Robust Adaptive Tracking Control of a Class of Uncertain Multi-Mode Nonlinear Systems with Unknown Disturbances

This paper studies robust adaptive tracking control for a family of multi-mode nonlinear systems. Adaptive laws using tuning functions are proposed to address the parametric uncertainties and unknown disturbances, which can avoid the problem of over-parameterization. In addition, the variation law of the modes is developed based on the mode-dependent sojourn time scheme, which exploits the information of each subsystem, i.e., sojourn time is realized in a subsystem sense. Based on the proposed time-constraint scheme, variation signals that are less conservative than those based on sojourn time are designed. Globally uniformly ultimately bounded stability of the closed-loop multi-mode system is guaranteed. Furthermore, the steady-state performance characterized by an ultimate bound of the tracking error is presented. A numerical simulation demonstrates the effectiveness of the proposed method.