A New Architecture for an Adaptive Switching Controller Based on Hybrid Multiple T-S Models

Abstract

The scope of this chapter is to provide the reader with the latest advances in the field of switching adaptive control based on hybrid multiple Takagi-Sugeno (T-S) models. The method presented here proposes a controller which is based on some semi-fixed and adaptive T-S identification models which are updating their parameters according to a specified updating rule. The main target of this enhanced scheme—compared with the fixed and adaptive multiple models case—is to control efficiently a class of unknown nonlinear dynamical fuzzy systems. The identification models define the control signal at every time instant with their own state feedback fuzzy controllers which are parameterized by using the certainty equivalence approach. A performance index and an appropriate switching rule are used to determine the T-S model that approximates the plant best and consequently to pick the best available controller at every time instant. Three types of identification models are contained in the models bank: some semi-fixed T-S models which are redistributed during the control procedure, a free adaptive T-S model which is randomly initialized, and finally a reinitialized adaptive model which uses the parameters of the best semi-fixed model at every time instant. The asymptotic stability of the system and the adaptive laws for the adaptive models are given by using Lyapunov stability theory. The combination of these different model categories, offers many advantages to the control scheme and as it is shown by computer simulations, the semi-fixed models method enhances the system’s performance and makes the initialization problem less significant than it is in the fixed models case.