Hierarchical Optimization-Based Model Predictive Control for a Class of Discrete Fuzzy Large-Scale Systems Considering Time-Varying Delays and Disturbances

TL;DR

This paper develops a hierarchical model predictive control approach for large-scale discrete fuzzy systems with time-varying delays and disturbances, using Razumikhin method and LMIs to ensure stability and robustness.

Contribution

It introduces a novel hierarchical MPC framework employing Razumikhin approach for large-scale fuzzy systems with delays and disturbances, enhancing stability and computational efficiency.

Findings

The proposed method achieves asymptotic stability of the closed-loop system.

Effectiveness demonstrated through two illustrative examples.

Comparison shows improvements over existing methods.

Abstract

Abstract-In this manuscript, model predictive control for class of discrete fuzzy large-scale systems subjected to bounded time-varying delay and disturbances is studied. The considered method is Razumikhin for time-varying delay large-scale systems, in which it includes a Lyapunov function associated with the original non-augmented state space of system dynamics in comparison with the Krasovskii method. As a rule, the Razumikhin method has a perfect potential to avoid the inherent complexity of the Krasovskii method especially in the presence of large delays and disturbances. The considered large-scale system in this manuscript is decomposed into several subsystems, each of which is represented by a fuzzy Takagi-Sugeno (T-S) model and the interconnection between any two subsystems is considered. Because the main section of the model predictive control is optimization, the hierarchical scheme is performed for the optimization problem. Furthermore, persistent disturbances are considered that robust positive invariance and input-to-state stability under such circumstances are studied. The linear matrix inequalities (LMIs) method is performed for our computations. So the closed-loop large-scale system is asymptotically stable. Ultimately, by two examples, the effectiveness of the proposed method is illustrated, and a comparison with other papers is made by remarks.