DISTRIBUTED SECURE STATE RECONSTRUCTION METHOD BASED ON DOUBLE-LAYER DYNAMIC SWITCHING OBSERVER

Abstract

The present disclosure discloses a distributed secure state reconstruction method based on a double-layer dynamic switching observer. The method includes the following steps: constructing a dynamics model of a sensing channel of a multi-agent system after the sensing channel is attacked according to the multi-agent system; building a double-layer observer for each multi-agent in combination with a specific multi-agent system model, constructing a proper observation communication topology, and designing a corresponding residual generator; analyzing dynamic information generating a residual threshold aiming at an observation model, checking a magnitude between each residual signal and the threshold, dynamically switching the communication topology between the observers according to the compared magnitude, and performing a new data communication interaction; and performing iterative updating to generate new observation data in combination with self observation data and received neighbor observation information, and taking whether the residual signal is greater than a current threshold or not as a standard for determining whether a corresponding communication channel is attacked or not. According to the present disclosure, all transmission channels subjected to malicious attacks can be correctly identified, and the real state of the system can be securely reconstructed.

Claims

1-5. (canceled)

6. A distributed secure state reconstruction method based on a double-layer dynamic switching observer, comprising the following steps: step 1: constructing a specific dynamics model of a sensing channel of a studied multi-agent system after the sensing channel is attacked according to the multi-agent system; and describing the dynamics model of the multi-agent system after the sensing channel is subjected to sparse attacks as follows: $\{\begin{array}{c}{\stackrel{.}{x}}_i\left(t\right)={\mathrm{Ax}}_i\left(t\right)+\mathrm{BK}\underset{j=1}{\overset{N}{.Math.}}{a}_{\mathrm{ij}}\left(x_j\left(t\right)-x_i\left(t\right)\right),\\ y_i\left(t\right)={\mathrm{Cx}}_i\left(t\right)+{\gamma }_i\left(t\right)d_i\left(t\right),\end{array}$ where x.sub.i(t), y.sub.i(t), d.sub.i(t) are an n-dimensional real state of an ith agent, a p-dimensional measurement output, and a p-dimensional attack input on a corresponding sensing channel, respectively, a.sub.ij represents weight information between two agents, γ.sub.i(t)∈{0,1} represents whether the sensing channel corresponding to the ith agent is attacked or not, |Σ.sub.i=1.sup.Nγ.sub.i(t)|<s<N/2, and N is the number of agents; matrices A,B,C are a system state parameter matrix and a measurement matrix, respectively, and a matrix K=1/λ.sub.2.sup.LB.sup.TP.sup.−1 is a consistency control input matrix and satisfies, for a positive definite matrix P and a constant κ>0, the following formula: AP+PA.sup.T−2BB.sup.T+κP<0, where A.sub.Z is a second small characteristic root of a Laplacian matrix L corresponding to the communication topology of the multi-agent system. step 2: building a double-layer observer for each multi-agent in combination with a specific multi-agent system model, constructing a proper observation communication topology, and designing a corresponding residual generator, specifically comprising the following steps: step 201: constructing a double-layer observer based on residual information for each agent, wherein when determining that a corresponding sensing channel is not attacked, the first-layer observer estimates the state of the multi-agent system mainly using a measurement residual, and sends observation data thereof to a second-layer observation neighbor; otherwise, when determining that the sensing channel is attacked, the observer achieves state observation using an error between the two layers of observers, and stops sending the observation data to the neighbor; and the second-layer observer performs distributed state estimation mainly based on the observation data sent by the observation neighbor thereof, and sends observation data thereof to the observation neighbor thereof only after the observer determines that the corresponding sensing channel is attacked; and step 202: constructing a corresponding residual generator based on the dynamics model of the multi-agent and the double-layer observer, specifically as follows: an observation residual of an agent i is denoted as ε.sub.i(t)=y.sub.i(t)−C{circumflex over (x)}.sub.i.sup.1(t), and a corresponding test residual is composed of an observation residual and a Lyapunov matrix, and denoted as z.sub.i(t)=∥Q.sup.−TC.sup.Tε.sub.i(t)∥.sup.2, where Q.sup.TQ=P is the Lyapunov matrix; step 3: analyzing dynamic information generating a residual threshold aiming at an observation model, checking a magnitude between each residual signal and the threshold, dynamically switching the communication topology between the observers according to the compared magnitude, and performing a new data communication interaction; and step 4: performing iterative updating to generate new observation data in combination with self observation data and received neighbor observation information, and taking whether the residual signal is greater than a current threshold or not as a standard for determining whether a corresponding communication channel is attacked or not.

7. The distributed secure state reconstruction method based on a double-layer dynamic switching observer according to claim 6, wherein the analyzing dynamic information generating a residual threshold aiming at an observation model, checking a magnitude between each residual signal and the threshold, dynamically switching the communication topology between the observers according to the compared magnitude, and performing a new data communication interaction in step 3 specifically comprises the following steps: step 301: determining, for each observer i, an upper bound of an initialization observation error threshold ρ.sub.i(0)=∥Q.sup.−TC.sup.Tε.sub.i(0)∥.sup.2 as prior information thereof by default; otherwise, obtaining a common initialization error upper bound threshold ρ.sub.i(0)=ρ.sub.0 according to an upper bound limitation of initial parameters; and step 302: when t>0, generating, by each observer i, threshold information of each moment according to the following dynamics model: ${\hat{\rho }}_i\left(t\right)=-\mu \left(1+\frac{m_0{\lambda }_m^P}{m_1{\lambda }_M^P}\right){\rho }_i\left(t\right),$ where λ.sub.m.sup.P and λ.sub.M.sup.P are minimum and maximum eigenvalues of the matrix P, respectively, and constant m.sub.0>0, constant m.sub.1>0, constant 0<μ<κ, and constant κ>0; then the magnitudes of z.sub.i(t) and ρ.sub.i(t) at each moment are compared, if z.sub.i(t)>ρ.sub.i(t), the observer determines that the ith sensing channel is attacked, and the communication topology thereof is switched; otherwise, the observer i still sends the observation information to all neighbors N.sub.i according to the original communication topology.

8. The distributed secure state reconstruction method based on a double-layer dynamic switching observer according to claim 6, wherein the performing iterative updating to generate new observation data in combination with self observation data and received neighbor observation information, and taking whether the residual signal is greater than a current threshold or not as a standard for determining whether a corresponding communication channel is attacked or not in step 4 specifically comprises the following steps: step 401: receiving, by the double-layer observer i, a measurement output and state estimation information of all the neighbors, and then representing the dynamic update thereof using the following formula: $\{\begin{array}{c}{\stackrel{.}{\hat{x}}}_i^1\left(t\right)=A{\hat{x}}_i^1\left(t\right)+L\left[{\theta }_i\left(t\right)\left(y_i\left(t\right)-C{\hat{x}}_i^1\left(t\right)\right)+\left(1-{\theta }_i\left(t\right)\right)C\left({\hat{x}}_i^2\left(t\right)-{\hat{x}}_i^1\left(t\right)\right)\right],\\ {\stackrel{.}{\hat{x}}}_i^2\left(t\right)=A{\hat{x}}_i^2\left(t\right)+\mathrm{BK}\underset{j=1}{\overset{N}{.Math.}}{a}_{\mathrm{ij}}\left[{\theta }_j\left(t\right){\hat{x}}_j^1\left(t\right)+\left(1-{\theta }_j\left(t\right)\right){\hat{x}}_j^2\left(t\right)-{\hat{x}}_i^2\left(t\right)\right],\end{array}$ where {circumflex over (x)}.sub.i.sup.1(t), {circumflex over (x)}.sub.i.sup.2(t) are states corresponding to two layers of observers, L=P.sup.−1C.sup.T is a gain matrix whereby A-LC is Hurwitz-stable, and there are a constant m.sub.0>0, m.sub.1>0 and a positive definite matrix P for a given constant 0<μ<κ whereby the following LMI is satisfied: $\left[\begin{array}{cc}{I}_N.Math.\left(\mathrm{PA}+A^{T}P-2C^{T}C+m_{0}I+\mu P\right)& -ℒ.Math.\mathrm{PBK}\\ -{\left(ℒ.Math.\mathrm{PBK}\right)}^T& I_N.Math.\left(-m_{1}I+\mu P\right)\end{array}\right]<0.$ where θ.sub.i(t)=0/1 represents that an observation center determines whether the ith channel is manipulated by an attacker or not, and the value thereof is changed whereby the communication topology of the double-layer observer is switched dynamically; and step 402: describing an assignment standard for an attack identification logic θ.sub.i(t) of the observer i as follows: ${\theta }_i\left(t\right)=\{\begin{array}{cc}1,& z_i\left(t\right)\le {\rho }_i\left(t\right),\\ 0,& z_i\left(t\right)>{\rho }_i\left(t\right).\end{array}$ where if θ.sub.i(t)=0, the observer determines that the ith transmission channel is attacked, otherwise, the observer determines that the ith transmission channel is not attacked.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0028] FIG. 1 is a schematic diagram of steps of a distributed secure state reconstruction method based on a double-layer dynamic switching observer according to the present disclosure.

[0029] FIG. 2 is a specific flowchart of a distributed secure state reconstruction method based on a double-layer dynamic switching observer according to the present disclosure.

[0030] FIG. 3 is a structural diagram of communication topology of a multi-agent system and a double-layer observer design provided by an example of the present disclosure.

[0031] FIG. 4 is a schematic diagram of the state of the real state and observer reconstruction for a multi-agent system provided by an example of the present disclosure.

[0032] FIG. 5 is a schematic diagram of a channel index of an actual attack and an attack index identified by an observer provided by an example of the present disclosure.

DETAILED DESCRIPTION

[0033] As shown in FIG. 1, a distributed secure state reconstruction method based on a double-layer dynamic switching observer includes the following steps:

[0034] step 1: constructing a specific dynamics model of a sensing channel of a studied multi-agent system after the sensing channel is attacked according to the multi-agent system.

[0035] In this embodiment of the present disclosure, the step specifically includes:

[0036] step 101: describing the dynamics model of the multi-agent system after the sensing channel is subjected to sparse attacks as follows:

[00006]$\{\begin{array}{c}{\hat{x}}_i\left(t\right)={\mathrm{Ax}}_i\left(t\right)+\mathrm{BK}\underset{j=1}{\overset{N}{.Math.}}{a}_{\mathrm{ij}}\left(x_j\left(t\right)-x_i\left(t\right)\right),\\ y_i\left(t\right)={\mathrm{Cx}}_i\left(t\right)+{\gamma }_i\left(t\right)d_i\left(t\right),\end{array}$

[0037] where x.sub.i(t), y.sub.i(t), d.sub.i(t) are an n-dimensional real state of an ith agent, a p-dimensional measurement output, and a p-dimensional attack input on a corresponding sensing channel, respectively, a.sub.ij represents weight information between two agents, γ.sub.i(t)∈{0,1} represents whether the sensing channel corresponding to the ith agent is attacked or not, |Σ.sub.i=1.sup.Nγ.sub.i(t)|<s<N/2, and N is the number of agents; matrices A,B,C are a system state parameter matrix and a measurement matrix, respectively, and K=1/λ.sub.2.sup.CB.sup.TP.sup.−1 is a consistency control input, and satisfies, for a positive definite matrix P and a constant κ>0, the following LMI: AP+PA.sup.T−2BB.sup.T+κP<0, where λ.sub.2.sup.C is a second small characteristic root of a Laplacian matrix corresponding to the communication topology of the multi-agent system.

[0038] step 2: constructing a double-layer dynamic switching observer for each agent, and generating a corresponding residual.

[0039] In this embodiment of the present disclosure, the step specifically includes:

[0040] step 201: constructing a double-layer observer based on residual information for each agent. When determining that a corresponding sensing channel is not attacked, the first-layer observer estimates the state of the multi-agent system mainly using a measurement residual mainly using a measurement residual, and sends observation data thereof to a second-layer observation neighbor: otherwise, when determining that the sensing channel is attacked, the observer achieves state observation using an error between the two layers of observers, and stops sending the observation data to the neighbor. The second-layer observer performs distributed state estimation mainly based on the observation data sent by the observation neighbor thereof, and sends observation data thereof to the observation neighbor thereof only after the observer determines that the corresponding sensing channel is attacked.

[0041] step 202: constructing a corresponding residual generator based on the dynamics model of the multi-agent and the double-layer observer, specifically as follows:

[0042] an observation residual of an agent i is denoted as ε.sub.i(t)=y.sub.i(t)−C{circumflex over (x)}.sub.i.sup.1(t), and a corresponding test residual is composed of an observation residual and a Lyapunov matrix, and denoted as z.sub.i(t)=∥Q.sup.−TC.sup.Tε.sub.i(t)∥.sup.2, where Q.sup.TQ=P is the Lyapunov matrix.

[0043] step 3: dynamically switching communication transmission channels between the observers by using a magnitude between the residual signal generated by each observer and a current threshold,

[0044] and performing observation signal transmission interaction with neighbors.

[0045] In this embodiment of the present disclosure, the step specifically includes:

[0046] step 301: determining, for each observer i, an upper bound of an initialization observation error threshold ρ.sub.i(0)=∥Q.sup.−TC.sup.Tε.sub.i(0)∥.sup.2 as prior information thereof by default; otherwise, obtaining a common initialization error upper bound threshold ρ.sub.i(0)=ρ.sub.0 according to an upper bound limitation of initial parameters; and

[0047] step 302: when t>0, generating, by each observer i, threshold information of each moment according to the following dynamics model:

[00007]${\hat{\rho }}_i\left(t\right)=-\mu \left(1+\frac{m_0{\lambda }_m^P}{m_1{\lambda }_M^P}\right){\rho }_i\left(t\right),$

[0048] where λ.sub.m.sup.P and λ.sub.M.sup.P are minimum and maximum eigenvalues of the matrix P, respectively, and parameters μ, m.sub.0, m.sub.1 are seen in step 401; then the magnitudes of z.sub.i(t) and ρ.sub.i(t) at each moment are compared, if z.sub.i(t)>ρ.sub.i(t), the observer determines that the ith sensing channel is attacked, and the communication topology thereof is switched; otherwise, the observer i still sends the observation information to all neighbors according to the original communication topology.

[0049] step 4: performing iterative updating to the neighbor observation signals received by each observer to complete the distributed state reconstruction, and generating a malicious sensing attack identification signal.

[0050] In this embodiment of the present disclosure, the step specifically includes:

[0051] step 401: receiving, by the double-layer observer i, a measurement output and state estimation information of all the neighbors, and then representing the dynamic update thereof using the following formula:

[00008]$\{\begin{array}{c}{\stackrel{.}{\hat{x}}}_i^1\left(t\right)=A{\hat{x}}_i^1\left(t\right)+L\left[{\theta }_i\left(t\right)\left(y_i\left(t\right)-C{\hat{x}}_i^1\left(t\right)\right)+\left(1-{\theta }_i\left(t\right)\right)C\left({\hat{x}}_i^2\left(t\right)-{\hat{x}}_i^1\left(t\right)\right)\right],\\ {\stackrel{.}{\hat{x}}}_i^2\left(t\right)=A{\hat{x}}_i^2\left(t\right)+\mathrm{BK}\underset{j=1}{\overset{N}{.Math.}}{a}_{\mathrm{ij}}\left[{\theta }_j\left(t\right){\hat{x}}_j^1\left(t\right)+\left(1-{\theta }_j\left(t\right)\right){\hat{x}}_j^2\left(t\right)-{\hat{x}}_i^2\left(t\right)\right],\end{array}$

[0052] where {circumflex over (x)}.sub.i.sup.1(t), {circumflex over (x)}.sub.i.sup.2(t) are states corresponding to two layers of observers, L=P.sup.−1C.sup.T is a gain matrix whereby A-LC is Hurwitz-stable, and there are a constant m.sub.0>0, m.sub.1>0 and a positive definite matrix P for a given constant 0<μ<κ whereby the following LMI is satisfied:

[00009]$\left[\begin{array}{cc}{I}_N.Math.\left(\mathrm{PA}+A^{T}P-2C^{T}C+m_{0}I+\mu P\right)& -ℒ.Math.\mathrm{PBK}\\ -{\left(ℒ.Math.\mathrm{PBK}\right)}^T& I_N.Math.\left(-m_{1}I+\mu P\right)\end{array}\right]<0.$

[0053] where θ.sub.i(t)=0/1 represents that an observation center determines whether the ith channel is manipulated by an attacker or not, and the value thereof is changed whereby the communication topology of the double-layer observer is switched dynamically; and

[0054] step 402: describing an assignment standard for an attack identification logic θ.sub.i(t) of the observer i as follows:

[00010]${\theta }_i\left(t\right)=\{\begin{array}{cc}1,& z_i\left(t\right)\le {\rho }_i\left(t\right),\\ 0,& z_i\left(t\right)>{\rho }_i\left(t\right).\end{array}$

[0055] where if θ.sub.i(t)=0, the observer determines that the ith transmission channel is attacked, otherwise, the observer determines that the ith transmission channel is not attacked.

Embodiment 1

[0056] step 1: a dynamics model of a multi-agent system composed of 5 unmanned trolleys is as follows:

[00011]$\{\begin{array}{c}\left(\begin{array}{c}{\stackrel{.}{p}}_i\\ {\stackrel{.}{v}}_i\\ {\stackrel{.}{a}}_i\end{array}\right)=\left(\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 0& 0& -2\end{array}\right)\left(\begin{array}{c}{p}_i\\ v_i\\ a_i\end{array}\right)+\left(\begin{array}{c}0\\ 0\\ 2\end{array}\right)\underset{j=1}{\overset{5}{.Math.}}{\mathrm{Ka}}_{\mathrm{ij}}\left(\left(\begin{array}{c}{p}_j\\ v_j\\ a_j\end{array}\right)-\left(\begin{array}{c}{p}_i\\ v_i\\ a_i\end{array}\right)\right),\\ y_i=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\end{array}\right)\left(\begin{array}{c}{p}_i\\ v_i\\ a_i\end{array}\right)+{\gamma }_i{d}_i\left(t\right),\end{array}$

[0057] an attacker randomly selects sensing transmission channels of 2 trolleys every 5 s to perform attack injection, and a bad data injection function thereof is d.sub.i(t)=(−ip.sub.i 0.5e.sup.i/20).sup.T.

[0058] Next, parameters are correspondingly solved in accordance with the flow described in FIG. 2 to achieve the distributed secure state observation of multi-agents.

[0059] step 2: the communication topology between 5 trolleys and a double-layer observer is shown in FIG. 3. The dotted circles represent a first-layer observer and a second-layer observer respectively. The solid line in an observer channel represents a communication topology channel when the observer determines that there is no malicious attack. The dashed line represents a communication channel which is switched dynamically when the observer determines that there is a malicious attack. step 3: relevant parameters of a controller and the observers are selected as follows:

[00012]$K=\left(1.11432.33760.9535\right),\kappa =1,\mu =0.8,\lambda =13.4795$$L=\left(\begin{array}{cc}3.1826& 2.4104\\ 2.4104& 5.1258\\ 1.0126& 2.6808\end{array}\right),P=\left(\begin{array}{ccc}0.4942& -0.2594& -0.0516\\ -0.2594& 0.4463& -0.247\\ -0.0516& -0.247& 0.426\end{array}\right).$

[0060] FIG. 4 shows a real state of an agent and observation data of a 2nd-layer observer. It can be seen that the double-layer observer proposed in the present disclosure can achieve the secure state reconstruction in the presence of malicious attackers.

[0061] FIG. 5 shows attack indexes of each sensing transmission channel at each moment and attack indexes identified by the observers. The hollow circles represent the actual attack channel indexes at the current moment, the crosses represent the attack indexes identified by the observers, and ordinate 0 represents the empty attack indexes. It can be seen that after t>10 s, the identification indexes of the double-layer observer about the attack may successfully match the real attack indexes, indicating that sparse sensing attacks may be detected and identified by the double-layer observer proposed in the present disclosure. The effectiveness of the distributed secure state estimation method based on a double-layer dynamic switching observer proposed in the present disclosure is proved.