Fuzzy adaptive controller for MIMO nonlinear systems with known and unknown control direction

This paper investigates fuzzy adaptive control schemes for a class of multi-input multi-output (MIMO) unknown nonlinear systems with known and unknown sign of the control gain matrix. Three fuzzy adaptive control schemes are developed. In the design of the second and third controller, we will exploit a decomposition of the control gain matrix into a symmetric positive-definite matrix, a diagonal matrix with diagonal entries +1 or -1 and a unity upper triangular matrix. The Nussbaum-type function is used to deal with the unknown control direction (i.e. the unknown sign of the control gain matrix). For updating the parameters of the fuzzy system, an adaptation proportional-integral (PI) law is proposed. Theoretical results are illustrated through two simulation examples.