Finite-time Attractive Ellipsoid Method Using Implicit Lyapunov Functions

Manuel Mera 1 Andrey Polyakov 1, 2 Wilfrid Perruquetti 1, 2, 3 Gang Zheng 1, 2
1 NON-A - Non-Asymptotic estimation for online systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
3 Ecole Centrale de Lille
Abstract : A finite-time version, based on Implicit Lyapunov Functions (ILF), for the Attractive Ellipsoid Method (AEM) is developed. Based on this, a robust control scheme is presented to ensure finite-time convergence of the solutions of a chain of integrators with bounded output perturbations to a minimal ellipsoidal set. The control parameters are obtained by solving a minimization problem of the " size " of the ellipsoid subject to a set of Linear Matrix Inequalities (LMI's) constraints, and by applying the implicit function theorem. A numerical example is presented to support the implementability of these theoretical results.
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Manuel Mera, Andrey Polyakov, Wilfrid Perruquetti, Gang Zheng. Finite-time Attractive Ellipsoid Method Using Implicit Lyapunov Functions. 54th conference on Decision and Control, IEEE, Dec 2015, Osaka, Japan. ⟨hal-01212602⟩

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