TY - GEN
T1 - Output feedback control of inhomogeneous parabolic PDEs with point actuation and point measurement using SOS and semi-separable kernels
AU - Gahlawat, Aditya
AU - Peet, Matthew
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/2/8
Y1 - 2015/2/8
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=84962010463&partnerID=8YFLogxK
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U2 - 10.1109/CDC.2015.7402377
DO - 10.1109/CDC.2015.7402377
M3 - Conference contribution
AN - SCOPUS:84962010463
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1217
EP - 1223
BT - 54rd IEEE Conference on Decision and Control,CDC 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 54th IEEE Conference on Decision and Control, CDC 2015
Y2 - 15 December 2015 through 18 December 2015
ER -