Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs

This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analy...

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Bibliographic Details
Published in:International journal of control 2017-10, Vol.90 (10), p.2152-2164
Main Authors: Aksikas, I., Moghadam, A. Alizadeh, Forbes, J. F.
Format: Article
Language:English
Subjects:
Catalysis
Computer simulation
Eigenvalues
eigenvalues problem
Eigenvectors
hyperbolic PDEs
linear-quadratic control
Mathematical models
operator Riccati equation
Optimal control
parabolic PDEs
Partial differential equations
Riccati equation
Uniqueness
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Summary:This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. 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 nonlinear model. Numerical simulations are performed to show the controller performances.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2016.1237046