RLS based adaptive IVT2 fuzzy controller for uncertain model of inverted pendulum

Abstract

In this paper, a recently developed theorem in the field of stability of interval valued type 2 fuzzy controllers has been studied and a new adaptive control strategy has been proposed due to this theorem. Mentioned theorem, present some constrains for the stability of the system which are dependent on the upper and lower bounds of membership function of the IVT2 model. These bounds are dependent on the parametric uncertainties in the plant. In this paper, it is proposed to use recursive least square algorithm to identify unknown parameters to narrow footprint of uncertainties in the membership functions of IVT2 model. Narrowing FOU through the time, studied theorem presents more relaxed constrains as a result of which, space of stabilizing controllers would be extended. Searching in the extended space, a controller with a better performance could be selected using genetic algorithm. Proposed algorithm is applied on uncertain model of inverted pendulum and results show that disturbances which are modeled in the format of initial conditions could be rejected faster.