Kybernetika 53 no. 2, 296-330, 2017

Improving the performance of semiglobal output controllers for nonlinear systems

Abdallah Benabdallah and Walid HdidiDOI: 10.14736/kyb-2017-2-0296

Abstract:

For a large class of nonlinear control systems, the main drawback of a semiglobal stabilizing output feedback controllers $(\mathcal{U}_R)_{R>0}$ with increasing regions of attraction $(\Omega_R)_{R>0}$ is that, when the region of attraction $\Omega_R$ is large, the convergence of solutions of the closed-loop system to the origin becomes slow. To improve the performance of a semiglobal controller, we look for a new feedback control law that preserves the semiglobal stability of the nonlinear system under consideration and that is equal to some ``fast" controller $\mathcal{U}_{R_0}$ on a neighborhood of the origin. Under an input-output-to-state stability (IOSS) assumption, we propose a new semiglobal stabilizing hybrid feedback controller that unifies a ``slow" controller that has a large region of attraction with a ``fast" controller having a small region of attraction. This unification is inspired from the elegant hybrid unification of a local controller with a global one given in \cite{Pri11}. Moreover, this unification is different from the recent result \cite{Pri13}, since in the cited paper the objective is just the stabilization; whereas in our study, the objective is the stabilization with \textit{high performance}. Finally, we illustrate our main result by means of two numerical examples.

Keywords:

nonlinear system, hybrid output feedback, semiglobal output stabilization, local performance

Classification:

93C10, 93D15

paper.pdf

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