Reach Set-Based Secure State Estimation against Sensor Attacks with Interval Hull Approximation

This paper deals with the problem of secure state estimation in an adversarial environment with the presence of bounded noises. The problem is given as min-max optimization, that is, the system operator seeks an optimal estimate which minimizes the worst-case estimation error due to the manipulation by the attacker. To derive the optimal estimate, taking the reach set of the system into account, we first show that the feasible set of the state can be represented as a union of polytopes, and the optimal estimate is given as the Chebyshev center of the union. Then, for calculating the optimal state estimate, we provide a convex optimization problem that utilizes the vertices of the union. On the proposed estimator, the estimation error is bounded even if the adversary corrupts any subset of sensors. For the sake of reducing the calculation complexity, we further provide another estimator which resorts to the interval hull approximation of the reach set and properties of zonotopes. This approximated estimator is able to reduce the complexity without degrading the estimation accuracy sorely. Numerical comparisons and examples finally illustrate the effectiveness of the proposed estimators.