Robust Control for Nonlinear Markov Jump Systems with Partially Unknown Transition Probabilities

Abstract

This note focuses on the finite horizon H2/H∞ control for stochastic nonlinear jump systems with partially unknown transition probabilities. We derive the nonlinear stochastic bounded real lemma and the nonlinear optimal regular result for the considered system at first. A sufficient condition and a necessary condition for the solution of H2/H∞ control are, respectively, offered by four cross-coupled Hamilton–Jacobi equations (HJEs). Besides, numerical examples show the effectiveness of the obtained results.

Fuzzy-Model-Based Control for Markov Switching Singularly Perturbed Systems with the Stochastic Communication Protocol

“…As a significant component of hybrid systems, Markov switching systems (MSSs) have gained extensive interest due to their capability in modeling subsystems [1][2][3][4]. Note that MSSs consist of a finite number of subsystems, and some abrupt variations can be depicted by a Markov process, which is recognized as a key feature of MSSs.…”