State constrained controller design for uncertain linear systems using polynomial Chaos

Souransu Nandi, Victor Migeon, Tarunraj Singh, Puneet Singla

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

3 Citations (Scopus)

Abstract

The focus of this paper is on the design of state constrained controllers which are robust to time invariant uncertain variables. Polynomial Chaos spectral expansion is used to parameterize the uncertain variables, which permits evaluation of the evolution of the uncertain states. The co-efficients of the truncated polynomial chaos expansion are determined using the Galerkin projection resulting in a set of deterministic equations. A mapping into Bernstein polynomial space permits determination of bounds on the evolving states. Linear programming is used on the deterministic set of equation with constraints as the predetermined bounds to determine controllers which are robust to the epistemic uncertainties. Numerical examples are used to illustrate the benefit of the proposed technique for the design of rest-to-rest controllers subject to deformation constraints; which are robust to uncertainties in the stiffness coefficient for the benchmark spring-mass system.

Original languageEnglish (US)
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2005-2010
Number of pages6
ISBN (Electronic)9781467386821
DOIs
StatePublished - Jul 28 2016
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Publication series

NameProceedings of the American Control Conference
Volume2016-July
ISSN (Print)0743-1619

Other

Other2016 American Control Conference, ACC 2016
CountryUnited States
CityBoston
Period7/6/167/8/16

Fingerprint

Chaos theory
Linear systems
Polynomials
Controllers
Linear programming
Stiffness
Uncertainty

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Nandi, S., Migeon, V., Singh, T., & Singla, P. (2016). State constrained controller design for uncertain linear systems using polynomial Chaos. In 2016 American Control Conference, ACC 2016 (pp. 2005-2010). [7525213] (Proceedings of the American Control Conference; Vol. 2016-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7525213
Nandi, Souransu ; Migeon, Victor ; Singh, Tarunraj ; Singla, Puneet. / State constrained controller design for uncertain linear systems using polynomial Chaos. 2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 2005-2010 (Proceedings of the American Control Conference).
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Nandi, S, Migeon, V, Singh, T & Singla, P 2016, State constrained controller design for uncertain linear systems using polynomial Chaos. in 2016 American Control Conference, ACC 2016., 7525213, Proceedings of the American Control Conference, vol. 2016-July, Institute of Electrical and Electronics Engineers Inc., pp. 2005-2010, 2016 American Control Conference, ACC 2016, Boston, United States, 7/6/16. https://doi.org/10.1109/ACC.2016.7525213

State constrained controller design for uncertain linear systems using polynomial Chaos. / Nandi, Souransu; Migeon, Victor; Singh, Tarunraj; Singla, Puneet.

2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 2005-2010 7525213 (Proceedings of the American Control Conference; Vol. 2016-July).

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

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Nandi S, Migeon V, Singh T, Singla P. State constrained controller design for uncertain linear systems using polynomial Chaos. In 2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc. 2016. p. 2005-2010. 7525213. (Proceedings of the American Control Conference). https://doi.org/10.1109/ACC.2016.7525213