Adaptive Fuzzy Control for MIMO Nonlinear Systems With Nonsymmetric Control Gain Matrix and Unknown Control Direction

In this paper, an indirect adaptive fuzzy control scheme is developed for a class of uncertain multi-input multi-output nonlinear systems with nonsymmetric control gain matrix and unknown control direction. The nonsymmetric control gain matrix is expressed as the sum of a symmetric matrix and a skew symmetric matrix, and the symmetric matrix, as well as the skew symmetric matrix, is approximated by fuzzy systems. By using the symmetric matrix decomposition technique, the estimated symmetric matrix is decomposed into the product of one diagonal matrix and two orthogonal matrixes. Based on the decomposition results, the adaptive fuzzy controller is developed to avoid the possible singularity problem and the parameter initialization problem. A robust control term is employed to compensate for the lumped errors, and a Nussbaum-type function is incorporated in the robust control term to deal with the unknown control direction. The proposed scheme guarantees that all the signals in the resulting closed-loop system are bounded and that the tracking errors converge asymptotically to zero. Two simulation examples are used to demonstrate the effectiveness of the proposed scheme.