Finite-frequency self-triggered model predictive control for Markov jump systems subject to actuator saturation

Abstract

In this paper, a self-triggered saturated model predictive control (SMPC) for Markov jump system (MJS) is studied in finite-frequency domain. First, the MJS with multi-modes is transformed into a single mode system with embedded transition probability to prepare for the use of generalized Kalman–Yakubovich–Popov (GKYP) lemma. Second, a dynamic self-triggered mechanism with time-varying threshold is developed to predict the next triggering time according to the current time, states, and jumping mode. Third, for disturbances that only possess finite-frequency band, a co-design of triggering condition and SMPC is realized by properly employing GKYP lemma. Compared with existing works, the main motivation of this paper is to improve the anti-interference ability within a specified frequency range. Moreover, we also aim to shorten the gap between the finite band control theory and its applications to practical engineering problems. Finally, the effectiveness of the proposed approach is demonstrated by both the numerical and practical simulations.