Stable inversion for nonlinear systems
The paper presents a solution to the stable inversion problem for a perturbation of a pure-feedback system. The proposed procedure provides bounded controls and bounded state trajectories in response to bounded output signals. It requests the following two steps: (1) computation of the control and state trajectory when ignoring the error of the pure-feedback part of the system; (2) computation of the remaining control and states by finding a non-causal and stable solution to an error-driven dynamical system. The whole approach relies on deriving a direct link between the bounded solution of the partial differential equation formulated by \textit{A. Isidori} and \textit{C. I. Byrnes} [IEEE Trans. Autom. Control 35, 131-140 (1990; Zbl 0704.93034)] and the integral representation formula developed by \textit{S. Devasia}, \textit{D. Chen} and \textit{B. Paden} [IEEE Trans. Autom. Control 41, 930-942 (1996; Zbl 0859.93006)].
scientific article; zbMATH DE number 1081896
scientific article