How Effective are Smooth Compositions in Predictive Control of TS Fuzzy Models?

Abstract

In this article, we study the structural properties that smooth compositions bring to predictive control of TS fuzzy models and examine how they affect the uncertainties, parameter variations of the system and environmental noises to die out. We have employed the smoothness structure of compositions to convert the MPC cost function of TS fuzzy model of the nonlinear systems to an incremental iterative algorithm. Hence, the proposed algorithm does not linearize the nonlinear dynamics, neither requires solving an NP optimization problem in MPC and, therefore, is very fast and simple. The connectivist identification—MPC approach—can be employed for the systems with the long-range horizons. Therefore, the technique is beneficial to the dead-time and non-minimum phase systems. The stability analysis of the algorithm has been carried out, and the performance of the smooth TS fuzzy identification–controller scheme to the classical ones has been compared on a non-min phase test problem with different uncertainties and working environments, including (a) the normal working conditions, (b) with the additive noises, (c) with the parametric changes, (d) with the additive time-varying disturbances to demonstrate the robust behavior of the smooth compositions.