Secure state estimation for cyber physical systems with state delay and sparse sensor attacks

Abstract

In this paper, the problem of secure state estimation for cyber physical systems (CPSs) with state delay and sparse sensor attacks is studied. An algorithm combining set cover approach and adaptive switching mechanism is proposed, which can realize off-line acquisition of candidate set and accurately locate the real attack mode. The contributions of this algorithm are that it can greatly reduce the search space, eliminate the impact of attacks on state estimation, improve the estimation speed and ensure the real-time performance of state estimation under the premise of effective estimation. The sufficient condition for the existence of the observer is obtained. Finally, the rapidity and effectiveness of the designed observer are verified by two examples.

Stochastic Models to Mitigate Sparse Sensor Attacks in Continuous-Time Non-Linear Cyber-Physical Systems

“…These models can be analytically manipulated to define protection algorithms based on Orthogonal-Triangular (QR) decomposition [42] or Linear-Quadratic (LQ) control [43], mitigating the impact of attacks. Models can be deterministic [44] or include some stochastic terms to represent noises [45]. Besides, continuous [44] and discrete [46] models may be found.…”

“…Models can be deterministic [44] or include some stochastic terms to represent noises [45]. Besides, continuous [44] and discrete [46] models may be found. However, most of these models are linear and only consider the selfmaintained evolution of the node output and the measurement errors (in line with traditional control theory models).…”

“…Regarding the probability density function 1 , the probability μ 1 j of any unreconstructed state y j [k] for the j-th state variable to happen in a given CPS, may be evaluated considering the previous reconstructed states Y j Rr achieved by that CPS and the Laplace definition of probability (44), and being δ [•] the Kronecker's delta function. The probability μ j pdf for the entire Y j Run series of unreconstructed states may be obtained as the mean value of all the individual probabilities (45).…”