ROBUST-CONTROL DESIGN FOR NONLINEAR UNCERTAIN SYSTEMS WITH AN UNKNOWNTIME-VARYING CONTROL DIRECTION

In this paper, a continuous robust control design approach is proposed for first-order nonlinear systems whose dynamics contain both nonline ar uncertainty and an unknown time-varying control direction, The so-c alled control direction is the multiplier of the control term in the d ynamic equation, and it effectively represents the direction of motion under any given control. A nonlinear robust control is designed to on -line and continuously identify sign changes of the unknown control di rection and to guarantee stability of uniform ultimate boundedness. Th e proposed robust control design requires only three conditions: the n ominal system is stable, the control direction is smooth, and the unce rtainty in the system is bounded by a known function. The necessity of these conditions is established in this paper. Continuity of the prop osed robust control is achieved by using a so-called shifting lan that changes smoothly the sign of robust control and tracks the change of the unknown control direction, Analysis and design is shown by using t he Lyapunov's direct method.