CN110190599B - Island microgrid control method based on finite time consistency theory - Google Patents

Island microgrid control method based on finite time consistency theory Download PDF

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CN110190599B
CN110190599B CN201910495672.7A CN201910495672A CN110190599B CN 110190599 B CN110190599 B CN 110190599B CN 201910495672 A CN201910495672 A CN 201910495672A CN 110190599 B CN110190599 B CN 110190599B
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窦春霞
胡小龙
张博
张占强
吴迪
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Shanghai Julihe Energy Technology Co ltd
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Yanshan University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • H02J3/382—
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/388—Islanding, i.e. disconnection of local power supply from the network

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Abstract

The invention discloses a method for designing an island micro-grid control strategy based on a finite time consistency theory, and belongs to the field of intelligent grid control. In an island micro-grid based on a distributed secondary control strategy, a peer-to-peer sparse network is utilized to communicate with an adjacent agent, and information and local information are obtained through processing by a consistency algorithm; and feeding back the consistency deviation to a frequency and voltage controller designed by a finite time consistency strategy; then, the output of the controller is input to droop control, then transferred to a voltage and current control loop, finally frequency and voltage stabilization is realized and a nominal value is tracked; wherein, when the communication is interrupted, the historical data of the adjacent agent is predicted based on the improved extreme learning machine, and the prediction result is input to a frequency and voltage controller designed by a finite time consistency strategy. So as to realize secondary frequency and voltage regulation under communication fault.

Description

Island microgrid control method based on finite time consistency theory
Technical Field
The invention belongs to the field of intelligent power grid control, and particularly relates to a design method of an island micro-grid control strategy based on a finite time consistency theory.
Background
With the increasing severity of energy crisis and environmental pollution problems, the use of new energy sources including distributed power generation technology has received wide social attention, and micro-grids have also been rapidly developed.
The operation of AC microgrid may be divided into two modes: grid-connected and island modes. When operating in island mode, multiple distributed power supplies are used to operate in parallel to improve output power quality. In island mode, hierarchical control is generally used to optimize power quality, and different hierarchical structures are used to define and implement different control objectives. Droop control is typically used as the primary controller to perform frequency and voltage regulation, and power distribution can be achieved. However, the conventional droop control has poor adjusting effect, and when the impedance of the distribution line is not uniform, the power distribution effect is poor. Some existing improvements include dummy impedances to balance line resistance, and some adaptive droop control strategies. Although there are many improved strategies for droop control, simple droop control is always unable to accurately track the reference value due to inherent errors. Therefore, in order to obtain a more precise control effect, a two-stage control strategy is suggested. Currently, existing secondary control strategies are generally classified into centralized and distributed types, and are often used for compensating droop control. The centralized secondary control is formulated by a microgrid central controller (MGCC), which collects and calculates the entire network information in the microgrid and then issues commands to the physical layer. Although the centralized control precision is high, the communication pressure of the system is large, and the reliability and the expandability are poor. Distributed secondary control does not require a central node for communication and most use peer-to-peer sparse networks, which communicate only with neighboring agents, thus having better scalability and feasibility. The distributed secondary control strategy can realize frequency and voltage recovery and accurate power distribution.
However, when communication is interrupted due to a failure, the entire system may be unstable.
Disclosure of Invention
The invention provides an island microgrid control method based on a finite time consistency theory, and aims to provide a new secondary control algorithm based on the consistency theory and the finite time theory, combine the consistency theory and the finite time theory, take the communication interruption condition into consideration, predict historical data of adjacent agents based on an improved Extreme Learning Machine (ELM), replace the interrupted communication link information with the prediction result, realize prediction compensation and improve the system stability.
In order to solve the technical problems, the technical scheme provided by the invention is as follows: an island micro-grid control method based on finite time consistency theory is characterized by comprising the following steps:
in an island micro-grid based on a distributed secondary control strategy, a peer-to-peer sparse network is utilized to communicate with an adjacent agent, and information and local information are obtained through processing by a consistent algorithm; and feeding back the consistency deviation to a frequency and voltage controller designed by a finite time consistency strategy; then, the output of the controller is input to droop control, then transferred to a voltage and current control loop, finally frequency and voltage stabilization is realized and a nominal value is tracked;
wherein, when the communication is interrupted, the historical data of the adjacent agent is predicted based on the improved extreme learning machine, and the prediction result is input to a frequency and voltage controller designed by a finite time consistency strategy.
The island micro-grid is divided into a physical layer and a network layer; the physical layer mainly comprises a controller and distributed power supplies, wherein the controller stabilizes the output of each distributed power supply and then connects the output of each distributed power supply to a common coupling point through a static transfer switch; or the controller stabilizes the output of each distributed power supply and then supplies power to the load by using the distributed power supplies; and the network layer performs data exchange among different power electronic inverters to complete output synchronization of the distributed power supply in the whole microgrid.
The further technical solution is to proxy DGiThe output error of (c) can be calculated by the consistency algorithm as:
Figure GDA0002723368160000021
wherein e isiRepresenting the global output error, x, of agent iiRepresenting the actual output value, x, of agent ijValue, x, communicated from a neighboring agent j representing agent irefNominal value representing the output of agent i, Leader node as consistency algorithm, aijNetwork communication links representing weighted adjacency coefficients, i.e. agents i, biRepresenting the weight leading to the Leader, b if and only if agent i has access to the Leaderi＞0；
To achieve a time-limited adjustment effect, a sign function is introduced:
Figure GDA0002723368160000022
the designed finite time controller is as follows:
Figure GDA0002723368160000023
ui＝βsig(ei)α
wherein, alpha and beta are finite time control parameters, alpha is an exponential coefficient, alpha is more than 0 and less than 1, the system convergence performance is improved, beta is a proportionality coefficient, beta is more than 0, and the step length of a control variable is determined.
The technical scheme is that the step of predicting the historical data of the adjacent agents based on the improved extreme learning machine specifically comprises the following steps:
(1) establishment of prediction model
For any N different samples (X)i,Yi) Wherein X isi＝[xi1 xi2 … xin]T∈RnRepresenting the historical output frequency or voltage, Y, of each DGi＝[yi1 yi2 … yim]T∈RmRepresenting the frequency or voltage of the desired output of each DG, for a single hidden neural network with L hidden nodes, can be expressed as:
Figure GDA0002723368160000031
wherein g (x) is an excitation function, typically a Gaussian function, Wi＝[wi1 wi2 … win]TAs input weights, γiAs output weight, ciIs the bias of the ith hidden layer unit, ojRepresenting a prediction output;
when considering empirical and structural risks, the mathematical model of ES-ELM can be expressed as:
Figure GDA0002723368160000032
Figure GDA0002723368160000033
wherein | | | purple hair2Representing empirical risk, | γ | luminance2Representing structural risk, wherein eta epsilon R represents the optimal break point determined by two risk proportion parameters in a cross validation mode;
an LS-SVM algorithm is introduced, and an ES-ELM model is converted into a Lagrange equation as follows:
Figure GDA0002723368160000034
wherein λ ═ λ1 λ2 … λN]Representing lagrange multiplier, H representing hidden layer output, γ ═ γ1 γ2 … γL]TRepresenting output weights
Figure GDA0002723368160000035
According to the KTT optimal condition, solving the gradient of the Lagrange equation and making the gradient be 0 to obtain
Figure GDA0002723368160000036
Thereby obtaining
Figure GDA0002723368160000041
Wherein X+A generalized inverse matrix representing matrix X;
(2) training of predictive models
The following is made clear prior to training:training set N different samples (X)i,Yi) The number of hidden layers L, the excitation function g (x),
step 1, when the data change is large, in order to obtain a better training result, preprocessing the data, wherein a specific formula is as follows:
Figure GDA0002723368160000042
wherein x (i) and x' (i) represent the original data and the processed data, respectively, ExAnd σiMeans and standard deviations representing the raw data;
step 2: input weight wikAnd bias ciArbitrarily setting in the range of (0,1), and calculating hidden layer output H;
step 3: according to
Figure GDA0002723368160000043
And calculating an output weight gamma and a Lagrange multiplier lambda.
(3) Result prediction
DG with lost communication information through historical data after ES-ELM trainingiAnd carrying out local prediction to respectively obtain predicted values of the frequency and the voltage.
The invention adopting the technical scheme has the beneficial effects that
(1) The invention provides a voltage and frequency control method based on a distributed finite time consistency algorithm in order to realize more accurate frequency and voltage recovery. A finite time strategy is combined with a conformance algorithm to reduce frequency and voltage coupling caused by uneven line impedance and to reach a reference value within a set finite time.
(2) The Lyapunov is used for proving that the provided finite time consistency algorithm can accurately realize frequency and voltage secondary control and accurately track a reference value. In addition, through the analysis of the Lyapunov function, the relationship between the convergence rate and the parameter selection can be obtained.
(3) When communication data is lost and communication is interrupted, the ELM is improved by considering experience risks and structural risks for training historical data of frequency and voltage, and predicting the lost communication data, and then transmitting the prediction result to the auxiliary controller, thereby suppressing the influence of communication failure.
Drawings
FIG. 1 is a simplified diagram of an island microgrid based on a distributed secondary control strategy according to the invention;
FIG. 2 is a block diagram of an inverter in the ith DG of the present invention;
FIG. 3 is a control block diagram of the overall system;
Detailed Description
The invention is described in further detail below with reference to the following detailed description and accompanying drawings:
the embodiment of the invention discloses an island microgrid control method based on a finite time consistency theory, which is characterized by comprising the following steps:
in an island micro-grid based on a distributed secondary control strategy, a peer-to-peer sparse network is utilized to communicate with an adjacent agent, and information and local information are obtained through processing by a consistent algorithm; and feeding back the consistency deviation to a frequency and voltage controller designed by a finite time consistency strategy; then, the output of the controller is input to droop control, then transferred to a voltage and current control loop, finally frequency and voltage stabilization is realized and a nominal value is tracked;
wherein, when the communication is interrupted, the historical data of the adjacent agent is predicted based on the improved extreme learning machine, and the prediction result is input to a frequency and voltage controller designed by a finite time consistency strategy.
The invention specifically comprises the following contents:
(1) hierarchical control architecture for designing micro-grid
The microgrid control is mainly divided into two parts: physical layer and network layer as shown in fig. 1. The physical layer mainly includes a controller and a distributed power supply, the controller stabilizes the output of each DG, and then connects the output of the DG to a Point of Common Coupling (PCC) through a Static Transfer Switch (STS), so that a common load hung on the PCC can be supplied with power, and certainly, a certain DG can be used to supply power to a specific load. The network layer mainly realizes data exchange among different power electronic inverters and realizes output synchronization of all DGs in the whole microgrid.
Fig. 2 shows a block diagram of an inverter inside a DG, assuming that there are N DG units in the microgrid, and each DG is defined as a DG in a certain sequencei(i＝1,2,...,N)，DGiConnected to the PCC by a feed line. The controller of the inverter mainly includes: 1) a power calculator; 2) a power controller; 3) a voltage control loop for regulating the AC voltage v of the DG unitoi(ii) a 4) A current control loop for regulating the AC current i of DG unitli。DGiThe output three-phase electricity is converted by dp-frame to obtain vodi,voqi,iodi,ioqiAnd then v is obtained by calculationoi,iliTo thereby calculate DGiThe real and reactive power components of the output. The power controllers are used for droop control by combining the rated power values:
Figure GDA0002723368160000061
wherein m isiAnd niIs a unit DGiActive and reactive droop control coefficients, ωiIs DGiOutput frequency of omegarefIs the nominal frequency of the system (2 π x 50red/s),
Figure GDA0002723368160000062
is the nominal voltage of the system and is,
Figure GDA0002723368160000063
is an AC voltage v measured by an inverteroiAnd as a reference value of the voltage current loop, PiAnd QiAre respectively a unit DGiThe real and reactive power components of the output.
(2) And designing a finite time consistency control strategy to realize the adjustment of frequency and voltage.
2.1 algebraic graph theory
In order to better describe the structure of the communication network of the microgrid, algebraic directed graph theory is used here. As shown in fig. 3, a communication network in a microgrid includes N multiple agents (DGs), labeled from 1 to N, and then mapped to a directed graph G (V, a), where a set of nodes V ═ a1,v2,...,vNRepresents all DGs, edge sets
Figure GDA0002723368160000064
Representing a communication link capable of information exchange. A ═ aij]N×NIs a weighted adjacency matrix coefficient, aii0 and aij≧ 0, if and only if (v)i,vj) E is when aijIs greater than 0. The neighbor node of the ith agent is defined as Ni＝{vj∈V:(vi,vj) E, the membership matrix (degree matrix) of the directed graph G is set to D ═ diag { D {1,d2,...,dNAnd are of
Figure GDA0002723368160000065
The laplacian matrix Ω ═ D-a is a symmetric semi-positive definite matrix.
2.2 finite time consistency Algorithm
The method is characterized in that the droop of the frequency and the voltage of the whole network caused by the fact that pure droop control cannot avoid is carried out, therefore, a finite time consistency algorithm is provided, the output of the distributed power supply is compensated by applying the previous graph theory analysis, and finally the output frequency and the output voltage of each agent are kept consistent and can be continuously and respectively tracked to the set nominal value omega of the frequency and the voltagerefAnd vrefAnd the dynamic performance of the system is improved.
To, the proxy DGiThe output error of (d) can be calculated with a consistency policy as:
Figure GDA0002723368160000066
wherein e isiGlobal input on behalf of agent iError, xiRepresenting the actual output value, x, of agent ijValue, x, communicated from a neighboring agent j representing agent irefNominal value representing the output of agent i, Leader node as consistency algorithm, aijNetwork communication links representing weighted adjacency coefficients, i.e. agents i, biRepresenting the weight leading to the Leader, b if and only if agent i has access to the Leaderi＞0。
To achieve a time-limited adjustment effect, a sign function is introduced.
Figure GDA0002723368160000071
The output global error of the agent i can be eliminated under a certain suitable condition, and finally the output of each agent in the microgrid is consistent and approaches to a nominal value.
The designed finite time controller is as follows:
Figure GDA0002723368160000072
wherein, alpha and beta are finite time control parameters, alpha is an exponential coefficient, alpha is more than 0 and less than 1, the system convergence performance is improved, beta is a proportionality coefficient, beta is more than 0, and the step length of a control variable is determined.
To verify the feasibility and stability of the designed finite time controller, the following Lyapunov function was constructed:
Figure GDA0002723368160000073
therefore, the temperature of the molten metal is controlled,
Figure GDA0002723368160000074
wherein e ═ e1 e2 … eN],B＝diag{b1 b2 … bNIs a semi-positive definite matrix, and, obviously,
Figure GDA0002723368160000075
defining a bounded matrix
Figure GDA0002723368160000076
For successive e Φ, functionTIs also continuous, and
Figure GDA0002723368160000077
and is present and greater than 0, defined as ρ.
Therefore, the temperature of the molten metal is controlled,
Figure GDA0002723368160000078
without being provided with
Figure GDA0002723368160000079
Then
Figure GDA0002723368160000081
Re-suppose that
Figure GDA0002723368160000082
Finally, one can obtain:
Figure GDA0002723368160000083
according to the above proof
Figure GDA0002723368160000084
Will be in a limited time
Figure GDA0002723368160000085
Approaches 0, and thus at time t*The output error e of the inner agent will approach 0, i.e. it can be realized
Figure GDA0002723368160000086
That is to say
Figure GDA0002723368160000087
A detailed distributed secondary control strategy is shown in fig. 3. As shown, information of the neighboring DGs is obtained through the peer-to-peer sparse network, and the obtained information and the local information are processed through a consistency algorithm. The compliance bias is fed back to the frequency and voltage controllers designed by the finite time compliance strategy. The output of the controller is then input to droop control, then transferred to the voltage and current control loops, finally achieving frequency and voltage stabilization and tracking to nominal values.
(3) Designing a predictive compensation strategy for communication interruptions
The traditional ELM is based on an empirical risk minimization principle, training errors are reduced to the minimum, but in the training process, an overfitting problem occurs, and the generalization capability of a model is reduced. Therefore, we introduce the structure risk minimization theory, reasonably balance the empirical risk and the structure risk, and propose an improved ELM model (ES-ELM). When communication data are lost and interfered, the improved extreme learning machine is utilized, historical data of voltage and frequency are trained, so that original data are predicted, and finally the predicted data are input into consistency control.
For any N different samples (X)i,Yi) Wherein X isi＝[xi1 xi2 … xin]T∈RnRepresenting the historical output frequency or voltage, Y, of each DGi＝[yi1 yi2 … yim]T∈RmRepresenting the frequency or voltage of the desired output of each DG, for a single hidden neural network with L hidden nodes, can be expressed as:
Figure GDA0002723368160000088
wherein g (x) is an excitation function, typically a Gaussian function, Wi＝[wi1 wi2 … win]TAs input weights, γiAs output weight, ciIs the bias of the ith hidden layer unit, ojRepresenting the prediction output.
When considering empirical and structural risks, the mathematical model of ES-ELM can be expressed as:
Figure GDA0002723368160000091
Figure GDA0002723368160000092
wherein | | | purple hair2Representing empirical risk, | γ | luminance2And representing structural risk, wherein the eta epsilon R represents the optimal break point determined by the cross validation of two risk proportion parameters.
An LS-SVM algorithm is introduced, and an ES-ELM model is converted into a Lagrange equation as follows:
Figure GDA0002723368160000093
wherein λ ═ λ1 λ2 … λN]Representing lagrange multiplier, H representing hidden layer output, γ ═ γ1 γ2 … γL]TRepresenting output weights
Figure GDA0002723368160000094
According to the KTT optimal condition, solving the gradient of the Lagrange equation and making the gradient be 0 to obtain
Figure GDA0002723368160000095
Thereby obtaining
Figure GDA0002723368160000096
Wherein X+Representing the generalized inverse of matrix X.
In summary, the ES-ELM considers both empirical risk and structural risk, so that the overfitting of the model is reduced and the generalization capability is excellent.
The following is made clear prior to training: training set N different samples (X)i,Yi) The number L of hidden layers, the excitation function g (x), the prediction process based on ES-ELM mainly comprises the following steps:
step 1, when the data change is large, in order to obtain a better training result, preprocessing the data, wherein a specific formula is as follows:
Figure GDA0002723368160000101
wherein x (i) and x' (i) represent the original data and the processed data, respectively, ExAnd σiMean and standard deviation of the raw data are indicated.
Step 2: input weight wikAnd bias ciThe hidden layer output H is calculated by arbitrarily setting the hidden layer output H within the range of (0, 1).
Step 3: the output weight γ and the lagrange multiplier λ are calculated according to equation (14).
After the ES-ELM training, the communication information DG that has been lost is paired by the historical dataiThe local prediction is carried out, the predicted values of the frequency and the voltage are respectively obtained, and the system instability phenomenon caused by data loss can be reduced by short prediction time.
Based on the analysis, the stability of the whole system is improved by applying a prediction compensation mechanism under the condition of communication interruption.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (3)

1. An island micro-grid control method based on finite time consistency theory is characterized by comprising the following steps:
in an island micro-grid based on a distributed secondary control strategy, a peer-to-peer sparse network is utilized to communicate with an adjacent agent, and information and local information are obtained through processing by a consistent algorithm; and feeding back the consistency deviation to a frequency and voltage controller designed by a finite time consistency strategy; then, the output of the controller is input to droop control, then transferred to a voltage and current control loop, finally frequency and voltage stabilization is realized and a nominal value is tracked;
when communication is interrupted, predicting historical data of adjacent agents based on an improved extreme learning machine, and inputting a prediction result to a frequency and voltage controller designed by a finite time consistency strategy;
the step of predicting the historical data of the adjacent agents based on the improved extreme learning machine specifically comprises the following steps:
(1) establishment of prediction model
For any N different samples (X)i,Yi) Wherein X isi＝[xi1 xi2 … xin]T∈RnRepresenting the historical output frequency or voltage, Y, of each DGi＝[yi1 yi2 … yim]T∈RmThe frequency or voltage representing the desired output of each DG is expressed for a single hidden neural network having L hidden nodes as:
Figure FDA0002723368150000011
wherein g (x) is an excitation function and is highA function of si, Wi＝[wi1 wi2 … win]TAs input weights, γiAs output weight, ciIs the bias of the ith hidden layer unit, ojRepresenting a prediction output;
when considering empirical and structural risks, the mathematical model of ES-ELM is expressed as:
Figure FDA0002723368150000012
Figure FDA0002723368150000013
wherein | | | purple hair2Representing empirical risk, | γ | luminance2Representing structural risk, wherein eta epsilon R represents the optimal break point determined by two risk proportion parameters in a cross validation mode;
an LS-SVM algorithm is introduced, and an ES-ELM model is converted into a Lagrange equation as follows:
Figure FDA0002723368150000021
wherein λ ═ λ1 λ2 … λN]Representing lagrange multiplier, H representing hidden layer output, γ ═ γ1 γ2 … γL]TRepresenting output weights
Figure FDA0002723368150000022
According to the KTT optimal condition, solving the gradient of the Lagrange equation and making the gradient be 0 to obtain
Figure FDA0002723368150000023
Thereby obtaining
Figure FDA0002723368150000024
Wherein X+A generalized inverse matrix representing matrix X;
(2) training of predictive models
The following is made clear prior to training: training set N different samples (X)i,Yi) The number of hidden layers L, the excitation function g (x),
step 1, when the data change is large, in order to obtain a better training result, preprocessing the data, wherein a specific formula is as follows:
Figure FDA0002723368150000031
wherein x (i) and x' (i) represent the original data and the processed data, respectively, ExAnd σiMeans and standard deviations representing the raw data;
step 2: input weight wikAnd bias ciArbitrarily setting in the range of (0,1), and calculating hidden layer output H;
step 3: according to
Figure FDA0002723368150000032
Calculating an output weight gamma and a Lagrange multiplier lambda;
(3) result prediction
DG with lost communication information through historical data after ES-ELM trainingiAnd carrying out local prediction to respectively obtain predicted values of the frequency and the voltage.
2. The island microgrid control method based on the finite time consistency theory is characterized in that the island microgrid is divided into a physical layer part and a network layer part; the physical layer mainly comprises a controller and distributed power supplies, wherein the controller stabilizes the output of each distributed power supply and then connects the output of each distributed power supply to a common coupling point through a static transfer switch; or the controller stabilizes the output of each distributed power supply and then supplies power to the load by using the distributed power supplies; and the network layer performs data exchange among different power electronic inverters to complete output synchronization of the distributed power supply in the whole microgrid.
3. The island microgrid control method based on the finite time consistency theory of claim 1, characterized in that DG is applied to an agentiThe output error consistency algorithm is as follows:
ei＝∑aij(xj-xi)+bi(xref-xi)
wherein e isiRepresenting the global output error, x, of agent iiRepresenting the actual output value, x, of agent ijValue, x, communicated from a neighboring agent j representing agent irefNominal value representing the output of agent i, Leader node as consistency algorithm, aijNetwork communication links representing weighted adjacency coefficients, i.e. agents i, biRepresenting the weight leading to the Leader, b if and only if agent i accesses the Leaderi＞0；
To achieve a time-limited adjustment effect, a sign function is introduced:
Figure FDA0002723368150000041
the designed finite time controller is as follows:
Figure FDA0002723368150000042
ui＝βsig(ei)α
wherein, alpha and beta are finite time control parameters, alpha is an exponential coefficient, alpha is more than 0 and less than 1, the system convergence performance is improved, beta is a proportionality coefficient, beta is more than 0, and the step length of a control variable is determined.
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