Singular Perturbation Theory in Output Feedback Control of Pure-Feedback Systems

this paper studies output feedback control of pure-feedback systems with immeasurable states and completely non-affine property. Since availability of all the states is usually impossible in the actual process, we assume that just the system output is measurable and the system states are not available. First, to estimate the immeasurable states a state observer is designed. Relatively fewer results have been proposed for purefeedback systems because the cascade and non-affine properties of pure-feedback systems make it difficult to find the explicit virtual controls and actual control. Therefore, by employing the singular perturbation theory in back-stepping control procedure, the virtual/actual control inputs are derived from the solutions of a series of fast dynamical equations which can avoid the “explosion of complexity’’ inherently existing in the conventional back-stepping design. The stability of the resulting closed-loop system is proved by Tikhonov’s theorem in the singular perturbation theory. Finally, the detailed simulation results are provided to demonstrate the effectiveness of the proposed controller, which can overcome the non-affine property of pure-feedback systems with lower complexity and fewer design parameters.