Adaptive fuzzy control for a class of MIMO nonlinear systems with nonsymmetric gain matrix

In this paper, an indirect adaptive fuzzy controller is developed for a class of uncertain MIMO nonlinear systems with nonsymmetric control gain matrix. Within this scheme, the fuzzy logic systems are used to approximate the plant´s unknown nonlinear functions. By using the symmetric matrix decomposition technique, the estimated symmetric gain matrix is decomposed into the product of one diagonal matrix and two orthogonal matrixes. Based on the decomposition results, the controller is developed to avoid the possible controller singularity problem, as well as not to depend upon any parameter initialization conditions, and a dynamic robust controller 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.