Indirect adaptive fuzzy control for MIMO nonlinear systems with nonsymmetric control gain matrix

In this paper, an indirect adaptive fuzzy control scheme is developed for a class of uncertain multi-input multi-output (MIMO) nonlinear systems with nonsymmetric control gain matrix. 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 are 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 constraints problem of controller. A robust control term is employed to compensate for the lumped errors. The proposed scheme guarantees that all the signals in the resulting closed-loop system are bounded and the tracking errors converge asymptotically to zero. A simulation example is used to demonstrate the effectiveness of the proposed scheme.