Model Predictive Control for T-S Fuzzy Markovian Jump Systems Using Dynamic Prediction Optimization

TL;DR

This paper develops a dynamic prediction optimization-based model predictive control approach for constrained Takagi-Sugeno fuzzy Markovian jump systems, ensuring stability and feasibility through a two-stage design and demonstrating effectiveness on a robot arm example.

Contribution

It introduces a novel DPO-MPC scheme with mode-dependent controllers and perturbation design for FMJS, balancing control performance and computational load.

Findings

Ensures recursive feasibility and stability of the control scheme.

Enlarges feasible region via perturbation design.

Validated effectiveness on a robot arm system.

Abstract

In this paper, the model predictive control (MPC) problem is investigated for the constrained discrete-time Takagi-Sugeno fuzzy Markovian jump systems (FMJSs) under imperfect premise matching rules. To strike a balance between initial feasible region, control performance, and online computation burden, a set of mode-dependent state feedback fuzzy controllers within the frame of dynamic prediction optimizing (DPO)-MPC is delicately designed with the perturbation variables produced by the predictive dynamics. The DPO-MPC controllers are implemented via two stages: at the first stage, terminal constraints sets companied with feedback gain are obtained by solving a ``min-max'' problem; at the second stage, and a set of perturbations is designed felicitously to enlarge the feasible region. Here, dynamic feedback gains are designed for off-line using matrix factorization technique, while the dynamic controller state is determined for online over a moving horizon to gradually guide the system state from the initial feasible region to the terminal constraint set. Sufficient conditions are provided to rigorously ensure the recursive feasibility of the proposed DPO-MPC scheme and the mean-square stability of the underlying FMJS. Finally, the efficacy of the proposed methods is demonstrated through a robot arm system example.