Observer-based fuzzy adaptive control for multi-input multi-output nonlinear systems with a nonsymmetric control gain matrix and unknown control direction

In this study, we present an observer-based fuzzy adaptive control scheme for a class of uncertain multi-input multi-output nonlinear systems with a nonsymmetric control gain matrix, unknown control direction, and unmeasured states. In this scheme, fuzzy systems are used to approximate the unknown nonlinear functions and an adaptive fuzzy state observer is designed to estimate the unmeasured states. The parameter adaptive laws are designed by fuzzy basis functions rather than by its filtering and a robust control term is used to compensate for the lumped errors. The proposed method solves the problem of the nonsymmetric control gain matrix and it requires no a priori knowledge of the control direction for the states that are unmeasured. We prove that all of the signals in the resulting closed-loop systems are bounded and that the tracking errors converge asymptotically to zero. Two simulation examples are used to demonstrate the effectiveness of the proposed scheme.