Optimal state feedback boundary control of parabolic PDEs using SOS polynomials

Aditya Gahlawat, Matthew Peet

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

2 Citations (Scopus)

Abstract

We synthesize L(L2)-optimal full-state feedback controllers for a one dimensional linear PDE with point actuation and distributed disturbances. We use Sum-of-Squares (SOS) polynomials and Semi-Definite Programming (SDP) to parametrize positive operators which define quadratic Lyapunov functions and the controller gains. Additionally, we calculate the upper bound on the system state ensured by the calculated controllers. Moreover, we provide numerical results, but not proofs, for PDEs with additional types of boundary conditions.

Original languageEnglish (US)
Title of host publication2016 American Control Conference, ACC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4350-4355
Number of pages6
Volume2016-July
ISBN (Electronic)9781467386821
DOIs
StatePublished - Jul 28 2016
Event2016 American Control Conference, ACC 2016 - Boston, United States
Duration: Jul 6 2016Jul 8 2016

Other

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

Fingerprint

State feedback
Polynomials
Controllers
Lyapunov functions
Mathematical operators
Boundary conditions

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Gahlawat, A., & Peet, M. (2016). Optimal state feedback boundary control of parabolic PDEs using SOS polynomials. In 2016 American Control Conference, ACC 2016 (Vol. 2016-July, pp. 4350-4355). [7525606] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7525606

Optimal state feedback boundary control of parabolic PDEs using SOS polynomials. / Gahlawat, Aditya; Peet, Matthew.

2016 American Control Conference, ACC 2016. Vol. 2016-July Institute of Electrical and Electronics Engineers Inc., 2016. p. 4350-4355 7525606.

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

Gahlawat, A & Peet, M 2016, Optimal state feedback boundary control of parabolic PDEs using SOS polynomials. in 2016 American Control Conference, ACC 2016. vol. 2016-July, 7525606, Institute of Electrical and Electronics Engineers Inc., pp. 4350-4355, 2016 American Control Conference, ACC 2016, Boston, United States, 7/6/16. https://doi.org/10.1109/ACC.2016.7525606
Gahlawat A, Peet M. Optimal state feedback boundary control of parabolic PDEs using SOS polynomials. In 2016 American Control Conference, ACC 2016. Vol. 2016-July. Institute of Electrical and Electronics Engineers Inc. 2016. p. 4350-4355. 7525606 https://doi.org/10.1109/ACC.2016.7525606
Gahlawat, Aditya ; Peet, Matthew. / Optimal state feedback boundary control of parabolic PDEs using SOS polynomials. 2016 American Control Conference, ACC 2016. Vol. 2016-July Institute of Electrical and Electronics Engineers Inc., 2016. pp. 4350-4355
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