Continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction

In this paper, a robust control scheme is proposed for a class of nonlinear systems that have not only additive nonlinear uncertainties but also unknown multiplicative signs. These signs are called control directions since they represent effectively the direction of motion under any given control. Except for the unknown control directions, the class of systems satisfy the generalized matching conditions. The proposed robust control is continuous and guarantees global stability of uniform ultimate boundedness without a priori knowledge of the control directions nor the knowledge of nonlinear dynamics except their size bounding functions. This is achieved by on-line identifying control directions and by utilizing shifting laws that change smoothly and accordingly the signs of robust controls. The analysis and design is done using Lyapunov\u27s direct method