On controlled mode discernibility for nonlinear hybrid systems with unknown exogenous input

Abstract

This paper considers the mode discernibility and controlled mode discernibility for nonlinear hybrid systems with unknown switchings and unknown exogenous input, motivated by its potential applications to fault detection and isolation, cyber-security, and robust control. We formally define the mode discernibility and controlled mode discernibility, and then characterize these properties from a geometric perspective. Specifically, we review and complement the concept of controlled invariance for nonlinear systems, based on which a new concept called strongly controlled invariance is proposed as a tool to characterize the controlled mode discernibility. Besides the general characterization of controlled mode discernibility, we discuss some commonly considered special nonlinearities, and demonstrate that the discerning control design problem can be formulated as a quadratic game for some cases.