A convex optimization approach to robust iterative learning control for linear systems with time-varying parametric uncertainties

Hoa Dinh Nguyen, David Banjerdpongchai

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

In this paper, we present a new robust iterative learning control (ILC) design for a class of linear systems in the presence of time-varying parametric uncertainties and additive input/output disturbances. The system model is described by the Markov matrix as an affine function of parametric uncertainties. The robust ILC design is formulated as a minmax problem using a quadratic performance criterion subject to constraints of the control input update. Then, we propose a novel methodology to find a suboptimal solution of the minmax optimization problem. First, we derive an upper bound of the worst-case performance. As a result, the minmax problem is relaxed to become a minimization problem in the form of a quadratic program. Next, the robust ILC design is cast into a convex optimization over linear matrix inequalities (LMIs) which can be easily solved using off-the-shelf optimization solvers. The convergences of the control input and the error are proved. Finally, the robust ILC algorithm is applied to a physical model of a flexible link. The simulation results reveal the effectiveness of the proposed algorithm.

Original languageEnglish
Pages (from-to)2039-2043
Number of pages5
JournalAutomatica
Volume47
Issue number9
DOIs
Publication statusPublished - Sep 1 2011
Externally publishedYes

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Convex optimization
Linear systems
Linear matrix inequalities
Uncertainty

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this

A convex optimization approach to robust iterative learning control for linear systems with time-varying parametric uncertainties. / Nguyen, Hoa Dinh; Banjerdpongchai, David.

In: Automatica, Vol. 47, No. 9, 01.09.2011, p. 2039-2043.

Research output: Contribution to journalArticle

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