Dynamic output feedback control for discrete-time stochastic nonlinear systems with adversaries

This paper is concerned with the security control problem for a class of discrete-time stochastic nonlinear systems subject to randomly occurring deception attacks. A set of Bernoulli distributed white sequences is introduced to govern the random occurrences of deception attacks. The purpose of the problem under consideration is to design a dynamic output feedback controller such that the closed-loop system achieves the desired security in probability. First of all, a theoretical framework is established for analyzing the so-called input-to-state stability in probability (ISSiP) for general discrete-time stochastic nonlinear systems. Within such a theoretical framework, some sufficient conditions are proposed to guarantee that the closed-loop system is secure. Furthermore, the main results are shown to be extendable to the case of discrete-time stochastic linear systems whose controller parameters are characterized via solving a set of matrix inequalities with a nonlinear inequality constraint. Finally, a simulation example is utilized to illustrate the usefulness of the proposed controller design scheme.