LQ-optimal boundary control of infinite-dimensional linear systems

Student thesis: Doc typesDoctor of Sciences


A class of boundary control systems with boundary observation is considered, for which the unbounded operators often lead to technical difficulties. An extended model is described and analyzed, which involves no unbounded operator except for the dynamics generator. It is shown that, under suitable conditions, the model is well-posed and, in particular, that the dynamics operator is the generator of a C0-semigroup. Moreover, the model is shown to be observable and to carry controllability, stabilizability and detectability properties from the nominal system. A method for the resolution of the LQ-optimal control problem for this model is described and the solution provides a stabilizing feedback for the nominal system. This methodology is based on the problem of spectral factorization of a multi-dimensional operator-valued spectral density. It is applied to parabolic and hyperbolic partial differential equations (PDE) systems modeling convection-diffusion-reaction phenomena and a Poiseuille flow, respectively. This approach seems to lead to a good trade-off between the theoretical investment required by the modeling and the efficiency of methods of resolution of control problems for such systems.
Date of Award8 Oct 2015
Original languageEnglish
Awarding Institution
  • University of Namur
SupervisorJoseph Winkin (Supervisor), Timoteo Carletti (Jury), ANNE-SOPHIE LIBERT (President), Denis Dochain (Jury) & Christophe Prieur (Jury)


  • Modeling
  • Boundary control
  • Boundary observation
  • Infinite-dimensional system
  • Distributed parameter system
  • LQ-optimal control

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