Robust MPC With Mode-Dependent Dissipative Performance for Non-Homogeneous MJSs Subjected to Fuzzy Switching Mechanism

This article aims to address the issue of model predictive control with optimization predictive dynamics for a class of non-homogeneous Markov jump systems. The principal concept is to construct a robust predictive control strategy by developing a fuzzy switching Markov process and a mode-dependent dissipative index to relax performance constraints. In particular, intending to depict the effects of interference on the Markov process, a high-level fuzzy switching rule, which adopts the interference factors as premise variables, is firstly proposed to orchestrate the resulting time-varying transition probabilities. This further constructs a generalized framework that takes time-invariance and high-level deterministic switching of transition probabilities as special cases. Secondly, to surmount the difficulty of acquiring relaxed stability criteria in the designing of controller and improving control performance, a novel dissipative index with mode dependence is proposed as a means of characterizing the varying dynamic system performance. What’s more, taking into account the optimization predictive dynamics-based model predictive control with bounded disturbance, a dissipation-type cost function is developed to promote the analysis of terminal constraint, dissipative performance and stability, which is distinct from $H_{2}/H_{\infty } $ type. Furthermore, the offline and online optimization algorithms are presented for achieving desired performance. Finally, the practicabilities and advantages of the theoretical results are illustrated by a modified DC motor device system model. Note to Practitioners—Markov jump systems are useful for modelling systems with random changes in parameters or structures, making them valuable in practical engineering applications, for instance the continuous stirred tank heater, the HiMAT vehicle and the F-404 aircraft. However, obtaining an accurate transition probability matrix can be challenging due to the influence of the work environment. This article proposes a high-level fuzzy switching mechanism governed Markov process to achieve more practical modeling. Additionally, a mode-dependent dissipative index is proposed to characterize time-varying performance, considering that system performance may vary with system parameters. Model predictive control is widely used in engineering applications due to its ability to handle uncertainty and hard constraints effectively. This article presents an optimization predictive dynamics-based model predictive control scheme to reduce computational pressure and constructs a dissipative-type cost function to promote interference handling analysis. Finally, the application effect of the proposed method was verified through DC motor device system model.