Adaptive tracking for MIMO nonlinear systems with Unknown fast time-varying parameters

In this paper, we consider a class of MIMO nonlinear systems with fast time-varying parametric uncertainties. First, the tracking problem of general nonlinearly time-varyingly parameterized systems is solved. Then, a Lyapunov-based singularity free adaptive controller is proposed for the considered system. Specifically, an estimation approach with a proportional plus integral adaptation scheme is utilized to update the estimations of the unknown parameters under a mild assumption that the signs of the leading minors of the input gain matrix are known. The asymptotic stability is achieved with full state feedback. Furthermore, we design an output feedback controller by utilizing a standard high-gain observer and achieve uniformly ultimately bounded convergence. Simulation examples illustrate the effectiveness of the proposed methods.