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. Nonlinear robust control is designed to identify on-line unknown control directions and to guarantee global stability of uniform ultimate boundedness without the knowledge of nonlinear dynamics except their size bounding functions. It is also shown that the proposed robust control can be made continuous through utilizing the so-called shifting laws that change smoothly and accordingly the signs of robust controls and that, no matter what time constants and gains of the shifting laws are, global stability is always ensured. The analysis and design is done using Lyapunov´s direct method