Optimal LPV control with hard constraints

Andrew White, Guoming Zhu, Jongeun Choi

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

This paper considers the optimal control of polytopic, discrete-time linear parameter varying (LPV) systems with a guaranteed ℓ2 to ℓ gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, H performance criterion is also considered as well. Controllers with a guaranteed ℓ2 to ℓ gain and a guaranteed H performance (ℓ2 to ℓ2 gain) are a special family of mixed H2=H controllers. Normally, H2 controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain an optimal controller with a guaranteed ℓ2 to ℓ gain (closely related to the physical performance constraint), the cost function used in the H2 control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with linear matrix inequality (LMI) constraints. The main contribution of this paper is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed ℓ2 to ℓ gain and >H performance. A numerical example is presented to demonstrate the effectiveness of the convex optimization.

Original languageEnglish
Pages (from-to)148-162
Number of pages15
JournalInternational Journal of Control, Automation and Systems
Volume14
Issue number1
DOIs
Publication statusPublished - 2016 Feb 1

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Controllers
Convex optimization
Cost functions
Linear matrix inequalities
Closed loop systems

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications

Cite this

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Optimal LPV control with hard constraints. / White, Andrew; Zhu, Guoming; Choi, Jongeun.

In: International Journal of Control, Automation and Systems, Vol. 14, No. 1, 01.02.2016, p. 148-162.

Research output: Contribution to journalArticle

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