CN112558476B - Non-linear multi-wisdom system leader-free consistent control method based on attack compensation - Google Patents

Non-linear multi-wisdom system leader-free consistent control method based on attack compensation Download PDF

Info

Publication number
CN112558476B
CN112558476B CN202011403180.XA CN202011403180A CN112558476B CN 112558476 B CN112558476 B CN 112558476B CN 202011403180 A CN202011403180 A CN 202011403180A CN 112558476 B CN112558476 B CN 112558476B
Authority
CN
China
Prior art keywords
attack
agent system
neural network
representing
compensation
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202011403180.XA
Other languages
Chinese (zh)
Other versions
CN112558476A (en
Inventor
周琪
陈广登
鲁仁全
李鸿一
姚得银
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Guangdong University of Technology
Original Assignee
Guangdong University of Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Guangdong University of Technology filed Critical Guangdong University of Technology
Priority to CN202011403180.XA priority Critical patent/CN112558476B/en
Publication of CN112558476A publication Critical patent/CN112558476A/en
Application granted granted Critical
Publication of CN112558476B publication Critical patent/CN112558476B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • 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
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L41/00—Arrangements for maintenance, administration or management of data switching networks, e.g. of packet switching networks
    • H04L41/12—Discovery or management of network topologies
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
    • H04L63/1441—Countermeasures against malicious traffic

Abstract

The invention provides a non-leader consistent control method of a non-linear multi-agent system based on attack compensation, which solves the problem that the prior method can not realize the consistent control of a continuous time non-linear system under malicious attack, firstly establishes a continuous time non-linear multi-agent system model which is subjected to double attacks of a sensor and an executor, introduces a directed graph to describe the communication relation of the non-leader intelligent system, establishes an auxiliary variable and a consistent error based on the directed graph to realize the state consistency of agents, designs an attack compensation variable, establishes a new coordinate transformation auxiliary variable based on the attacked sensor data and the attack compensation variable, designs a virtual controller and an actual controller, designs a neural network weight adaptive law for regulating the weight of a radial basis neural network at the moment, and ensures the realization of good consistent control effect of the controllers, under the condition of considering double attacks, the states of the agents are enabled to be consistent and can be kept bounded.

Description

Non-linear multi-wisdom system leaderless consistency control method based on attack compensation
Technical Field
The invention relates to the technical field of information physical system safety and nonlinear multi-intelligence system control, in particular to a non-leader consistent control method of a nonlinear multi-intelligence system based on attack compensation.
Background
In recent decades, with the rapid development of electronic information technology, computer technology and network technology, the scale of many control systems becomes increasingly large and the internal association becomes increasingly complex, and if the traditional centralized control method is still used, the adverse consequences of large calculation amount, difficult expansion and the like are brought. Therefore, a multi-agent system based on group behaviors arises, and the multi-agent system means that a certain number of individuals (nodes) show certain behaviors and orders on a group level through self-organization and mutual cooperation.
In addition, with the rapid development of communication technology, Cyber-Physical Systems (CPS) have been developed. The CPS is mainly divided into a sensing execution layer, a network layer and an information layer. The perception execution layer mainly comprises various physical sensors and the like and is a source of information in the whole physical information system. In order to adapt to a variable environment, the network information physical system nodes are mostly arranged in an unsupervised environment and are easy to attack by attackers. Common attack approaches to the perceptual execution layer are: 1) data destruction: an attacker is unauthorized, and tampering, addition and deletion or damage and the like are carried out on the information acquired by the perception execution layer; 2) information interception: an attacker acquires information by wiring or by utilizing electromagnetic leakage in a transmission process, so that problems such as data privacy leakage and the like are caused; 3) and (3) node capture: an attacker controls part of network nodes, which may cause key leakage and endanger the communication security of the whole system. For the control aspect, whether the sensor can accurately acquire data and whether the actuator can accurately execute the control instruction has a great decisive role in whether the control performance of the system is good, and the traditional control method cannot realize good control performance when the data is damaged. Due to the characteristics of malicious attacks, existing research on security problems is basically directed at linear systems or discrete systems, and is difficult to conduct research on continuous time nonlinear systems.
The consistency control is used as a basic problem of multi-agent system research, has important theoretical research and practical application values, and the multi-agent system in real life has a plurality of applications, such as spacecrafts, unmanned planes, underwater vehicles, sensor networks, multi-mechanical arm cooperative equipment and the like. The consistency control is divided into leader consistency control and leaderless consistency control. 11/13/2018, a chinese patent (CN108803349A) discloses an optimal consistency control method and system for a nonlinear multi-agent system, which adopts a leader-follower control mode to form a multi-agent system composed of individual reference behavior models, and can efficiently solve the consistency problem of a complex multi-agent system while ensuring optimal control performance, and has practical application value and high expandability, however, in many cases, there is no leader or information of the leader cannot be normally received, for example, in a severe working environment, there is no reliable leader in the multi-agent system or the multi-agent system can communicate with the outside, and the agents can only rely on mutual information transfer to achieve consistency. Therefore, the problem of leaderless consistency is a problem of practical significance.
Disclosure of Invention
The invention provides a non-linear multi-wisdom system leaderless consistency control method based on attack compensation, which aims to solve the problem that the existing system consistency control method research cannot realize consistency control of a continuous time non-linear system under malicious attack, and does not consider the double attack condition of sensor attack and actuator attack at the same time.
In order to achieve the technical effects, the technical scheme of the invention is as follows:
a non-linear multi-intelligence system leaderless consistency control method based on attack compensation at least comprises the following steps:
s1, establishing a continuous time nonlinear multi-agent system model suffering from dual attacks of a sensor and an actuator;
s2, approximating a composite uncertainty nonlinear item in a nonlinear multi-agent system model based on a radial basis function neural network;
s3, confirming a communication topological relation among the agents in the leader-free multi-agent system by utilizing a directed graph;
s4, constructing an auxiliary variable without considering sensor attack by adopting a dynamic surface technology, and defining a consistent error;
s5, determining an attack compensation variable when the sensor is attacked, and constructing a new coordinate transformation auxiliary variable based on the attacked sensor data and the attack compensation variable;
and S6, designing a virtual controller, an actual controller and a neural network weight value self-adaptation law based on the new coordinate transformation auxiliary variable.
In the technical scheme, firstly, a continuous time nonlinear multi-agent system model suffering from double attacks of a sensor and an actuator is established, then a directed graph is introduced to describe a communication relation of a leader-free intelligent system, an auxiliary variable and a consistent error are established based on the directed graph, considering that an actual system state cannot be used for control design due to the fact that the sensor of the continuous time nonlinear multi-agent system is attacked, an attack compensation variable is designed, a new coordinate transformation auxiliary variable is established based on attacked sensor data and the attack compensation variable, a virtual controller and an actual controller are designed, at the moment, in order to adjust the weight of a radial basis neural network, a neural network weight adaptive law is designed, and the realization of a good consistent control effect of the controller is further ensured.
Preferably, the continuous-time nonlinear multi-agent system model building process of step S1 is:
defining parameters: k is 1,2,. n; q-1, 2,. n-1; p ═ 2,3,. n; r-3, 4.,. n-1, and obtaining a model expression of the continuous-time nonlinear multi-agent system as follows:
Figure BDA0002817631290000031
Figure BDA0002817631290000032
Figure BDA0002817631290000033
wherein x isi＝[xi,1,...,xi,n]TIs a state vector of a continuous-time nonlinear multi-agent system;
Figure BDA0002817631290000034
represents a complex non-linear term of uncertainty, an
Figure BDA0002817631290000035
uiA controller representing a continuous time nonlinear multi-agent system to be designed, to achieve consistency control;
Figure BDA0002817631290000036
representing an actuator attack vector;
Figure BDA0002817631290000037
representing a sensor attack vector;
Figure BDA0002817631290000038
and
Figure BDA0002817631290000039
are functions of state vector and time; x is the number ofa,i＝[xa,i,1,...,xa,i,n]TSensor data representing a continuous-time non-linear multi-agent system model after an attack. Here, xa,iCan be used to control the design rather than the actual system state xi。
Preferably, the uncertainty nonlinear term is compounded in step S2
Figure BDA00028176312900000310
Is uniformly set tof (x), using radial basis function neural network to compact
Figure BDA00028176312900000311
To any degree of accuracy
Figure BDA00028176312900000312
The process of approximating f (x) satisfies:
Figure BDA00028176312900000313
wherein x represents the input of the radial basis function neural network, and q is the input dimension of the radial basis function neural network; epsilon (x) is an approximation error, and satisfies the following conditions:
Figure BDA00028176312900000314
φ(x)＝[φ1(x),φ2(x),…,φl(x)]a vector of basis functions is represented as,
Figure BDA00028176312900000315
represents an ideal weight, defined as: for all that
Figure BDA00028176312900000316
The value of θ that minimizes the approximation error | ε (x) is expressed as:
Figure BDA00028176312900000317
in this case, the problem that it is difficult to accurately model the intelligent system, that is, the system model
Figure BDA00028176312900000318
The specific expression of the method cannot be accurately known, which makes the design of the controller of the continuous-time nonlinear multi-agent system to be designed difficult, namely, the method adopts neural network technology to approximate the unknown nonlinear item of the system. In fact, the disturbance related to the system state and the actuator attack function can be solved by using the neural network technology.
Preferably, the basis function vector phii(x) Selecting a Gaussian function, wherein the expression is as follows:
Figure BDA0002817631290000048
wherein l is the number of nodes of the neural network, ζi＝[ζi,1,…,ζiq]The acceptance domain of the basis function is represented,
Figure BDA0002817631290000049
representing the width of the gaussian function.
Preferably, the process of applying the directed graph to confirm the communication topology relationship between the agents in the leaderless multi-agent system in step S3 is:
providing a directed graph G ═ { V, E }, wherein V ═ 1, 2.., N } represents the set of nodes in the directed graph G, and "1, 2.., N" represents the number of the multi-agent system;
Figure BDA0002817631290000041
represents the set of directed edges in the directed graph, and (j, i) means that the multi-agent system i can receive information from the multi-agent system j, the multi-agent system j is a neighbor of the multi-agent system i, and the expression of the set of neighbors of the multi-agent system i is as follows: n is a radical ofi＝{j∈V(i,j)∈E,i≠j}；
Definition a ═ aij]∈Rn×nWeight matrix as directed graph G, aijIs the weight matrix element of the directed graph G; if the multi-agent system i is able to receive information from the multi-agent system j, then aij1(i ≠ j), otherwise, aij＝0。
Preferably, in step S4, the dynamic surface technique is used to construct the auxiliary variable and the consistent error without considering sensor attack, and the expression of the auxiliary variable is:
Figure BDA0002817631290000042
wherein, betaiAuxiliary variables are represented to achieve leaderless consistent control.
The consistent error expression is:
ei,1＝xi,1-βi
in fact, when ei,1X → 0 timei,1→βiThe output of the agent i in the multi-agent system is consistent with the output of the neighbor; the error table expression is:
Figure BDA0002817631290000043
wherein the content of the first and second substances,
Figure BDA0002817631290000044
representing a virtual controller alphai,p-1Output after passing through a first order filter to avoid the need for repeating pairs of alpha in controller designi,p-1The differentiation causes a problem of an increase in the amount of calculation;
Figure BDA0002817631290000045
the expression is satisfied:
Figure BDA0002817631290000046
wherein, taui,p-1Denotes the time constant, τi,p-1And if the filtering error is more than 0, the filtering error is obtained as follows:
Figure BDA0002817631290000047
wherein eta isi,p-1Representing the filtering error.
Preferably, the attack compensation variable when the sensor attack is suffered in step S5 is set as
Figure BDA0002817631290000051
Attack compensation variable
Figure BDA0002817631290000052
Satisfies the following conditions:
Figure BDA0002817631290000053
Figure BDA0002817631290000054
wherein, bi,k,ci,k,di,k,ρi,kAre all design parameters, bi,k,ci,k,di,k,ρi,kAre all greater than 0.
Preferably, the attacked sensor data in step S5 is xa,iBased on the attacked sensor data as xa,iAnd attack compensation variables
Figure BDA0002817631290000055
The expression for constructing the new coordinate transformation is as follows:
Figure BDA0002817631290000056
Figure BDA0002817631290000057
wherein z isi,pRepresenting sensor data based on attacks as xa,iAnd attack compensation variables
Figure BDA0002817631290000058
And constructing a new auxiliary variable after coordinate transformation. Due to unknown data injection attacks
Figure BDA0002817631290000059
The actual state vector xiCan not be accurately measured, error variable ei,kCannot be used for subsequent design of controllers or adaptation lawsThus, the auxiliary variable z is constructedi,pAnd a subsequent virtual controller can be designed by combining the neural network technology.
Preferably, the expression of the designed virtual controller in step S6 is:
Figure BDA00028176312900000510
Figure BDA00028176312900000511
Figure BDA00028176312900000512
actual controller u based on virtual controller relates toiComprises the following steps:
Figure BDA00028176312900000513
wherein phi isi,kIs a Gaussian function of the neural network,
Figure BDA00028176312900000514
the self-adaptive parameters are the weights of the radial basis function neural network.
In order to avoid the problem of excessive calculation caused by repeatedly deriving the virtual controller, a dynamic surface technology is adopted, and the virtual control signal is made to pass through a first-order filter to obtain the virtual control signal and an approximate value of a derivative of the virtual control signal.
Preferably, the adaptive parameters of the weights of the radial basis function neural network
Figure BDA00028176312900000515
The self-adaptive rate of (2) satisfies:
Figure BDA0002817631290000061
Figure BDA0002817631290000062
Figure BDA0002817631290000063
Figure BDA0002817631290000064
wherein, gamma isi,kRepresenting the adaptive law gain matrix, σi,kTo modify the parameter matrix.
The weight of the adaptive law on-line adjusting neural network is designed based on the Lyapunov stability theorem, and a good control effect is achieved by combining an actual controller.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention provides a leader-free consistent control method of a nonlinear multi-agent system based on attack compensation, which comprises the steps of firstly establishing a continuous time nonlinear multi-agent system model suffering from dual attacks of a sensor and an actuator, introducing a directed graph to describe a communication relation of the leader-free intelligent system, establishing an auxiliary variable and a consistent error based on the directed graph to realize the state consistency of the intelligent system, considering that the actual system state cannot be used for control design due to the fact that the sensor of the continuous time nonlinear multi-agent system is attacked, designing an attack compensation variable, establishing a new coordinate transformation auxiliary variable based on attacked sensor data and the attack compensation variable, designing a virtual controller and an actual controller, designing a neural network weight self-adaption law for adjusting the weight of a radial basis neural network, and further ensuring the realization of good consistent control effect of the controller, under the condition of considering double attacks, the states of the intelligent agents are consistent, the bounded state can be kept, and the consistency control of the nonlinear multi-intelligent-agent system without a leader is realized.
Drawings
Fig. 1 shows a flow chart of a non-linear multi-intelligence system leaderless coherent control method based on attack compensation proposed in an embodiment of the present invention;
FIG. 2 is a topological diagram of communication relationships between multi-agent systems in accordance with an embodiment of the present invention;
FIG. 3 shows state x of the multi-agent system proposed in the embodiment of the present inventioni,1A graph of the relationship over time t;
FIG. 4 shows state x of the multi-agent system proposed in the embodiment of the present inventioni,2A graph of the relationship over time t;
FIG. 5 shows state x of the multi-agent system proposed in the embodiment of the present inventioni,1，xi,2A relation curve chart of the time t and the time t;
FIG. 6 shows a controller signal u according to an embodiment of the present inventioniA graph of the relationship over time t;
FIG. 7 is a representation of a leader-less uniform auxiliary variable signal β as set forth in an embodiment of the present inventioniA graph of the relationship over time t;
FIG. 8 shows a first attack compensation signal proposed in an embodiment of the present invention
Figure BDA0002817631290000071
A graph of the relationship over time t;
FIG. 9 shows a second shot compensation signal proposed in an embodiment of the present invention
Figure BDA0002817631290000072
Graph of the relationship over time t.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for better illustration of the present embodiment, certain parts of the drawings may be omitted, enlarged or reduced, and do not represent actual dimensions;
it will be understood by those skilled in the art that certain well-known descriptions of the figures may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
a flow chart of a method for leaderless cooperative control of a nonlinear multi-wisdom system based on attack compensation as shown in fig. 1, the steps of the method comprising:
s1, establishing a continuous time nonlinear multi-agent system model suffering from double attacks of a sensor and an actuator;
s2, approximating a composite uncertainty nonlinear item in a nonlinear multi-agent system model based on a radial basis function neural network;
s3, confirming a communication topological relation among the agents in the leader-free multi-agent system by utilizing a directed graph;
s4, constructing an auxiliary variable without considering sensor attack by adopting a dynamic surface technology, and defining a consistent error;
s5, determining an attack compensation variable when the sensor is attacked, and constructing a new coordinate transformation auxiliary variable based on the attacked sensor data and the attack compensation variable;
and S6, designing a virtual controller, an actual controller and a neural network weight self-adaptation law based on the new coordinate transformation auxiliary variable.
The process of establishing the continuous-time nonlinear multi-agent system model in step S1 is as follows:
defining parameters: k is 1,2,. n; q-1, 2,. n-1; p ═ 2,3,. n; r-3, 4.,. n-1, and obtaining a model expression of the continuous-time nonlinear multi-agent system as follows:
Figure BDA0002817631290000081
Figure BDA0002817631290000082
Figure BDA0002817631290000083
wherein x isi＝[xi,1,...,xi,n]TIs a state vector of a continuous-time nonlinear multi-agent system;
Figure BDA0002817631290000084
represents a complex non-linear term of uncertainty, an
Figure BDA0002817631290000085
uiA controller representing a continuous time nonlinear multi-agent system to be designed, to achieve consistency control;
Figure BDA0002817631290000086
representing an actuator attack vector;
Figure BDA0002817631290000087
representing a sensor attack vector;
Figure BDA0002817631290000088
and
Figure BDA0002817631290000089
are functions of state vector and time; x is the number ofa,i＝[xa,i,1,...,xa,i,n]TSensor data representing a continuous-time non-linear multi-agent system model after an attack. Here, xa,iCan be used to control the design rather than the actual system state xi。
In the present embodiment, the uncertainty nonlinear term is compounded in step S2
Figure BDA00028176312900000810
Uniformly set as f (x), and tightly gather by using radial basis function neural network
Figure BDA00028176312900000811
To any degree of accuracy
Figure BDA00028176312900000812
The process of approximating f (x) satisfies:
Figure BDA00028176312900000813
wherein x represents the input of the radial basis function neural network, and q is the input dimension of the radial basis function neural network; epsilon (x) is the approximation error, and satisfies:
Figure BDA00028176312900000814
φ(x)＝[φ1(x),φ2(x),...,φl(x)]a vector of basis functions is represented as,
Figure BDA00028176312900000815
represents an ideal weight, defined as: for all
Figure BDA00028176312900000816
The value of θ that minimizes the approximation error | ε (x), expressed as:
Figure BDA00028176312900000817
the problem that the intelligent system is difficult to accurately model is solved, namely in the system model
Figure BDA00028176312900000818
The specific expression of the method cannot be accurately known, which makes the design of the controller of the continuous-time nonlinear multi-agent system to be designed difficult, namely, the method adopts neural network technology to approximate the unknown nonlinear item of the system. In fact, the disturbance related to the system state and the actuator attack function can be solved by using the neural network technology. Vector of basis functions phii(x) Selecting a Gaussian function, wherein the expression is as follows:
Figure BDA00028176312900000819
wherein l is the number of nodes of the neural network, ζi＝[ζi,1,...,ζiq]The acceptance domain of the basis function is represented,
Figure BDA00028176312900000820
representing the width of the gaussian function.
In this embodiment, the process of applying the directed graph to confirm the communication topology relationship between the agents in the leaderless multi-agent system in step S3 is as follows:
providing a directed graph G ═ { V, E }, wherein V ═ 1, 2.., N } represents the set of nodes in the directed graph G, and "1, 2.., N" represents the number of the multi-agent system;
Figure BDA0002817631290000091
represents the set of directed edges in the directed graph, and (j, i) means that the multi-agent system i can receive information from the multi-agent system j, the multi-agent system j is a neighbor of the multi-agent system i, and the neighbor set expression of the multi-agent system i is as follows: n is a radical ofi＝{j∈V(i,j)∈E,i≠j}；
Definition A ═ aij]∈Rn×nWeight matrix as directed graph G, aijIs the weight matrix element of the directed graph G; if the multi-agent system i is able to receive information from the multi-agent system j, then aij1(i ≠ j), otherwise, aij＝0。
Step S4, constructing the auxiliary variable and the consistent error without considering the sensor attack by using the dynamic surface technique, where the expression of the auxiliary variable is:
Figure BDA0002817631290000092
wherein, betaiAuxiliary variables are represented to achieve leaderless consistent control.
The consistent error expression is:
Figure BDA0002817631290000093
in fact, when ei,1X → 0 timei,1→βiThe output of the agent i in the multi-agent system is consistent with the output of the neighbor; the error table expression is:
Figure BDA0002817631290000094
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002817631290000095
representing a virtual controller alphai,p-1Output after passing through a first order filter to avoid the need for repeating pairs of alpha in controller designi,p-1Differentiation causes a problem of an increase in the amount of calculation;
Figure BDA0002817631290000096
the expression is satisfied:
Figure BDA0002817631290000097
wherein, taui,p-1Denotes the time constant, τi,p-1And if the filtering error is more than 0, the filtering error is obtained as follows:
Figure BDA0002817631290000098
wherein eta isi,p-1Representing the filtering error.
In the present embodiment, the attack compensation variable when the sensor attack is applied in step S5 is set as
Figure BDA0002817631290000099
Attack compensation variable
Figure BDA00028176312900000910
Satisfy the requirement of：
Figure BDA00028176312900000911
Figure BDA00028176312900000912
Wherein, bi,k,ci,k,di,k,ρi,kAre all design parameters, bi,k,ci,k,di,k,ρi,kAre all greater than 0.
In this embodiment, the attacked sensor data in step S5 is xa,iBased on the attacked sensor data as xa,iAnd attack compensation variables
Figure BDA0002817631290000101
The expression for constructing the new coordinate transformation is as follows:
Figure BDA0002817631290000102
Figure BDA0002817631290000103
wherein z isi,pRepresenting sensor data based on attacks as xa,iAnd attack compensation variables
Figure BDA0002817631290000104
And constructing a new auxiliary variable after coordinate transformation. Due to unknown data injection attacks
Figure BDA0002817631290000105
The actual state vector xiCan not be accurately measured, error variable ei,kCannot be used for subsequent design of the controller or adaptation law, and therefore the auxiliary variable z is constructedi,pAfter being designed by combining with neural network technologyAnd continuing to virtualize the controller.
The expression of the designed virtual controller is as follows:
Figure BDA0002817631290000106
Figure BDA0002817631290000107
Figure BDA0002817631290000108
actual controller u based on virtual controller relates toiComprises the following steps:
Figure BDA0002817631290000109
wherein phii,kIs a Gaussian function of the neural network,
Figure BDA00028176312900001010
the self-adaptive parameters are the weights of the radial basis function neural network. In order to avoid the problem of overlarge calculated amount caused by repeatedly carrying out derivation on the virtual controller, a dynamic surface technology is adopted, and the virtual control signal is made to pass through a first-order filter to obtain the virtual control signal and an approximate value of a derivative of the virtual control signal.
Adaptive parameters of radial basis function neural network weight
Figure BDA00028176312900001011
The self-adaptive rate of (2) satisfies:
Figure BDA00028176312900001012
Figure BDA00028176312900001013
Figure BDA00028176312900001014
Figure BDA00028176312900001015
wherein, gamma isi,kRepresenting the adaptive law gain matrix, σi,kTo modify the parameter matrix.
In order to further verify the effectiveness of the method provided by the present invention, the following is further described in combination with an actual simulation, in the present simulation, the control objective is to make the states of the multi-agent systems consistent from the unordered initial state under the attack of the sensors and the actuators, and the ith multi-agent system in the simulation is:
Figure BDA0002817631290000111
Figure BDA0002817631290000112
Figure BDA0002817631290000113
wherein the sensor attack signal is
Figure BDA0002817631290000114
The actuator attack signal is
Figure BDA0002817631290000115
To avoid loss of generality, the initial values for the randomly chosen agent states are:
x1(0)＝[-1；-0.1]；x2(0)＝[1.2；-0.5]；x3(0)＝[0.8；1](ii) a Other initial states such as the initial states of the adaptive law and the attack compensation signalIs 0; the design parameters of the controller are as follows:
bi,1＝bi,2＝2；ci,1＝ci,2＝2；di,1＝di,2＝1；τi＝0.1；σi,1＝σi,2＝0.1；ρi＝1；Γi,1＝Γi,10.1; a communication relationship topology diagram of a multi-agent system is shown in FIG. 2, FIG. 2 is a directed graph represented by 4 nodes (1,2,3,4), wherein arrows represent information transmission directions, FIG. 3 represents a first agent system state xi,1Graph with time t; FIG. 4 shows a second agent system state xi,2Graph with time t; in fig. 3 and 4, the abscissa represents time, and the ordinate represents the state value of the smart system, where i is 1,2,3, 4; for a clearer presentation, FIG. 5 shows state x of the multi-agent system from a three-dimensional perspectivei,1，xi,2And the relation curve chart of the time t, as can be seen from fig. 3 to 5, after about 4s of adjustment time, the different initial states of the agent are consistent, that is, the states are all converged to 0. FIG. 6 shows a controller signal u according to an embodiment of the present inventioniA graph of the relationship over time t; FIG. 7 is a leader-less uniform auxiliary variable signal βiThe control signal also tends to 0 after the system is consistent with the curve chart of the relation changing along with the time t, and the control signal also tends to be 0 at betaiAfter going to 0, the agent has reached full agreement. FIGS. 8-9 are graphs of attack compensation variable signals, with FIG. 8 showing a first attack compensation signal
Figure BDA0002817631290000116
A graph of the relationship over time t; FIG. 9 shows a second attack compensation signal
Figure BDA0002817631290000117
Graph of the relationship over time t. Since the attack signal is related to the system state, when the state goes to 0, the attack signal also gradually goes to 0, so that attack compensation is not needed, and the attack compensation signal also gradually goes to 0.
The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (6)

1. A non-linear multi-intelligence system leaderless consistency control method based on attack compensation is characterized by at least comprising the following steps:
s1, establishing a continuous time nonlinear multi-agent system model suffering from double attacks of a sensor and an actuator;
s2, approximating a composite uncertainty nonlinear item in a nonlinear multi-agent system model based on a radial basis function neural network;
s3, confirming a communication topological relation among the agents in the leader-free multi-agent system by utilizing a directed graph;
s4, constructing an auxiliary variable without considering sensor attack by adopting a dynamic surface technology, and defining a consistent error;
s5, determining an attack compensation variable when the sensor is attacked, and constructing a new coordinate transformation auxiliary variable based on the attacked sensor data and the attack compensation variable;
let the attack compensation variable when the sensor attack is applied in step S5 be
Figure FDA0003578034820000011
Attack compensation variable
Figure FDA0003578034820000012
Satisfies the following conditions:
Figure FDA0003578034820000013
Figure FDA0003578034820000014
wherein, bi,k,ci,k,di,k,ρi,kAre all design parameters, bi,k,ci,k,di,k,ρi,kAre all larger than 0;
the attacked sensor data in step S5 is xa,iBased on the attacked sensor data as xa,iAnd attack compensation variables
Figure FDA0003578034820000015
The expression for constructing the new coordinate transformation is as follows:
Figure FDA0003578034820000016
Figure FDA0003578034820000017
wherein z isi,1And zi,pRepresenting sensor data based on attacks as xa,iAnd attack compensation variables
Figure FDA0003578034820000018
Constructing a new auxiliary variable after coordinate transformation;
s6, designing a virtual controller, an actual controller and a neural network weight value self-adaptation law based on the new coordinate transformation auxiliary variable,
the expression of the designed virtual controller in step S6 is:
Figure FDA0003578034820000021
Figure FDA0003578034820000022
Figure FDA0003578034820000023
actual controller u based on virtual controller relates toiComprises the following steps:
Figure FDA0003578034820000024
wherein phi isi,kIs a Gaussian function of the neural network,
Figure FDA0003578034820000025
self-adaptive parameters of the radial basis function neural network weight; adaptive parameters of radial basis function neural network weight
Figure FDA0003578034820000026
The self-adaptive rate of (2) satisfies:
Figure FDA0003578034820000027
Figure FDA0003578034820000028
Figure FDA0003578034820000029
Figure FDA00035780348200000210
wherein, gamma isi,kRepresenting the adaptive law gain matrix, σi,kTo modify the parameter matrix.
2. The non-leader consensus control method for nonlinear multi-agent system based on attack compensation according to claim 1, wherein the process of continuous-time nonlinear multi-agent system model building of step S1 is:
defining parameters: k is 1,2,. n; q-1, 2,. n-1; p ═ 2,3,. n; r-3, 4.,. n-1, and obtaining a model expression of the continuous-time nonlinear multi-agent system as follows:
Figure FDA00035780348200000211
Figure FDA00035780348200000212
Figure FDA00035780348200000213
wherein x isi＝[xi,1,...,xi,n]TIs a state vector of a continuous-time nonlinear multi-agent system;
Figure FDA00035780348200000214
Figure FDA00035780348200000215
represents a complex non-linear term of uncertainty, an
Figure FDA00035780348200000216
uiA controller representing a continuous time nonlinear multi-agent system to be designed, to achieve consistency control;
Figure FDA00035780348200000217
representing an actuator attack vector;
Figure FDA00035780348200000218
representing a sensor attack vector;
Figure FDA00035780348200000219
and
Figure FDA00035780348200000220
are functions of state vector and time; x is the number ofa,i＝[xa,i,1,...,xa,i,n]TSensor data representing a continuous-time non-linear multi-agent system model after an attack.
3. The non-linear multi-intelligence system leaderless consistency control method based on attack compensation according to claim 2, wherein the uncertainty non-linear term is compounded in step S2
Figure FDA0003578034820000031
Figure FDA0003578034820000032
Uniformly set as f (x), and tightly gather by using radial basis function neural network
Figure FDA0003578034820000033
To any degree of accuracy
Figure FDA0003578034820000034
The process of approximating f (x) satisfies:
Figure FDA00035780348200000310
wherein x represents a radial basis function neural networkH is the input dimension of the radial basis function neural network; epsilon (x) is the approximation error, and satisfies:
Figure FDA0003578034820000035
φ(x)＝[φ1(x),φ2(x),...,φl(x)]a vector of basis functions is represented as,
Figure FDA0003578034820000036
represents an ideal weight, defined as: for all
Figure FDA0003578034820000037
The value of θ that minimizes the approximation error | ε (x) |, expressed as:
Figure FDA0003578034820000038
4. the non-linear multi-intelligence system leader-less consensus control method based on attack compensation according to claim 3, wherein the basis function vector φi(x) I 1, 2., l selects a gaussian function, the expression:
Figure FDA00035780348200000312
wherein l is the number of nodes of the neural network, ζi＝[ζi,1,...,ζiq]The acceptance domain of the basis function is represented,
Figure FDA00035780348200000311
representing the width of the gaussian function.
5. The attack compensation-based nonlinear multi-agent system leaderless consistency control method as claimed in claim 4, wherein the process of applying the directed graph to confirm the communication topology relationship between the agents in the leaderless multi-agent system in step S3 is as follows:
providing a graph G ═ { V, E }, wherein V ═ 1, 2., N } represents a set of nodes in the directed graph G, wherein 1,2, …, N represents the number of the multi-agent system;
Figure FDA0003578034820000039
represents the set of directed edges in the directed graph, and (j, i) means that the multi-agent system i can receive information from the multi-agent system j, the multi-agent system j is a neighbor of the multi-agent system i, and the neighbor set expression of the multi-agent system i is as follows: n is a radical ofi＝{j∈V|(i,j)∈E,i≠j}；
Definition A ═ aij]∈Rn×nWeight matrix as directed graph G, aijIs the weight matrix element of the directed graph G; if the multi-agent system i is able to receive information from the multi-agent system j, then aij1, i ≠ j, otherwise, aij＝0。
6. The non-linear multi-wisdom system leaderless consistency control method based on attack compensation as claimed in claim 5, wherein the step S4 adopts dynamic surface technique to construct auxiliary variables and consistency errors without considering sensor attack, and the expression of the auxiliary variables is as follows:
Figure FDA0003578034820000041
wherein beta isiRepresenting an auxiliary variable;
the consistent error expression is:
ei,1＝xi,1-βi
in fact, when ei,1X → 0 timei,1→βiThe output of the agent i in the multi-agent system is consistent with the output of the neighbor; the error table expression is:
Figure FDA0003578034820000042
wherein the content of the first and second substances,
Figure FDA0003578034820000043
representing a virtual controller alphai,p-1Output after passing through a first order filter to avoid the need for repeating pairs of alpha in controller designi,p-1Differentiation causes a problem of an increase in the amount of calculation;
Figure FDA0003578034820000044
satisfying the expression:
Figure FDA0003578034820000045
wherein, taui,p-1Denotes the time constant, τi,p-1And if the filtering error is more than 0, obtaining the filtering error as:
Figure FDA0003578034820000046
wherein eta isi,p-1Representing the filtering error.
CN202011403180.XA 2020-12-04 2020-12-04 Non-linear multi-wisdom system leader-free consistent control method based on attack compensation Active CN112558476B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011403180.XA CN112558476B (en) 2020-12-04 2020-12-04 Non-linear multi-wisdom system leader-free consistent control method based on attack compensation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011403180.XA CN112558476B (en) 2020-12-04 2020-12-04 Non-linear multi-wisdom system leader-free consistent control method based on attack compensation

Publications (2)

Publication Number Publication Date
CN112558476A CN112558476A (en) 2021-03-26
CN112558476B true CN112558476B (en) 2022-06-14

Family

ID=75048354

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011403180.XA Active CN112558476B (en) 2020-12-04 2020-12-04 Non-linear multi-wisdom system leader-free consistent control method based on attack compensation

Country Status (1)

Country Link
CN (1) CN112558476B (en)

Families Citing this family (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113156821B (en) * 2021-04-16 2022-09-30 山东师范大学 Self-adaptive tracking method of nonlinear system under false data injection attack
CN114563953B (en) * 2022-01-31 2023-05-09 四川大学 Adaptive fault-tolerant reliable control system and method for wheeled robot considering multi-factor influence
CN114509948B (en) * 2022-02-21 2023-01-17 东北电力大学 Method for constructing state constraint quantization controller of high-order multi-agent system

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104881044A (en) * 2015-06-11 2015-09-02 北京理工大学 Adaptive tracking control method of multi-mobile-robot system under condition of attitude unknown
CN109445447A (en) * 2019-01-14 2019-03-08 北京航空航天大学 A kind of multiple agent formation tracking and controlling method and system
CN109683477A (en) * 2018-12-12 2019-04-26 中国地质大学（武汉） A kind of design method and system of random multi-agent system finite-time control device
CN110109351A (en) * 2019-04-08 2019-08-09 广东工业大学 A kind of multiple agent consistency control method based on specified performance
CN110262247A (en) * 2019-07-05 2019-09-20 青岛大学 The distributed command filtered blurry control method of multi-robot system

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104881044A (en) * 2015-06-11 2015-09-02 北京理工大学 Adaptive tracking control method of multi-mobile-robot system under condition of attitude unknown
CN109683477A (en) * 2018-12-12 2019-04-26 中国地质大学（武汉） A kind of design method and system of random multi-agent system finite-time control device
CN109445447A (en) * 2019-01-14 2019-03-08 北京航空航天大学 A kind of multiple agent formation tracking and controlling method and system
CN110109351A (en) * 2019-04-08 2019-08-09 广东工业大学 A kind of multiple agent consistency control method based on specified performance
CN110262247A (en) * 2019-07-05 2019-09-20 青岛大学 The distributed command filtered blurry control method of multi-robot system

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Mahnaz Hashemi.etc.Distributed robust adaptive control of high order nonlinear multi agent systems.《ISA Transactions》.2018,第74卷第14-27页. *
周琪等.基于干扰观测器的输入饱和多智能体系统事件触发控制.《中国科学: 信息科学》.2019,第49卷(第11期),第1502-1516页. *
杨彬等.具有指定性能和全状态约束的多智能体系统事件触发控制.《自动化学报》.2019,第45卷(第8期),第1527-1535页. *

Also Published As

Publication number Publication date
CN112558476A (en) 2021-03-26

Similar Documents

Publication Publication Date Title
CN112558476B (en) Non-linear multi-wisdom system leader-free consistent control method based on attack compensation
CN109445447B (en) Multi-agent formation tracking control method and system
CN107422741B (en) Learning-based cluster flight distributed attitude tracking control method for preserving preset performance
WO2022222229A1 (en) Coupled neural network bounded cluster projection synchronization adjustment control method and system
CN108536017B (en) Random distribution interconnection system cooperation fault-tolerant control method based on dynamic feedback control
CN106227700B (en) A kind of uncatalyzed coking dissipation filtering method of network control system
CN109471364A (en) A kind of reliable control method of the switched nonlinear systems with actuator failures
CN111880412A (en) Reconfigurable robot zero and neural optimal control method based on single evaluation network
CN113156821B (en) Self-adaptive tracking method of nonlinear system under false data injection attack
Modares et al. Static output‐feedback synchronisation of multi‐agent systems: a secure and unified approach
Elhage et al. Laplacian-based consensus on spatial computers
Ma et al. Event‐triggered adaptive finite‐time secure control for nonlinear cyber‐physical systems against unknown deception attacks
Kong et al. Stable fault-tolerance control for a class of networked control systems
CN113459083B (en) Self-adaptive fixed time control method and system for mechanical arm under event trigger
CN116127519A (en) Dynamic differential privacy federal learning system based on blockchain
CN113934224B (en) Unmanned aerial vehicle elastic strategy design method and system based on heterogeneous game method
CN115356929A (en) Proportional allowable tracking control method for actuator attack singularity multi-agent system
CN114326382A (en) Adaptive elastic tracking control method and system with spoofing attack
CN113031644B (en) Communication time lag oriented aircraft formation control system event triggering method, device and medium
Jiang et al. Intelligent consensus asymptotic tracking control for nonlinear multiagent systems under denial-of-service attacks
Li et al. Finite‐time dissipative control of fuzzy distributed parameter CPSs with quantization under cyber attacks
Ni et al. Predefined-time consensus tracking of high-order multiagent system with deception attack
CN106200382B (en) A kind of uncatalyzed coking dissipative control method of nonlinear network networked control systems
CN114509948B (en) Method for constructing state constraint quantization controller of high-order multi-agent system
Kharrat et al. Neural-networks-based adaptive fault-tolerant control of nonlinear systems with actuator faults and input quantization

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant