller of the ith follower is represented as:
Figure FDA0002285592910000032
wherein s isi，1Error between 1 st order state of ith follower system and virtual controller, Si，1Is a radial basis function vector, Si，1＝Si，1(Xi，1),Xi，1＝[xi，1，xj，1]T，xi，1Indicating the 1 st order state, x, of the ith followerj，1、xj，2Respectively representing the 1 st order state of the jth follower,
Figure FDA0002285592910000033
to the adaptation rate, ci，1And ai，1In order to be a positive adjustable parameter,
Figure FDA0002285592910000034
8. a method of quantitative control of a multi-agent system as claimed in claim 1, wherein the second virtual controller of the ith follower is represented as:
Figure FDA0002285592910000035
wherein c isi，2And ai，2Is a positive adjustable parameter, si，2Error between 2 nd order state of ith follower system and virtual controller, Si，2Is a radial basis function vector, Si，2＝Si，2(Xi，2) And is
Figure FDA0002285592910000036
Figure FDA0002285592910000037
Figure FDA0002285592910000038
Is the adaptive rate;
the qth virtual controller for the ith follower is represented as:
Figure FDA0002285592910000039
wherein c isi，qAnd ai，qIs a positive adjustable parameter, wherein Si，qIs a radial basis function vector, Si，q＝Si，q(Xi，q) And is
Figure FDA00022855929100000310
Figure FDA00022855929100000311
In order to be able to adapt the rate,
Figure FDA00022855929100000312
Figure FDA0002285592910000041
xi，q、xj，qrespectively representing the q-order states of the ith follower and the jth follower systems.
9. A method of quantitative control of a multi-agent system as claimed in claim 1, wherein the ith follower designs a control input represented as:
Figure FDA0002285592910000042
wherein:
Figure FDA0002285592910000043
Figure FDA0002285592910000044
Figure FDA0002285592910000045
wherein
Figure FDA0002285592910000046
ai，k,
Figure FDA0002285592910000047
ki，0，ki，1，gi，riIn order to be a positive adjustable parameter,
Figure FDA0002285592910000048
si，kn for the ith follower systemiThe states of the order and the k order,
Figure FDA0002285592910000049
is a radial basis function vector and
Figure FDA00022855929100000410
Figure FDA00022855929100000411
Figure FDA00022855929100000412
n representing the ith and jth follower systems, respectivelyiThe state of the step is that of the step,
Figure FDA00022855929100000413
is composed of
Figure FDA00022855929100000414
The derivative of (a) of (b),
Figure FDA00022855929100000415
to the adaptive rate
Figure FDA00022855929100000416
The derivative of (c).
10. A quantitative control method of a multi-agent system as claimed in claim 1, characterized in that the ith follower calculates the error between the outputs by obtaining the information of the leader and other followers it can obtain, the calculated first order error establishes the first virtual controller, then the first controller compares with its own second order state, calculates the second order error, establishes the second virtual controller, then compares with the third order state, calculates the third order error, calculates the third virtual controller; and so on until n is finally obtainediOrder error, then calculate the true input ui；uiThrough the quantizer model, a real quantized control signal Q is generatedi(ui) And the quantized signal is self-adapted by using the self-adapting rate, so that the ith follower can follow the output of the leader to realize quantization control.
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