CN116781754A - Multi-agent robust fault-tolerant cooperative control method under network attack - Google Patents
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Abstract
The invention discloses a method for cooperatively controlling a leader-follower system under the condition of composite fault and Dos attack; in order to simulate faults and network attacks, a traditional time-lag model is adopted to simulate Dos attacks, and additive faults and multiplicative faults of a controller simulate composite faults; compensating faults by adopting an RBF neural network and a self-adaptive fault observer; a new exchange model is provided for Dos attack, and a controller is designed based on a linear matrix inequality; the feasibility of the method is ensured through simulation.
Description
Technical Field
The invention relates to the field of multi-agent cooperative control, in particular to a multi-agent stable control problem under network attack and composite faults.
Background
In recent years, the multi-agent cooperative control has made remarkable progress, and the multi-agent formation model can be expanded into various fields, such as multi-unmanned aerial vehicle, multi-trolley model and the like, and plays a great role in some high-risk work or military applications, such as cruise reconnaissance, military rescue and the like. Dos attacks, also known as denial of service attacks, may act on communication networks between multiple agents and on the propagation of information in a single agent, potentially resulting in reduced performance and even loss of stability of the multi-agent system. Therefore, it is practical to reduce the impact of network attacks to a great extent without determining the strength of the attack and the target of the attack. The patent CN110297497A discloses a control method for multi-agent system consistency based on a mixed trigger mechanism under network attack, and mainly contributes to providing an algorithm of a time and event mixed trigger mechanism under network attack, but the problem of actuator faults existing in a system is not solved. The patent CN116027809A discloses a multi-four-rotor unmanned aerial vehicle formation control method under DoS attack, which researches the cooperative control of unmanned aerial vehicle formation under DoS attack and establishes a singular perturbation model of the unmanned aerial vehicle, but only considers the situation that network attack acts on a communication network among unmanned aerial vehicles, and does not consider the situation that an internal communication loop of a single unmanned aerial vehicle is also attacked by the network.
At present, because the influence of the faults of the actuator and the like on the control performance of the system is larger, the research of the students at home and abroad at present also proves that the fault observer can effectively compensate the influence, the neural network approximator has a better effect for approximately compensating the faults of the actuator, and meanwhile, the stability and the robustness of the closed-loop system in the global range can be ensured by designing the robust controller. In addition, the method has not been reported in detail in multi-agent control based on network attack.
Disclosure of Invention
In view of the defects in the prior art, the invention provides a multi-agent fault-tolerant robust control method based on a fault observer and an RBF neural network, which comprises the following steps:
step 1, establishing a virtual leader state equation model, as follows:
y 0 (t)＝C 0 x 0 (t)
wherein ,x0 Representing the status of the virtual leader, y 0 Output representing virtual leader, A 0 And C 0 Is a known constant matrix.
The state equation for the i-th frame follower agent is as follows:
y i (t)＝C i x i (t)
wherein i=1, 2,..n represents the i-th agent, x i 、u i and yi Respectively representing the state quantity, control quantity and output quantity of the rack intelligent body, A i ，B i ，C i Is a known constant matrix.
Step 2, simulating Dos network attack by using a traditional time-lag model, and setting attack strength as d epsilon P 1 E {0,1,., where l represents the maximum attack strength, the states under the influence of Dos attacks are as follows:
wherein Representing the state quantity of the controller, +.>Representing the output quantity of the intelligent agent and the state quantity of the controller under the network attack, sigma ij Indicating the cooperative error of the ith frame and the jth frame of intelligent agent under cooperative control, +.>Representing a collaborative error value, a, under the influence of a network attack ij Is an element in the adjacency matrix g i Indicating whether the ith intelligent agent has information communication with the virtual leader, if so, g i =1, otherwise, g i ＝0。
The controller design of the system is as follows:
wherein ,Ki，l 、H l Is the matrix gain to be designed in relation to the maximum attack intensity l, y i 、Λ i Is a matrix to be designed, which can be obtained by solving the following linear matrix inequality:
and (3) making:
e i (t)＝y i (t)-y 0 (t)
x c (t)＝[ε T (t)，θ T (t)] T
the closed loop system under network attack is obtained as follows:
e(t)＝C c x c (t)
wherein ：
wherein ,l is the laplace matrix of the system, g=diag { G 1 ，...，g n }. Ensuring the stability of the closed loop system, namely ensuring that θ, ε approaches 0 when t-infinity, thus proper matrix gain K is required to be designed i，l 、H l The stability of the closed loop system is ensured.
The closed loop system described above is broken down as follows:
wherein
Representing all possible error signals under the influence of network attack as a new variableAnd->If the variable +.>And->When the tracking system approaches zero, the tracking system can be ensured to be stable for the maximum network attack intensity l;
design matrix gain K i，l ，H l The method meets the following conditions:
wherein Pi，l ，Q l Is a symmetrical positive definite matrix, 0 < alpha l ＜1。
Meeting the above conditions ensures that the controller stabilizes the tracking system.
In particular, assuming that the kth agent is affected by a composite fault, its state equation is as follows:
wherein p∈Rm×1 Defined as the multiplicative fault factor of the system, f (t) defined as the additive fault of the system, E k ∈R m×1 Representing the additive fault coefficients.
Step 3, designing a self-adaptive fault observer:
wherein Is an estimate of the system state and output, +.>Is the fault estimated value, L is the gain matrix to be designed, and a positive definite matrix P epsilon R exists n×n 、F∈R r×p And (3) enabling the mixture to be subjected to the following steps:
E T P＝FC
order theThe fault estimation algorithm is as follows:
where Γ is a positive definite symmetric matrix representing the adaptive learning law.
Estimating a fault value through an RBF neural network, wherein the algorithm is as follows:
f＝W *T h(x)+ε
wherein W* For ideal weights, h (x) is the radial basis function, ε is the estimated error, where ε is bounded, and we noteAs an estimate of epsilon, the estimate of the fault is:
and 4, verifying the stability of the system. Let Lyapunov function be:
V(t)＝V 1 (t)+V 2 (t)+V 3 (t)
wherein
The derivative equivalent transformation of the Lyapunov function can be obtained by:
from the matrix gain K in step 2 i，l ，H l The condition to be satisfied willThe process is as follows:
from E T P＝FC，The process is as follows:
definition of the definition The process is as follows:
finally, the proper matrix gain K is selected i，l ，H l The closed loop of the system is stable under the conditions of the observer gain L and the weight coefficient W.
Drawings
In order to better embody the superiority of the method designed by the invention, aiming at network attack and actuator fault solutions, independent Robust Control (RC) is selected and compared with adaptive Robust Fault Tolerant Control (RFTC) based on a fault observer, and the result shows that the approximation rate and the precision of the RFTC to the actuator fault are superior to the RC. In addition, the robust fault-tolerant control adopted by the invention can better solve the generated actuator faults and give compensation.
FIG. 1 is a block diagram showing a multi-agent robust fault-tolerant cooperative control method under network attack
FIG. 2 is a diagram of a multi-agent control input
FIG. 3 is a comparative simulation of the states of RC and RFTC in the x-direction
FIG. 4 is a diagram showing the comparison simulation of the states of RC and RFTC in the y-direction
FIG. 5 is a simulation diagram of tracking error of RC and RFTC in x-direction
FIG. 6 is a simulation diagram of tracking errors in the y-direction RC and RFTC
FIG. 7 is a simulation diagram of the system output in the RFTC method
Detailed Description
The invention will be explained in further detail below with reference to the drawings and embodiments. The specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In order that those skilled in the art can better understand the implementation of the present invention, the present invention will employ Matlab software to perform simulation of multi-agent cooperative control to verify its reliability. We consider the case of three agent formations.
Respectively taking parameters of the intelligent agentC 1 ＝C 2 ＝C 3 ＝[1 0 0]，Assuming that agent 1 is subject to additive fault f=0.5 sin (5 t) and multiplicative fault, fault factor +.>Maximum attack intensity l=2.
Let the initial position x of three intelligent bodies 0 ＝[0 0 0] T Initial rateThe virtual leader system is:
when the multiple agents cooperatively control, the corresponding adjacency matrix A and fixed gain matrix G are:
on the premise of meeting the stability and the limitation of the closed-loop system, constant parameters in the controller are respectively set as follows:Λ 1 ＝[0 2.5 0]，Λ 2 ＝[0 5 0]，Λ 3 ＝[0 2 0]。
the fault observer gain matrix l= [ -2.2361-3-2 ], taking the learning law Γ= 2,F =5. The result shows that the RFTC has better dynamic performance and lower tracking error than RC, compared with robust control, fault-tolerant control can effectively compensate fault offset, and the effectiveness and feasibility of the self-adaptive robust fault-tolerant control method provided by the invention are verified through comparison of the simulation results, so that the method meets the expectations.
Finally, it is not intended that the present invention be limited to the specific embodiments disclosed as the best mode contemplated for carrying out the present invention, but rather that the present invention shall be construed according to the appended claims.
Claims (3)
1. H-based ∞ The fault-tolerant cooperative control method of the multi-agent under the Dos network attack of the control and fault observer comprises the following steps:
step 1, establishing a state equation model of a virtual leader and a follower;
step 2, simulating Dos network attack by using a traditional time-lag model, and simultaneously considering composite additive and multiplicative faults and designing a controller;
step 3, designing an RBF neural network and a fault observer to compensate the fault of the actuator according to the fault in the step 2;
and 4, verifying the closed loop stability of the multi-agent formation.
2. An H-based system according to claim 1 ∞ The fault-tolerant cooperative control method of the multi-agent under the Dos network attack of the control and fault observer is characterized in that the state equation model of the leader and the follower in the step 1 is as follows:
y 0 (t)＝C 0 x 0 (t)
wherein ,x0 Representing the status of the virtual leader, y 0 Output representing virtual leader, A 0 And C 0 Is a matrix of known constants;
the state equation of the i-th frame follower agent in the absence of a fault is as follows:
y i (t)＝C i x i (t)
wherein i=1, 2,..n represents the i-th agent, x i 、u i and yi Respectively representing the state quantity, control quantity and output quantity of the rack intelligent body, A i ，B i ，C i Is alreadyKnowing a constant matrix;
assuming that the kth agent is affected by a composite fault, its state equation is as follows:
wherein p∈Rm×1 Defined as the multiplicative fault factor of the system, f (t) defined as the additive fault of the system, E k ∈R m×1 Representing an additive fault coefficient;
the controller design in step 2 is as follows:
wherein Representing the state quantity of the controller, +.>Representing the output quantity of the intelligent agent and the state quantity of the controller under the network attack, sigma ij Indicating the cooperative error of the ith frame and the jth frame of intelligent agent under cooperative control, +.>Represent the collaborative error value, K, under the influence of network attacks i，l 、H l Is the matrix gain to be designed, gamma, related to the maximum attack intensity l i 、Λ i Is a matrix to be designed, and can be obtained by solving a linear matrix inequality;
the fault observer in step 3 is designed as follows:
wherein Is an estimate of the system state and output, +.>Is a fault estimated value, A i ，B i ，C i ，E i Is a known constant matrix, L is a gain matrix to be designed, and a positive definite matrix P epsilon R exists n×n 、F∈R r×p And (3) enabling the mixture to be subjected to the following steps:
E T P＝FC
order theThe fault estimation algorithm is as follows:
wherein Γ is a positive definite symmetric matrix representing an adaptive learning law;
according to the RBF neural network fault compensation method in the step 3, the observed value is taken as input, the state predicted value is taken as output, and the output can be effectively approximated to the target value by selecting a proper weight W, and the algorithm is as follows:
f＝W *T h(x)+ε
wherein W* For ideal weights, h (x) is the radial basis function and ε is the estimation error.
3. An H-based system according to claim 1 ∞ The fault-tolerant cooperative control method of multiple agents under Dos network attack of control and fault observer is characterized in that in step 4, the closed loop stability of the system needs to be verified, and the following steps are performed:
e i (t)＝y i (t)-y 0 (t)
x c (t)＝[ε T (t)，θ T (t)] T
the closed loop system is defined as follows:
e(t)＝C c x c (t)
wherein ：
wherein ,l is the laplace matrix of the system, g=diag { G 1 ，...，g n }；
The closed loop system is broken down into two low-dimensional systems:
wherein
Representing all possible error signals under the influence of network attack as a new variableAnd->If the variable +.>And->When the tracking system approaches zero, the tracking system can be ensured to be stable for the maximum network attack intensity l;
for the first low-dimensional system, selecting a Lyapunov function V 1a ：
wherein ,Pi，l Is a positive diagonal matrix;
deriving the Lyapunov function:
selecting K i，l Satisfying the following requirements;
then:
from 0 < alpha l < 1 is easy to obtainI.e. by choosing the appropriate K i，l The stability of the low-dimensional system can be satisfied;
for the second low-dimensional system, the Lyapunov function V is taken i ′：
wherein Ql Is a positive diagonal matrix;
deriving the Lyapunov function:
selecting H l The method meets the following conditions:
similarly, by selecting an appropriate H l Can meet the requirement of stabilizing the low-dimensional system
And (3) making:
both low-dimensional systems are stable, and the high-dimensional systems are stable, which proves that the proper matrix gain K is selected i，l and Hl The tracking stability of the controller under the network attack can be ensured;
next consider lyapunov stabilization of the fault observer, defining the fault observation error asConsider the lyapunov function:
deriving the Lyapunov function:
from E T P=fc, yielding:
from the above, the observer gain matrix L is designed such that P (a i -LC i )+(A i -LC i ) T P is less than 0, and the stable condition of the observer can be met.
Finally, considering the Lyapunov stability of the RBF neural network, estimating a fault value of the system by using the RBF neural network, wherein the estimated output is as follows:
wherein W* For ideal weight, h (x) is radial basis function, epsilon is estimated value of approximation error of neuron network, letRepresents the estimated weight, ε * Representing the actual error, define->The lyapunov function was constructed as:
wherein γ1 ，γ 2 > 0, deriving the lyapunov function:
order theFrom the above, it is proved that->The closed loop stability of the system is verified.
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| CN117075638B (en) * | 2023-09-26 | 2024-02-06 | 南京航空航天大学 | Cluster unmanned aerial vehicle cooperative toughness control method for DoS network attack |
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