An optimization framework for resilient batch estimation in Cyber-Physical Systems

Alexandre Kircher (1) , Laurent Bako (1) , Eric Blanco (1) , Mohamed Benallouch (2)

1 AIS - Ampère, Département Automatique pour l'Ingénierie des Systèmes
2 ECAM Lyon - ECAM Lyon

This paper proposes a class of resilient state estimators for LTV discrete-time systems. The dynamic equation of the system is assumed to be affected by a bounded process noise. As to the available measurements, they are potentially corrupted by a noise of both dense and impulsive natures. The latter in addition to being arbitrary in its form, need not be strictly bounded. In this setting, we construct the estimator as the set-valued map which associates to the measurements, the minimizing set of some appropriate performance functions. We consider a family of such performance functions each of which yielding a specific instance of the proposed general estimation framework. It is then shown that the proposed class of estimators enjoys the property of resilience, that is, it induces an estimation error which, under certain conditions, is independent of the extreme values of the (impulsive) measurement noise. Hence, the estimation error may be bounded while the measurement noise is virtually unbounded. Moreover, we provide several error bounds (in different configurations) whose expressions depend explicitly on the degree of observability of the system being observed and on the considered performance function. Finally, a few simulation results are provided to illustrate the resilience property.

Mots clés: secure state estimation; resilient estimators; optimal estimation; cyber-physical systems

Domaines: Automatique / Robotique

Alexandre Kircher, Laurent Bako, Eric Blanco, Mohamed Benallouch. An optimization framework for resilient batch estimation in Cyber-Physical Systems. IEEE Transactions on Automatic Control, 2022, ⟨10.1109/TAC.2021.3121223⟩. ⟨hal-03424305⟩