Design and analysis of nonlinear control for uncertain linear systems

By using the input-output information, the problem of robust output tracking control is addressed for linear dynamical systems with arbitrary relative degrees. The considered systems are confined to minimum phase systems with unknown parameters, and unmatched disturbances composed of a bounded part and a class of unmodeled dynamics. The a priori knowledge concerning the disturbance bounds is unknown. The development of the nonlinear robust controller involves three steps. First, a special signal is generated, which can be thought of as an estimate of a filter of the input signal. Second, the derivatives up to a certain order of this special signal are derived. Third, the output tracking control input is synthesized by using the derivatives of the special signal. In the above process, the upper bounds of the disturbances are adaptively updated on-line. The proposed control law ensures the uniform boundedness of all the signals in the closed-loop system and achieves the output tracking to within a desired precision. The effectiveness of the proposed method is demonstrated through simulation.