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In this article, the asynchronous resilient robust model predictive control (RMPC) problem is investigated for Markovian jump systems (MJSs) subject to polytopic parameter uncertainties and hard constraints on states and inputs. A hidden Markov model with partially available mode detection probabilities is introduced to characterize the asynchronous phenomenon between the detected modes and the system modes. A novel resilient control law is formulated such that, in the framework of the RMPC approach, the MJSs are mean-square stable in spite of partly accessible mode detection probabilities. Subsequently, by resorting to the stochastic analysis technique, sufficient conditions are derived, where the requirement of the terminal invariant set is met and the upper bound of the worst-case infinite horizon cost function is obtained. Moreover, by means of solving certain auxiliary optimization problems, the explicit expression of the desired controller is parameterized. Finally, simulation examples are presented to verify the validity of the proposed methods.
Zhang et al. (Thu,) studied this question.