A leaderless consensus method for multiple Euler-Lagrange systems under deception attacks

Abstract

A method for achieving leaderless consistency of multiple Euler-Lagrange systems under deception attacks. When deception attacks occur randomly in the communication channels between Euler-Lagrange systems, a safety consistency strategy based on impulse control is designed in combination with neural network control, so that the networked multiple Euler-Lagrange systems can achieve bounded consistency in the mean square sense of position. The present invention is applicable to the design of a method for achieving consistency control of nonlinear multi-agent systems under deception attacks.

Description

Technical Field

[0001] The present invention belongs to the technical field of networked multi-agent systems, and in particular relates to a method for achieving leaderless consistency in multiple Euler-Lagrange systems under deception attacks. Background Art

[0002] As a dynamic system model based on the law of conservation of energy, the Euler-Lagrange system can be used to represent the structure and motion characteristics of almost all physical and mechanical systems, such as drones, industrial robots, and automatic vehicles. Compared with a single Euler-Lagrange system, maneuverability, flexibility, operability, and executability are the main characteristics of a multi-Euler-Lagrange system. The consistency control of a networked multi-Euler-Lagrange system can be applied to fields such as spacecraft rendezvous and docking, satellite attitude adjustment, and multi-manipulator coordination.

[0003] In order to achieve the consistency of multi-Euler-Lagrange systems, each agent needs to establish local communication with its neighbors. The communication information can be position coordinates, velocity vectors, torque vectors or other valid data. However, since actual multi-agent systems are usually exposed to various complex communication networks, malicious network attacks may directly destroy the consistency of the system. If the impact of network attacks is not considered in advance, especially for major national critical infrastructure such as water, electricity, nuclear and chemical plants, it will cause huge economic losses and affect the normal life of the people. Therefore, for the consistency problem of multi-Euler-Lagrange, it is very practical to consider the deception attacks suffered during the network communication process. Summary of the invention

[0004] The present invention considers that a networked Euler-Lagrange system is subjected to a deception attack by randomly injecting false data, proposes a method for achieving leaderless consistency of multiple Euler-Lagrange systems under deception attacks, uses pulse control to reduce the impact of attack signals, and combines the nonlinear part of a neural network control processing system to design a consistency strategy based on pulse control, thereby achieving leaderless safe bounded consistency of multiple Euler-Lagrange systems and providing a method for the safe consistency of networked multi-agent systems.

[0005] In order to achieve the above invention purpose, the present invention applies the following technical solutions:

[0006] 1. Modeling a model in which the communication channel of multiple Euler-Lagrange systems is subjected to deception attacks during communication;

[0007] 2. Design the control input torque of the networked multi-Euler-Lagrange system, including local feedback control terms and impulse control terms, and give the impulse consistency control criterion so that the networked multi-Euler-Lagrange system can achieve bounded consistency in the mean square sense of position when it is attacked by deception.

[0008] Explanation of the above content:

[0009] First, consider a multi-agent system consisting of N Euler-Lagrange systems. The dynamic equation of the i-th (i=1, 2, ···N) agent is:

[0010]

[0011] In the formula, q i , Represent the generalized coordinates, velocity and acceleration vectors of the i-th Euler-Lagrange system respectively. is a positive definite symmetric inertia matrix, are the Coriolis and centrifugal torque vectors, is the center-of-gravity torque vector, is the system control input torque.

[0012] At the same time, a directed graph G = (V, E, A) is used to represent the communication network topology between N Euler-Lagrange systems, with a node set of V = {i|i = 1, 2, ..., N} and a directed edge set of E = {(i, j)|i∈V, j∈V, i≠j}. The adjacency matrix A = [a ij ]∈R N×N , N i ={j|(j,i)∈E} represents the neighbor set of the i-th node. The Laplacian matrix of the directed graph G is L=DA, where the diagonal matrix D=diag{d1,d2,...,d N}∈R N×N , And assume that the communication directed topology graph G describing N Euler-Lagrange systems is strongly connected.

[0013] The control target is the consistency error q of the Euler-Lagrange system i (t)-q j (t) eventually reaches bounded consistency in the sense of mean square boundedness and belongs to the following set: Where Δ represents the bound of the consistency error.

[0014] Step 1: Model the model in which the communication channel of multiple Euler-Lagrange systems is subjected to deception attacks during communication;

[0015] In order to achieve system consistency, the Euler-Lagrange system needs to obtain the status information of other systems. The output information of the jth Euler-Lagrange system is set as: In the formula, λ>0. In view of the randomness of the deception attack, the random variable γ that follows the Bernoulli distribution is used ij (t)∈{0,1} to describe whether a spoofing attack occurs. ij When (t) = 0, no deception attack occurs; when γ ij When (t) = 1, the communication channel represented by the directed graph edge (j, i) undergoes a spoofing attack. ij The probability distribution of (t) satisfies And the random variables are independent of each other. Therefore, the i-th Euler-Lagrange receives the following deception attack information from the j-th Euler-Lagrange system:

[0016]

[0017] In the formula, r j (t) is the information transmitted by the jth Euler-Lagrange to its neighbor individuals, y j (t) is the unknown and time-varying false data imposed on the communication channel that does not depend on the state of the agent, is the information received by the neighbors of the i-th Euler-Lagrange system from the j-th Euler-Lagrange system. It should be noted that the information that the Euler-Lagrange system i cannot receive from its neighbors is Identify the normal signal r j (t) and the attack signal y j (t).

[0018] Since the attack size is limited by the system defense and energy, the attack signal y j (t) There are the following assumptions: Assume that the energy of the attack signal is bounded, that is, there exists a constant y>0 such that ||Y(t)|| 2 ≤y holds. And define the random variable matrix Υ(t k ) is

[0019] Step 2: Design the control input torque of the networked multi-Euler-Lagrange system, including the local feedback control term and the impulse control term, and give the impulse consistency control criterion so that the networked multi-Euler-Lagrange system can achieve bounded consistency in the mean square sense of position when it is attacked by deception;

[0020] The control input torque of the i-th Euler-Lagrange system is:

[0021]

[0022] In the formula, parameter k i >0, is the estimated value of the optimal weight matrix of the uncertain nonlinear part of the neural network estimation system, θ i (·) is the activation function. For the uncertain nonlinear part of the Euler-Lagrange system Perform neural network adaptive estimation: In the formula, parameters γ>0, u>0.

[0023] Pulse control term u i (t) Using the information received from neighbor individuals that they are under attack With its own output information r i The error of (t) is designed as follows: Wherein, the gain α>0, δ(t) is the Dirac pulse control function. When t=0, δ(t)=+∞; when t≠0, δ(t)=0. is a pulse sequence, satisfying 0=t0<t1<…<t k-1 <t k <…, Define the pulse interval τ k =t k+1 -t k , and satisfy 0 k ≤h2<+∞. h1 and h2 are the lower and upper bounds of the pulse interval respectively.

[0024] Next, the Lyapunov function of the system is constructed, the stability conditions for the bounded stability of the system consistency error are determined, and the bounded value of the consistency error is obtained;

[0025] Under the control input torque, the Euler-Lagrange system can be expressed as:

[0026]

[0027] In the formula, represents the i-th Euler-Lagrange system at the pulse triggering time t​k A jump in time coordinate and velocity space. and Respectively represent r i (t) at t = t k The left and right limits of the moment, Assume r i (t) except at time t = t k It is continuous outside and at t = t k is left continuous, that is

[0028] Define the neural network constant weight matrix estimation error as The state equation of the estimated error is:

[0029] definition M=diag[M1,M2,…,M N ],Υ(t k )=[γ ij (t k )]∈R N×N , because So we can Written in the following form:

[0030]

[0031] The Lyapunov function of the constructed system is:

[0032] When t∈[t k-1 ,t k ), taking the derivative of V(t) yields because Satisfies antisymmetry. At the same time, external disturbance ω i , neural network error ε i are all bounded, that is, there must be a constant σ>0 such that ||ω i +ε i ||≤σ. Therefore, when t∈[t k-1 ,t k )hour, for: In the formula, k min =min{k i}, satisfy Therefore, when t∈[t k-1 ,t k )

[0033] When t = t k When V(t) is calculated, we can get Where μ = ζ + ε -1 ,

[0034] By mathematical induction, we can get Therefore, it can be known that Therefore

[0035] Therefore, the stability condition for bounded uniformity of a multi-Euler-Lagrange system is: if there exists α, ε, γ, u, ζ, δ > 0, and the following conditions are satisfied: 2δk min -1>0, Consistency error q of multiple Euler-Lagrange systems with communication channels under spoofing attacks i (t)-q j (t) can converge to the neighborhood of the following zero point:

[0036]

[0037] The beneficial effects of the present invention are as follows:

[0038] The present invention provides a safe and reliable solution to the phenomenon of deception attacks in network communication when a multi-agent system achieves leaderless consistency. The present invention can effectively reduce the impact of attack signals and improve the security bounded consistency of the system. The multi-agent system model considered is a strongly nonlinear and strongly coupled Euler-Lagrange system. Since the system can describe a large number of physical systems, such as robots, drones, etc., the present invention is more general in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flow chart of a design method for leaderless consistency of multiple Euler-Lagrange systems based on pulse control under a deception attack in the present invention.

[0040] Figure 2 It is a communication topology diagram of a multi-Euler-Lagrange system in a simulation experiment of an embodiment of the present invention.

[0041] Figure 3 This is the change in the position of multiple Euler-Lagrange systems in the simulation experiment of the embodiment of the present invention.

[0042] Figure 4It is the change of the position error between the first Euler-Lagrange system and the other Euler-Lagrange systems in the simulation experiment of the embodiment of the present invention. DETAILED DESCRIPTION

[0043] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings.

[0044] In order to demonstrate the effectiveness of the design method for leaderless consistency of multiple Euler-Lagrange systems based on pulse control under deception attacks proposed in the present invention, a simulation experiment of realizing the consistency of a dual-joint robotic arm is carried out using the design method.

[0045] Simulation parameters: Consider a multi-agent system consisting of six Euler-Lagrange systems. The dynamic equation of the i-th Euler-Lagrange system is:

[0046]

[0047] In the formula, q i =(q ix q iy ) T Matrix, M i (q i ), G i (q i ) are:

[0048]

[0049]

[0050]

[0051]

[0052] In the formula, J i1 =0.21kg·m 2 , J i2 =0.42kg·m 2 ;m i1 =1.02kg, m i2 =1.12kg; l i1 = l i2 =1m represents the moment of inertia, mass and length respectively, and the acceleration due to gravity g=9.801m / s 2 Therefore k m =0.28.

[0053] Let the neural network activation function vector θ of each Euler-Lagrange system be i (z i )=[θ i1 (z i ),θ i2 (z i ),…,θ i6 (z i )] T , where Select θ i1 (z i ) is the Guassian function, that is In the formula, the width σ of the neuron activation function is set ij =2, the initial neural network weight matrix is ​​0, that is, The center position c of the neuron activation function ij Uniformly distributed in the range [-5,5] 2 ×[-0.5,0.5] 2 Inside.

[0054] The control parameter of the input control torque is selected as k i =1, ζ=0.01, λ=100, so β=0.7326. Assume that the pulse interval is the same h1=h2=0.03, the pulse control parameter α=0.03, ε=1. Assume that the attack upper bound y=0.2, and the expected matrix Π is:

[0055]

[0056] The selection of the above parameters satisfies the conditions in step 2.

[0057] The initial position states of the six Euler-Lagrange system models are [10 0.1] T , [-2 10] T , [0 0] T , [20 30] T , [-1 2] T ,[-twenty two] T .

[0058] Simulation analysis: Figure 3 and Figure 4 It can be seen that when the output information of a multi-Euler-Lagrange system is subjected to bounded deception attacks when being transmitted between individuals, the use of impulse control can make the system error tend to a bounded value, that is, maintain bounded consistency.

[0059] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed by the present invention should be included in the protection scope recorded in the claims.

Claims

1. A method for achieving leaderless consensus in multiple Euler-Lagrange systems under deception attacks, characterized by: The method comprises the following steps: Step 1, modeling the situation in which the communication channel of a networked multi-Euler-Lagrange system is subjected to a deception attack during communication; When the jth Euler-Lagrange system sends data to its neighbors, it sends the output of the jth Euler-Lagrange system. Where, constant λ>0, are the generalized coordinates and velocity vector of the Euler-Lagrange system, respectively, and N is the number of individuals in the networked multi-Euler-Lagrange system; The communication channel where the jth Euler-Lagrange sends data to its neighbors is subject to a deception attack by injecting false data, and its model is: In the formula, r j (t) is the information transmitted by the jth Euler-Lagrange to its neighbor individuals, y j (t) is the unknown and time-varying false data imposed on the communication channel that does not depend on the state of the agent, is the information received by the ith Euler-Lagrange system from its neighbor, the jth Euler-Lagrange system, γ ij are mutually independent random variables that obey the Bernoulli distribution, and their probability distribution satisfies E{γ ij (t) = 1} = ω ij ,E{γ ij (t) = 0} = 1-ω ij ; The information that the i-th Euler-Lagrange system cannot receive from it The output signal r of the jth Euler-Lag dye system is distinguished j (t) and the attack signal y j (t); Step 2, design the control input torque of the networked multi-Euler-Lagrange system, including the local feedback control term and the impulse control term, and give the impulse consistency control criterion, so that the networked multi-Euler-Lagrange system can achieve bounded consistency in the mean square sense of position when it is attacked by deception; The control input torque of the designed networked multi-Euler-Lagrange system is: In the formula, parameter k i >0, α>0, γ>0, u>0, Ni represents the set of neighbor individuals of the i-th Euler-Lagrange system, is the estimated value of the neural network weight matrix used to estimate the nonlinear uncertainty part of the i-th Euler-Lagrange system, θ i (·) is the activation function of the neural network, δ(t) is the Dirac impulse control function, and u i (t) is the pulse control term, with gain α>0; The controller parameters meet the following conditions: α>0,ε>0,γ>0,u>0,ζ>0,δ>0 2δk min -1>0 In the formula, k min =min{k i },μ=ζ+ε -1 , is the lower bound of the inertia matrix of the ith Euler-Lagrange system, is the lower bound of the inertia matrix of the ith Euler-Lagrange system, L is the Laplace matrix of the networked Euler-Lagrange system, λ min (L+L T ) is the matrix L+L T The minimum eigenvalue of max (LL T ) is the matrix LL T The maximum eigenvalue of , h2 is the maximum pulse interval; Consistency error q of networked multi-Euler-Lagrange systems under spoofing attack i (t)-q j The norm of (t) is bounded by: In the formula, σ is the sum of the bounded value of the external disturbance to the Euler-Lagrange system and the bound of the neural network estimation error. I n is the n×n unit matrix, λ max (Π) represents the maximum eigenvalue of the matrix Π,

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