Nonlinear Fuzzy Control Based on The Vector Fields of The Phase Portrait Assignment Algorithm

Abstract

A design technique and the stability analysis of fuzzy-logic controllers for a class of nonlinear systems are studied. A new algorithm called `the phase portrait assignment algorithm', is introduced in order to establish a control rulebase that stabilizes a nonlinear feedback system by using the vector fields in the state space. This technique can substitute for classical control methods when the latter suffer from uncertainties since it provides flexibility, robustness, and asymptotic stability. The methodology provides a bridge between qualitative reasoning and stability of nonlinear feedback control systems even if a priori information is relatively unreliable. The design procedure of the phase portrait assignment algorithm is followed by stability analysis for nonlinear fuzzy regulators. As an example, a one degree-of-freedom robot arm is used for demonstrating the performance and the merits of the proposed fuzzy control mechanism.