Output feedback control of inhomogeneous parabolic PDEs with point actuation and point measurement using SOS and semi-separable kernels

Aditya Gahlawat, Matthew Peet

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

4 Citations (Scopus)

Abstract

In this paper we use Sum-of-Squares (SOS) and Semi-Definite Programming (SDP) to design output feedback controllers for a class of one-dimensional parabolic partial differential equations with point measurements and point actuation. Our approach is based on the use of SOS to search for positive quadratic Lyapunov functions, controllers and observers. These Lyapunov functions, controllers and observers are parameterized by linear operators which are defined by SOS polynomials. The main result of the paper is the development of an improved class of observer-based controllers and evidence which indicates that when the system is controllable and observable, these methods will find a observer-based controller for sufficiently high polynomial degree (similar to well-known results from backstepping).

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1217-1223
Number of pages7
Volume2016-February
ISBN (Print)9781479978861
DOIs
StatePublished - Feb 8 2016
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Other

Other54th IEEE Conference on Decision and Control, CDC 2015
CountryJapan
CityOsaka
Period12/15/1512/18/15

Fingerprint

Parabolic PDEs
Output Feedback Control
Sum of squares
Feedback control
Observer
kernel
Controller
Controllers
Lyapunov functions
Lyapunov Function
Polynomials
Polynomial
Backstepping
Semidefinite Programming
Parabolic Partial Differential Equations
Output Feedback
Quadratic Function
Partial differential equations
Linear Operator
Mathematical operators

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Gahlawat, A., & Peet, M. (2016). Output feedback control of inhomogeneous parabolic PDEs with point actuation and point measurement using SOS and semi-separable kernels. In Proceedings of the IEEE Conference on Decision and Control (Vol. 2016-February, pp. 1217-1223). [7402377] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7402377

Output feedback control of inhomogeneous parabolic PDEs with point actuation and point measurement using SOS and semi-separable kernels. / Gahlawat, Aditya; Peet, Matthew.

Proceedings of the IEEE Conference on Decision and Control. Vol. 2016-February Institute of Electrical and Electronics Engineers Inc., 2016. p. 1217-1223 7402377.

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

Gahlawat, A & Peet, M 2016, Output feedback control of inhomogeneous parabolic PDEs with point actuation and point measurement using SOS and semi-separable kernels. in Proceedings of the IEEE Conference on Decision and Control. vol. 2016-February, 7402377, Institute of Electrical and Electronics Engineers Inc., pp. 1217-1223, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 12/15/15. https://doi.org/10.1109/CDC.2015.7402377
Gahlawat A, Peet M. Output feedback control of inhomogeneous parabolic PDEs with point actuation and point measurement using SOS and semi-separable kernels. In Proceedings of the IEEE Conference on Decision and Control. Vol. 2016-February. Institute of Electrical and Electronics Engineers Inc. 2016. p. 1217-1223. 7402377 https://doi.org/10.1109/CDC.2015.7402377
Gahlawat, Aditya ; Peet, Matthew. / Output feedback control of inhomogeneous parabolic PDEs with point actuation and point measurement using SOS and semi-separable kernels. Proceedings of the IEEE Conference on Decision and Control. Vol. 2016-February Institute of Electrical and Electronics Engineers Inc., 2016. pp. 1217-1223
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