CN115390516A - Unknown nonlinear system distributed control method based on state event triggering - Google Patents

Unknown nonlinear system distributed control method based on state event triggering Download PDF

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CN115390516A
CN115390516A CN202210705973.XA CN202210705973A CN115390516A CN 115390516 A CN115390516 A CN 115390516A CN 202210705973 A CN202210705973 A CN 202210705973A CN 115390516 A CN115390516 A CN 115390516A
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state
intermittent
representing
time
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黄秀财
陈开政
王啸
孙丽贝
谢承果
赖俊峰
凌凯
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Chongqing University
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
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    • G05B19/41865—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS] or computer integrated manufacturing [CIM] characterised by job scheduling, process planning, material flow
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention relates to a distributed control method of an unknown nonlinear system based on state event triggering, which comprises the following steps: constructing a multi-agent system consisting of a plurality of agents, presetting an expected track of a control signal and constructing an intermittent state feedback distributed control model; calculating a running tracking path of the input analog control signal through the model; calculating a tracking error between the running tracking path and the expected track, and performing online training; and stopping training when the tracking error value is attenuated to a residual error range after training to obtain a trained intermittent state feedback distributed control model. The method can realize stable tracking control on the analog control signals of the multiple intelligent systems.

Description

Unknown nonlinear system distributed control method based on state event triggering
Technical Field
The invention relates to the field of automatic control, in particular to a distributed control method of an unknown nonlinear system based on state event triggering.
Background
Today, control systems are typically implemented over a network. On-board communication bandwidth and stored energy can be saved if network resources are shared among the sensors/actuators and control input channels, but both resources are limited in an autonomously operating network system. Therefore, maintaining stability under certain communication and energy constraints is critical for networked control systems. A common data transmission/communication method used in conventional digital control techniques is fixed time scheduled sampling, which, however, results in unnecessary overloading of the communication network.
To deal with the above problems of limited resources of microprocessors and limited bandwidth networks, event triggering techniques have been introduced. However, the existing event-triggered control is mainly applied to linear systems, and can be applied to some single non-linear systems, but has a certain limitation. However, a large number of actual networked engineering systems are not within the scope of the above-described applications.
On the other hand, most networked multi-agent systems often lack communication and energy resources, especially when the agents themselves or their internal devices are battery powered, the communication bandwidth and channels between subsystems are limited, which facilitates distributed event-triggered research. The existing distributed state trigger control has the problems of either some strict condition limitation or explosive complexity increase due to repeated/recursive derivation of the virtual controller in the backstepping technique. In addition, under the framework of event-triggered control, the research results of the network nonlinear strict feedback system with mismatch uncertainty are still limited, and the related problems are not solved well.
Disclosure of Invention
Aiming at the problems in the prior art, the technical problems to be solved by the invention are as follows: the current technical method can not stably track and control the analog control signals of a multi-intelligent system.
In order to solve the technical problem, the invention adopts the following technical scheme:
a distributed control method of an unknown nonlinear system based on state event triggering comprises the following steps:
s100: constructing a multi-agent system consisting of a plurality of agents:
Figure RE-GDA0003912015160000011
Figure RE-GDA0003912015160000012
y i ＝x i，1 ；(1)
wherein i represents the ith agent, i =1,2, \8230;, N; x is the number of i，k ：R + →R，u i ：R + →R，y i ：R + → R respectively represent the status, control input and control output of the ith agent, f i，k ：R k → R, k =1, \8230;, n denotes an unknown smooth nonlinear function,
Figure RE-GDA0003912015160000021
first derivative, x, representing the state of the ith agent at time k i，k+1 Represents the state at the moment of the ith agent k +1, x i，1 Represents the initial time state of the ith agent, x i，k Indicating the state at time instant of the ith agent k,
Figure RE-GDA0003912015160000022
first derivative, f, representing the state at the end n of the ith agent i，n Representing the unknown smooth non-linear function, x, corresponding to the last n moments of the ith agent i，n Representing the state of the ith agent at the end n moment;
wherein the content of the first and second substances,
Figure RE-GDA0003912015160000023
wherein x is i，k ∈R l Is a neural network input vector, W i，k ∈R p Is an ideal weight matrix of the weight of the image,
Figure RE-GDA0003912015160000024
is W i，k Is transposed, [ phi ] i，k (x i，k )＝[φ i，k1 (x i，k )，…，φ i，kp (x i，k )] T ∈R p Is a vector of basis functions; epsilon i，k (x i，k ) Belongs to R as an approximate error, and satisfies | | | phi i，k (x i，k )||≤φ m ，|ε i，k (x i，k )|≤ε m ，
Figure RE-GDA0003912015160000025
Wherein phi is m And ε m Is an unknown normal number, phi i，kh (x i，k ) Denotes a Gaussian function, C = [) 1 ，…，C l ] T To accept domain centers, b h Is the width of the gaussian function;
s200: presetting the expected track y of the control signal 0 The method comprises the following steps of constructing an intermittent state feedback distributed control model of the multi-agent system:
s210: an event trigger mechanism of intermittent state feedback is constructed, and the expression is as follows:
Figure RE-GDA0003912015160000026
Figure RE-GDA0003912015160000027
Figure RE-GDA0003912015160000028
Figure RE-GDA0003912015160000029
wherein, the first and the second end of the pipe are connected with each other,
Figure RE-GDA00039120151600000210
and
Figure RE-GDA00039120151600000211
in order to trigger the threshold value(s),
Figure RE-GDA00039120151600000212
for subsystem i, which represents itself when i =0, the first instant of equation (3) is completed,
Figure RE-GDA00039120151600000213
is the first trigger time of the adjacent subsystem j, l =0,1,2, \8230;, k = 1.., n.;
Figure RE-GDA00039120151600000214
and
Figure RE-GDA00039120151600000215
respectively, the time taken by agent i and its adjacent agent j to publish their respective state information in the ith event, and the state of agent i and its adjacent agent j remains unchanged, that is, the state of agent i and its adjacent agent j remains unchanged
Figure RE-GDA00039120151600000216
And
Figure RE-GDA0003912015160000031
s220: defining the tracking error of the intermittent state feedback, and the expression is as follows:
Figure RE-GDA0003912015160000032
Figure RE-GDA0003912015160000033
Figure RE-GDA0003912015160000034
wherein, the first and the second end of the pipe are connected with each other,
Figure RE-GDA0003912015160000035
Figure RE-GDA0003912015160000036
wherein, the first and the second end of the pipe are connected with each other,
Figure RE-GDA0003912015160000037
is indicative of a trigger threshold value that is,
Figure RE-GDA0003912015160000038
is that
Figure RE-GDA0003912015160000039
A first trigger time after completion;
s230: an intermittent state feedback distributed control model is constructed according to an event trigger mechanism and a tracking error of intermittent state feedback, and the expression is as follows:
Figure RE-GDA00039120151600000310
Figure RE-GDA00039120151600000311
Figure RE-GDA00039120151600000312
Figure RE-GDA00039120151600000313
and
Figure RE-GDA00039120151600000314
expression ofThe formula is as follows:
Figure RE-GDA00039120151600000315
Figure RE-GDA00039120151600000316
wherein the content of the first and second substances,
Figure RE-GDA00039120151600000317
represents W i,k Is estimated by the estimation of (a) a,
Figure RE-GDA00039120151600000318
Γ i,k is a matrix of positive determinations of the position of the object,
Figure RE-GDA00039120151600000319
indicating intermittent state feedback tracking error;
s300: simulating control signals for any multi-agent system
Figure RE-GDA00039120151600000320
As an input intermittent state feedback distributed control model to obtain a running tracking path y of a signal i ；
S400: calculating out
Figure RE-GDA00039120151600000321
Tracking error of (e = y) i -y 0 ；
S500: if the tracking error epsilon is attenuated to be within the range of the residual set, obtaining a trained intermittent state feedback distributed control model, and considering that the signal can be stably tracked and controlled at the moment;
if the tracking error epsilon is not attenuated to the range of the residual set, updating by adopting a least square method
Figure RE-GDA0003912015160000041
And returning to S300; the residual set expression is as follows:
Figure RE-GDA0003912015160000042
wherein | (t) | [0,T] Indicating that the output tracking error is [0, T ]]T is a certain time greater than 0, κ 1 For positive design parameters, Q is a positive definite symmetric matrix, λ min (Q) represents the minimum eigenvalue, V, of the matrix Q n (0) Express Lyapunov function V n Of an initial value of, Δ n Is a constant.
Preferably, the limiting conditions for the event triggering mechanism in S210 are expressed as follows:
Figure RE-GDA0003912015160000043
Figure RE-GDA0003912015160000044
wherein, Δ z i,k ,ρ i,kr And τ i,k Is a normal number, and is,
Figure RE-GDA0003912015160000045
z i，k denotes z i,k ＝x i,k -α i,kf K =2, \8230, n-1, which is a continuous state tracking error,
Figure RE-GDA0003912015160000046
trigger threshold, Δ z, representing the time instant k =1 i，1 Denotes the absolute value of the difference between the two at the time k =1, α i，k Representing first order filters in continuous states
Figure RE-GDA0003912015160000047
Wherein k =2, \8230;, n, u i,k > 0 is a time constant; alpha is alpha i,k-1 Is virtually controlled and serves as an input to a first order filter, and alpha i,kf Denotes alpha i,k-1 Output of (a), a i,k ，γ yi0 And σ yi0 Is a positive design parameter for the purpose of,
Figure RE-GDA0003912015160000048
for a positive design parameter in the intermittent regime, Δ α i，k Representing the absolute value of the difference between the design parameters in continuous and intermittent conditions, where Δ z i,k ,ρ i,kr And τ i,k Being a normal number, dependent on the trigger threshold Δ y 0 ,
Figure RE-GDA0003912015160000049
Topology parameter d i ,μ i Design parameter κ 1 ,μ i,k ,c i,k And b h ,l＝2,…,n,h＝1,…,p。
Since the proposed distributed state-triggered control is constructed by replacing states with the ones they are triggered, it is important that such replacement not only saves communication and energy resources, but also maintains consensus stability. The application of bandwidth can be effectively reduced by setting the trigger condition, and system resources are saved.
Compared with the prior art, the invention has at least the following advantages:
1. the method constructs intermittent state feedback distributed control based on the existing continuous state feedback distributed control according to a constructed event trigger mechanism, and allows the signal to be continuously transmitted backwards when the signal conforms to the trigger mechanism, so that the communication resource of the system is saved, the consensus stability is kept, in addition, the trigger mechanism is added, the control condition is improved, the tracking track of the signal can be basically coincided with the expected track, and the stable tracking control of the multi-agent system is realized.
2. Compared with the existing distributed state trigger control, the method has more loose application conditions and universality. In addition, the control method also solves the problem of explosive increase of complexity caused by repeated/recursive derivation of the virtual controller in the backstepping technology.
3. The existing distributed state trigger control has the limit of some severe conditions, or the problem of complexity explosive growth exists due to repeated/recursive derivation of a virtual controller in a backstepping technology; the control scheme of the invention avoids the problem of complexity explosive growth while relaxing the conditions of the application objects, and can stably track and control the multi-agent system.
Drawings
FIG. 1 is a block diagram of an agent i control strategy based on state trigger settings.
Fig. 2 is a diagram of a multi-agent system communication topology.
Fig. 3 shows the simulation result of the experiment performed by the method.
Detailed Description
The present invention is described in further detail below.
Referring to fig. 1-2, a distributed control method for an unknown nonlinear system based on state event triggering includes the following steps:
s100: constructing a multi-agent system consisting of a plurality of agents:
Figure BDA0003705312350000051
wherein i represents the ith agent, i =1,2, \8230;, N; x is the number of i，k ：R + →R，u i ：R + →R，y i ：R + → R respectively represent the status, control input and control output of the ith agent, f i，k ：R k → R, k =1, \ 8230;, n denotes an unknown smooth non-linear function,
Figure BDA0003705312350000052
first derivative, x, representing the state at time k of the ith agent i，k+1 Represents the state at the moment of the ith agent k +1, x i，1 Indicating the initial time state, x, of the ith agent i，k Indicating the state at time instant of the ith agent k,
Figure BDA0003705312350000053
first derivative, f, representing the state at the end (n) of the ith agent i，n To representUnknown smooth non-linear function, x, corresponding to the end (n) time of the ith agent i，n Representing the state of the ith agent at the end (n) of the agent;
wherein the content of the first and second substances,
Figure BDA0003705312350000061
wherein x is i,k ∈R l Is a neural network input vector, W i,k ∈R p Is an ideal weight matrix of the weight of the image,
Figure BDA0003705312350000062
is W i,k Is transposed, [ phi ] i , k (x i,k )＝[φ i,k1 (x i,k ),···,φ i,kp (x i,k )] T ∈R p Is a vector of basis functions; epsilon i,k (x i,k ) E is an approximation error satisfying
Figure BDA00037053123500000618
Wherein phi is m And ε m Is an unknown normal number, phi i,kh (x i,k ) Denotes a Gaussian function, C = [) 1 ,…,C l ] T To accept domain centers, b h Is the width of the gaussian function;
s200: presetting the expected track y of the control signal 0 The method comprises the following steps of constructing an intermittent state feedback distributed control model of the multi-agent system:
s210: an event trigger mechanism of intermittent state feedback is constructed, and the expression is as follows:
Figure BDA0003705312350000063
Figure BDA0003705312350000064
Figure BDA0003705312350000065
Figure BDA0003705312350000066
wherein the content of the first and second substances,
Figure BDA0003705312350000067
and
Figure BDA0003705312350000068
in order to trigger the threshold value(s),
Figure BDA0003705312350000069
for subsystem i, i =0, representing itself, the first instant of completing equation (3),
Figure BDA00037053123500000610
is the first trigger time of the adjacent subsystem j, l =0,1,2, \8230;, k =1, \8230;, n.;
Figure BDA00037053123500000611
and
Figure BDA00037053123500000612
respectively, the time taken by agent i and its adjacent agent j to publish their respective state information in the ith event, and the state of agent i and its adjacent agent j remains unchanged, that is, the state of agent i and its adjacent agent j remains unchanged
Figure BDA00037053123500000613
And
Figure BDA00037053123500000614
the limiting conditions for the event triggering mechanism in S210 are expressed as follows:
Figure BDA00037053123500000619
Figure BDA00037053123500000615
Figure BDA00037053123500000616
wherein, Δ z i,k ,ρ i,kr And τ i,k Is a normal number, i =1, \ 8230;, N,
Figure BDA00037053123500000617
k＝1,…,n，，z i，k denotes z i，k ＝x i，k -α i，kf K =2, \ 8230;, n-1, is the continuous state tracking error,
Figure BDA0003705312350000071
trigger threshold, Δ z, indicating the time instant k =1 i，1 Denotes the absolute value of the difference between the two at the time k =1, α i，k Representing first order filters in continuous states
Figure BDA0003705312350000072
α i，kf (0)＝α i，k-1 (0) Where k =2, \ 8230;, n, u i，k 0 is a time constant; alpha (alpha) ("alpha") i，k-1 Is virtually controlled and serves as an input to a first order filter, and alpha i，kf Denotes alpha i，k-1 Output of alpha i，k ，γ yi0 And σ yi0 Is a positive design parameter for the purpose of,
Figure BDA0003705312350000073
for positive design parameters in the intermittent regime, Δ α i，k Representing the absolute value of the difference between the design parameters in continuous and intermittent conditions, where Δ z i，k ，ρ i，kr And τ i，k Is a normal number, dependent on the trigger threshold Δ y 0 ，
Figure BDA0003705312350000074
Topology parameter d i ，μ i Design parameter κ 1 ，μ i，k ，c i，k And b h ，l＝2，…，n，h＝1，…，p。
S220: defining the tracking error of the intermittent state feedback, and expressing the following expression:
Figure BDA0003705312350000075
Figure BDA0003705312350000076
Figure BDA0003705312350000077
wherein the content of the first and second substances,
Figure BDA0003705312350000078
Figure BDA0003705312350000079
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00037053123500000710
which is indicative of a trigger threshold value, is,
Figure BDA00037053123500000711
is that
Figure BDA00037053123500000712
A first time trigger time after completion;
s230: an intermittent state feedback distributed control model is constructed according to an event triggering mechanism and a tracking error of intermittent state feedback, and the expression is as follows:
Figure BDA00037053123500000713
Figure BDA00037053123500000714
Figure BDA00037053123500000715
Figure BDA00037053123500000716
and
Figure BDA00037053123500000717
the expression of (c) is as follows:
Figure BDA00037053123500000718
Figure BDA00037053123500000719
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003705312350000081
represents W i,k Is estimated by the estimation of (a) a,
Figure BDA0003705312350000082
Γ i,k is a matrix of positive determinations of the position of the object,
Figure BDA0003705312350000083
indicating intermittent state feedback tracking error;
s300: simulating control signals for any multi-agent system
Figure BDA0003705312350000084
As an input intermittent state feedback distributed control model, obtaining a running tracking path y of a signal i ；
S400: calculating out
Figure BDA0003705312350000085
Tracking error of (e = y) i -y 0 ；
S500: stopping the pair when the tracking error epsilon decays to within the range of the residual set
Figure BDA0003705312350000086
The signal is considered to be capable of performing stable tracking control at the moment; if the attenuation is not within the range of the residual set, updating by adopting a least square method
Figure BDA0003705312350000087
Returning to the step S300, and stopping training until the tracking error epsilon is attenuated to the range of the residual set to obtain a trained intermittent state feedback distributed control model, wherein the expression of the residual set is as follows:
Figure BDA0003705312350000088
wherein | | Epsilon (t) | non-woven phosphor [0,T] Indicating that the output tracking error is [0, T ]]T is a certain time point greater than 0, κ 1 For positive design parameters, Q is a positive definite symmetric matrix, λ min (Q) represents the minimum eigenvalue of the matrix Q, V n (0) Representing the Lyapunov function V n Of initial value, Δ n Is a constant.
The training of the intermittent state feedback distributed control model adopts a self-adaptive online training method, which belongs to the prior art and comprises the following steps: the method is characterized in that an analog control signal is input into an intermittent state feedback distributed control model, when the input analog control signal of the multi-agent system meets the limiting condition of an event trigger mechanism, a signal is transmitted to the intermittent state feedback distributed control model according to the trigger condition to carry out self-adaptive online training, and the intermittent state feedback distributed control model is continuously updated
Figure BDA0003705312350000089
Thus, the device is provided withCan make it possible to
Figure BDA00037053123500000810
The updating of the method can adapt to the disturbance of factors such as external noise of the system and the like and the change of the intermittent state feedback distributed control model until the output tracking error is attenuated to the range of the residual set.
Simulation verification
Consider a set of systems consisting of 4 non-linear subsystems with the following kinetic model:
Figure BDA00037053123500000811
Figure BDA00037053123500000812
y i ＝x i,1
where i =1, \ 8230;, 4. Fig. 2 shows the interaction topology of the multi-agent system. In the simulation, a desired trajectory y is set 0 =0.5sin (0.1 t) +0.5sin (0.05 t), initial state x i,1 (0)＝1.0,x i,2 (0) =0, trigger threshold is
Figure BDA0003705312350000091
Δy 0 =0.005, parameters are set as: k is a radical of formula 1 ＝0.5,c 1 ＝c 2 ＝5.0, γ yi0 ＝1.5,σ yi0 ＝0.001,σ yi1 The RBFNN comprises 25 nodes, and the centers of the nodes are distributed in the space [ -5,5,5 ]]，b h Results are shown in fig. 3: FIG. 3 (a) shows the output traces of all subsystems, from which FIG. 3 (b) it can be determined that the output tracking error converges to a tight set near the origin, and FIG. 3 (c) shows the distributed protocol u i FIG. 3 (d) shows a state x i,2 A trigger time.
In addition, to test the impact of trigger thresholds on system tracking performance, selection was made
Figure BDA0003705312350000092
And the same other design parameter set was used, the results are shown in fig. 3 (e) -3 (f): shows two different trigger thresholds lower x i,1 ，x i,2 This indicates that the larger the trigger threshold used, the less trigger time is required, however, the larger the output tracking error is resolved.
Finally, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that various changes and modifications may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (2)

1. A distributed control method of an unknown nonlinear system based on state event triggering is characterized in that: the method comprises the following steps:
s100: constructing a multi-agent system consisting of a plurality of agents:
Figure RE-FDA0003912015150000011
Figure RE-FDA0003912015150000012
y i ＝x i，1 ； (1)
wherein i represents the ith agent, i =1,2, \8230;, N; x is the number of i，k ：R + →R，u i ：R + →R，y i ：R + → R denote the status, control input and control output, respectively, of the ith agent, f i，k ：R k → R, k =1, \8230;, n denotes an unknown smooth nonlinear function,
Figure RE-FDA0003912015150000013
first derivative, x, representing the state at time k of the ith agent i，k+1 Represents the state at the moment of the ith agent k +1, x i，1 Indicating the initial time state, x, of the ith agent i，k Indicating the state at time instant k of the ith agent,
Figure RE-FDA0003912015150000014
first derivative, f, representing the state at time n of the end of the ith agent i，n Representing the unknown smooth non-linear function, x, corresponding to the last n moments of the ith agent i，n Representing the state of the ith agent at the end n moment;
wherein the content of the first and second substances,
Figure RE-FDA0003912015150000015
wherein x is i,k ∈R l Is a neural network input vector, W i,k ∈R p Is an ideal weight matrix of the weight of the image,
Figure RE-FDA0003912015150000016
is W i,k Is transposed, [ phi ] i,k (x i,k )＝[φ i,k1 (x i,k ),…,φ i,kp (x i,k )] T ∈R p Is a vector of basis functions; epsilon i,k (x i,k ) Belongs to R as an approximate error and satisfies | | phi i,k (x i,k )||≤φ m ,|ε i,k (x i,k )|≤ε m ,
Figure RE-FDA00039120151500000110
Wherein phi is m And ε m Is an unknown normal number, phi i,kh (x i,k ) Denotes a Gaussian function, C = [) 1 ,…,C l ] T To accept domain centers, b h Is the width of the gaussian function;
s200: presetting the expected track y of the control signal 0 The method comprises the following steps of constructing an intermittent state feedback distributed control model of the multi-agent system:
s210: an event trigger mechanism of intermittent state feedback is constructed, and the expression is as follows:
Figure RE-FDA0003912015150000017
Figure RE-FDA0003912015150000018
Figure RE-FDA0003912015150000019
Figure RE-FDA0003912015150000021
wherein, the first and the second end of the pipe are connected with each other,
Figure RE-FDA0003912015150000022
and
Figure RE-FDA0003912015150000023
in order to trigger the threshold value(s),
Figure RE-FDA0003912015150000024
for subsystem i, i =0, representing itself, the first instant of completing equation (3),
Figure RE-FDA0003912015150000025
is the first trigger time of the adjacent subsystem j, l =0,1,2, \8230;, k =1, \8230;, n.;
Figure RE-FDA0003912015150000026
and
Figure RE-FDA0003912015150000027
respectively representing agent i and its neighborsThe time it takes for agent j to publish their respective state information in the l-th event indicates that agent i remains unchanged from its neighboring agent j state, i.e., the agent j state remains unchanged
Figure RE-FDA0003912015150000028
And
Figure RE-FDA0003912015150000029
s220: defining the tracking error of the intermittent state feedback, and expressing the following expression:
Figure RE-FDA00039120151500000210
Figure RE-FDA00039120151500000211
Figure RE-FDA00039120151500000212
wherein the content of the first and second substances,
Figure RE-FDA00039120151500000213
Figure RE-FDA00039120151500000214
wherein the content of the first and second substances,
Figure RE-FDA00039120151500000215
is indicative of a trigger threshold value that is,
Figure RE-FDA00039120151500000216
is that
Figure RE-FDA00039120151500000217
A first trigger time after completion;
s230: an intermittent state feedback distributed control model is constructed according to an event trigger mechanism and a tracking error of intermittent state feedback, and the expression is as follows:
Figure RE-FDA00039120151500000218
Figure RE-FDA00039120151500000219
Figure RE-FDA00039120151500000220
Figure RE-FDA00039120151500000221
and
Figure RE-FDA00039120151500000222
the expression of (c) is as follows:
Figure RE-FDA00039120151500000223
Figure RE-FDA00039120151500000224
wherein, the first and the second end of the pipe are connected with each other,
Figure RE-FDA0003912015150000031
represents W i,k The estimation of (a) is performed,
Figure RE-FDA0003912015150000032
Γ i,k is a matrix of positive determinations of the position of the object,
Figure RE-FDA0003912015150000033
representing intermittent state feedback tracking error;
s300: simulating control signals for any multi-agent system
Figure RE-FDA0003912015150000034
As an input intermittent state feedback distributed control model to obtain a running tracking path y of a signal i ；
S400: calculating out
Figure RE-FDA0003912015150000035
Tracking error of (e = y) i -y 0 ；
S500: if the tracking error epsilon is attenuated to be within the range of the residual set, a trained intermittent state feedback distributed control model is obtained, and at the moment, the signals are considered to be capable of performing stable tracking control;
if the tracking error epsilon is not attenuated to the range of the residual set, updating by adopting a least square method
Figure RE-FDA0003912015150000036
And returning to S300; the residual set expression is as follows:
Figure RE-FDA0003912015150000037
wherein | epsilon (t) | [0,T] Indicating that the output tracking error is 0, T]T is a certain time greater than 0, κ 1 For positive design parameters, Q is a positive definite symmetric matrix, λ min (Q) represents the minimum eigenvalue, V, of the matrix Q n (0) Express Lyapunov function V n Of initial value, Δ n Is a constant.
2. The distributed control method for the unknown nonlinear system based on the state event trigger as claimed in claim 1, characterized in that: the limiting conditions for the event trigger mechanism in S210 are expressed as follows:
Figure RE-RE-FDA0003912015150000038
Figure RE-RE-FDA0003912015150000039
wherein, Δ z i,k ,ρ i,kr And τ i,k Is a normal number of the blood vessel which is,
Figure RE-RE-FDA00039120151500000310
z i，k denotes z i,k ＝x i,k -α i,kf K =2, \ 8230;, n-1, is the continuous state tracking error,
Figure RE-RE-FDA00039120151500000311
trigger threshold, Δ z, indicating the time instant k =1 i，1 Denotes the absolute value of the difference between the two at the time k =1, α i，k Representing first order filters in continuous states
Figure RE-RE-FDA00039120151500000312
Wherein k =2, \ 8230;, n, u i,k 0 is a time constant; alpha (alpha) ("alpha") i,k-1 Is virtually controlled and serves as an input to a first order filter, and alpha i,kf Denotes alpha i,k-1 Output of (a), a i,k ，γ yi0 And σ yi0 Is a positive design parameter for the purpose of,
Figure RE-RE-FDA0003912015150000041
for a positive design parameter in the intermittent regime, Δ α i，k Representing the absolute value of the difference between the design parameters in continuous and intermittent conditions, where Δ z i,k ,ρ i,kr And τ i,k Being a normal number, dependent on the trigger threshold Δ y 0 ,
Figure RE-RE-FDA0003912015150000042
Topology parameter d i ,μ i Design parameter κ 1 ,μ i,k ,c i,k And b h ,l＝2,…,n,h＝1,…,p。
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