Abstract
Stabilization of the wave equation by the receding horizon framework is investigated. Distributed control, Dirichlet boundary control, and Neumann boundary control are considered. Moreover for each of these control actions, the well-posedness of the control system and the exponential stability of Receding Horizon Control (RHC) with respect to a proper functional analytic setting are investigated. Observability conditions are necessary to show the suboptimality and exponential stability of RHC. Numerical experiments are given to illustrate the theoretical results.
Highlights
In this work we deal with the stabilization of the wave equation within the scope of Receding Horizon Control (RHC)
We investigate the suboptimality and exponential stability of RHC for all the cases 1-3 of the wave equation with respect to an appropriate functional analytic setting
To the previous chapters, in this subsection we investigate well-posedness and the firstorder optimality conditions for the following optimal control problem min JT (u; (y01, y02)) | (y, u) satisfies (64), u ∈ L2(0, T ), (OPneu) where the performance index function JT is given by JT (u; (y01, y02)) :=
Summary
In this work we deal with the stabilization of the wave equation within the scope of Receding Horizon Control (RHC). The stabilization problem for the wave equation has been studied extensively by many authors, see for instance [2, 23, 26, 34, 38, 47, 50] and the references cited therein. To study the open-loop optimal control problems for the wave equation, numerically and analytically, we refer to [14, 24, 25, 32, 33, 45, 46]. Over all control functions u ∈ L2(0, ∞; U) with an appropriate control space U and subject to the following cases: 1.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
