Designing the Model Predictive Control for Interval Type-2 Fuzzy T-S Systems Involving Unknown Time-Varying Delay in Both States and Input Vector

TL;DR

This paper develops a model predictive control method for interval type-2 fuzzy Takagi-Sugeno systems with unknown, bounded, time-varying delays in states and inputs, using Razumikhin approach and LMIs for efficient online optimization.

Contribution

It introduces a novel MPC design for IT2 fuzzy T-S systems with unknown delays, employing Razumikhin method and LMIs to improve stability and computational efficiency.

Findings

Effective stabilization of systems with unknown delays.

Reduced computational burden via LMIs.

Successful application demonstrated through an example.

Abstract

In this paper, the model predictive control is designed for an interval type-2 Takagi-Sugeno (T-S) system with unknown time-varying delay in state and input vectors. The time-varying delay is a weird phenomenon that is appeared in almost all systems. It can make many problems and instability while the system is working. In this paper, the time-varying delay is considered in both states and input vectors and is the sensible difference between the proposed method here and previous algorithms, besides, it is unknown but bounded. To solve the problem, the Razumikhin approach is applied to the proposed method since it includes a Lyapunov function with the original nonaugmented state space of system models compared to Krasovskii formula. On the other hand, the Razumikhin method act better and avoids the inherent complexity of the Krasovskii specifically when large delays and disturbances are appeared. To stabilize output results, the model predictive control (MPC) is designed for the system and the considered system in this paper is interval type-2 (IT2) fuzzy T-S that has better estimation of the dynamic model of the system. Here, online optimization problems are solved by the linear matrix inequalities (LMIs) which reduce the burdens of the computation and online computational costs compared to the offline and non-LMI approach. At the end, an example is illustrated for the proposed approach.