On the robust control design for a class of nonlinearly affine control systems: The attractive ellipsoid approach

Vadim Azhmyakov; Alex Poznyak; Omar Gonzalez

doi:10.3934/jimo.2013.9.579

Article Contents

2013, Volume 9, Issue 3: 579-593. Doi: 10.3934/jimo.2013.9.579

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On the robust control design for a class of nonlinearly affine control systems: The attractive ellipsoid approach

1.
Department of Control and Automation, CINVESTAV, Av, Instituto Politecnico Nacional 2508, Mexico D.F.

Received: September 2011

Revised: October 2012

Published: July 2013

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Abstract

This paper is devoted to a problem of robust control design for a class of continuous-time dynamic systems with bounded uncertainties. We study a family of nonlinearly affine control systems and develop a computational extension of the conventional invariant ellipsoid techniques. The obtained method can be considered as a powerful numerical approach that makes it possible to design a concrete stabilizing control strategies for the resulting closed-loop systems. The design procedure for this feedback-type control is based on the classic Lyapunov-type stability analysis of invariant sets for the given dynamic system. We study the necessary theoretic basis and propose a computational algorithm that guarantee some minimality properties of the stability/attractivity regions for dynamic systems under consideration. The complete solution procedure contains an auxiliary LMI-constrained optimization problem. The effectiveness of the proposed robust control design is illustrated by a numerical example.

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Mathematics Subject Classification: Primary: 93C10, 37N40; Secondary: 93C41.

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