Robust tracking control design for a class of uncertain nonlinear systems

The problem of tracking control design for a class of uncertain nonlinear systems is considered in this paper. The design approach adopted in this paper is similar to the one used by Wang and Goodall (1996). The main contribution of the paper is that the bounding condition on ´residual´ uncertainty is modified so it is easier to verify than the condition given in Wang and Goodall (1996). The analysis shows that the controller developed in the paper is more robust if the function θ(t,e)>1. To encompass all possible realizations of uncertainty, differential inclusions are used to describe the class of uncertain systems in this paper. In particular, the uncertain systems are modelled as nonlinear perturbations to a known nominal nonlinear affine control system. The nonlinear tracking problem is reformulated to the problem of stabilizing nonlinear time-varying systems and then, a class of discontinuous feedback controls is developed such that the uncertain nonlinear system tracks desired trajectories to {0}.