Robust control for uncertain nonlinear systems with unknown and changing control direction

This paper studies the robust control problem for uncertain nonlinear systems with unknown and changing control direction. The control direction is the multiplier of the control term, and is allowed to cross zero and change its sign for unlimited number of times. Based on the analysis of system dynamics at the points where the control direction is zero, a robust controller is proposed by integrating with a Nussbaum-type gain. Under the proposed controller, the system converges to zero if zero is accessible, or to the accessible point closest to zero if zero is not accessible by any control. The control performance is illustrated by the simulated example.