Observer-based backstepping control for a class of non-affine systems

In this paper, a control approach is developed for a class of non-affine systems with immeasurable states. A state observer is designed to estimate the immeasurable states. By the combination of back-stepping control method and time scale separation, the virtual/actual control inputs are derived from the solutions of a series of fast dynamical equations. This strategy avoids the drawback of “explosion of complexity’’ inherently existing in the conventional backstepping design. Tikhonov’s theorem on singular perturbation theory can be employed for the stability analysis. It is shown that the proposed control approach can guarantee that the observer and tracking errors converge to a small neighborhood of the origin. Simulation results are presented to show the effectiveness of the approach.