Guaranteed ℓ2 to ℓ control for discrete-time polytopic LPV systems

Andrew White, Guoming Zhu, Jongeun Choi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 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 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 a 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 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
Title of host publication2013 American Control Conference, ACC 2013
Pages6066-6071
Number of pages6
Publication statusPublished - 2013
Event2013 1st American Control Conference, ACC 2013 - Washington, DC, United States
Duration: 2013 Jun 172013 Jun 19

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2013 1st American Control Conference, ACC 2013
CountryUnited States
CityWashington, DC
Period13/6/1713/6/19

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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  • Cite this

    White, A., Zhu, G., & Choi, J. (2013). Guaranteed ℓ2 to ℓ control for discrete-time polytopic LPV systems. In 2013 American Control Conference, ACC 2013 (pp. 6066-6071). [6580789] (Proceedings of the American Control Conference).