Resilient State Estimation for Control Systems Using Multiple Observers and Median Operation

Abstract

This paper addresses the problem of state estimation for linear dynamic systems that is resilient against malicious attacks on sensors. By “resiliency” we mean the capability of correctly estimating the state despite external attacks. We propose a state estimation with a bank of observers combined through median operations and show that the proposed method is resilient in the sense that estimated states asymptotically converge to the true state despite attacks on sensors. In addition, the effect of sensor noise and process disturbance is also considered. For bounded sensor noise and process disturbance, the proposed method eliminates the effect of attack and achieves state estimation error within a bound proportional to those of sensor noise and disturbance. While existing methods are computationally heavy because online solution of nonconvex optimization is needed, the proposed approach is computationally efficient by using median operation in the place of the optimization. It should be pointed out that the proposed method requires the system states being observable with every sensor, which is not a necessary condition for the existing methods. From resilient system design point of view, however, this fact may not be critical because sensors can be chosen for resiliency in the design stage. The gained computational efficiency helps real-time implementation in practice.

Zero-dynamics Attack, Variations, and Countermeasures

“…As a variation of the zero-dynamics attack, which is an actuator attack, we consider its dual 'pole-dynamics attack' that is a sensor attack studied in [7]. If we rewrite the controller using the normal form, the closed-loop system is written by…”

Fully Distributed Resilient State Estimation Based on Distributed Median Solver

“…1) If (C i , A) is observable for all i ∈ N , Assumption 4 holds with any basis because all U i 's are {0}. This is the class of systems considered in [9]. 2) If A has distinct eigenvalues, then the Jordan form is a diagonal matrix.…”

“…The algorithm that we use for a distributed majority voting is a distributed median solver developed in the next section. The use of (centralized) median functions has been considered in [9] and [10] to present a fast polynomial-time algorithm for resilient state estimation. Taking advantage of the recent development of "blended dynamics" approach [15], the designed local observers approximately recover the median of the local state estimates in a distributed manner.…”

On Redundant Observability: From Security Index to Attack Detection and Resilient State Estimation

“…Recently, new threats or vulnerabilities caused by malicious attacks have been reported as advances in computers and communications increase the connectivity and openness of systems [2]. Therefore, the resilience of control systems to attack has become a critical system design consideration [3]- [5] and the security problems of the system whose measurements are compromised by adversaries have been studied actively because sensors are one of the most vulnerable points for the security of control systems [6]- [15].…”