Adaptive control of nonlinear systems with severe uncertainties in the input powers

In this study, we discuss global adaptive stabilization for a class of uncertain nonlinear systems. The input powers of the system are unknown, and the upper bound and the nonzero lower bound are not known in advance. This suggests that the system suffers from severe uncertainties with respect to the input powers when compared with the related literature, which would considerably challenge the control design. The switching-based strategy can compensate for severe system uncertainties, especially new types of uncertainties, including those associated with the input powers. Herein, a switching adaptive controller is successfully designed to ensure that the resulting closed-loop system states are globally bounded and ultimately converge to the origin (the equilibrium point). The proposed controller is extended to the systems with unknown control directions by redefining the involved switching sequences. A simulation example demonstrates the effectiveness of the proposed switching adaptive controller.