Optimal control of coupled parabolic–hyperbolic non-autonomous PDEs: infinite-dimensional state-space approach

I. Aksikas, A. Alizadeh Moghadam and J. F. Forbes

International Journal of Systems Science, 2018, vol. 49, issue 5, 897-907

Abstract: This paper deals with the design of an optimal state-feedback linear-quadratic (LQ) controller for a system of coupled parabolic–hypebolic non-autonomous partial differential equations (PDEs). The infinite-dimensional state space representation and the corresponding operator Riccati differential equation are used to solve the control problem. Dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the LQ-optimal control problem and also to guarantee the exponential stability of the closed-loop system. Thanks to the eigenvalues and eigenfunctions of the parabolic operator and also the fact that the hyperbolic-associated operator Riccati differential equation can be converted to a scalar Riccati PDE, an algorithm to solve the LQ control problem has been presented. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ optimal controller designed in the early portion of the paper is implemented for the original non-linear model. Numerical simulations are performed to show the controller performances.

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/00207721.2018.1440027 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:tsysxx:v:49:y:2018:i:5:p:897-907

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/TSYS20

DOI: 10.1080/00207721.2018.1440027

Access Statistics for this article

International Journal of Systems Science is currently edited by Visakan Kadirkamanathan

More articles in International Journal of Systems Science from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().