LQ (optimal) control of hyperbolic PDAEs |
| |
| Authors: | Amir Alizadeh Moghadam Ilyasse Aksikas Stevan Dubljevic J Fraser Forbes |
| |
| Affiliation: | 1. Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canadaalizadeh@ualberta.ca;3. Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar;4. Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada |
| |
| Abstract: | The linear quadratic control synthesis for a set of coupled first-order hyperbolic partial differential and algebraic equations is presented by using the infinite-dimensional Hilbert state-space representation of the system and the well-known operator Riccati equation (ORE) method. Solving the algebraic equations and substituting them into the partial differential equations (PDEs) results in a model consisting of a set of pure hyperbolic PDEs. The resulting PDE system involves a hyperbolic operator in which the velocity matrix is spatially varying, non-symmetric, and its eigenvalues are not necessarily negative through of the domain. The C0-semigroup generation property of such an operator is proven and it is shown that the generated C0-semigroup is exponentially stable and, consequently, the ORE has a unique and non-negative solution. Conversion of the ORE into a matrix Riccati differential equation allows the use of a numerical scheme to solve the control problem. |
| |
| Keywords: | infinite-dimensional system LQ control hyperbolic PDE coupled PDE-algebraic system operator Riccati equation |
|
|
