Fuzzy adaptive tracking control for a class of nonlinearly parameterized systems with unknown control directions

This paper addresses the problem of adaptive fuzzy tracking control for a class of nonlinearly parameterized systems with unknown control directions. In this paper, the nonlinearly parameterized functions are lumped into the unknown continuous functions which can be approximated by using the fuzzy logic systems (FLS) in Mamdani type. Then, the Nussbaum-type function is used to detect the unknown control direction and based on the backstepping technique, the adaptive fuzzy controller is designed. The main advantages of this paper are that (1) in the existing results the separation principle is used to deal with the nonlinearly parameterized functions, unlike them in this paper, the FLS are applied to approximate the nonlinearly parameterized functions, (2) by using the minimal learning parameters (MLP) algorithm, only one parameter needs to be adjusted online in the controller design procedure, which reduces the online computation burden greatly, (3) the Nussbaum-gain technique is introduced to resolve the unknown control direction problems. It is proven that the proposed control scheme renders the closed-loop system stable in the sense of semiglobal uniformly ultimately bounded (UUB). Finally, simulation results are provided to show the effectiveness of the proposed approach.