Receding horizon control for the stabilization of the wave equation
type: Item
instance of: scholarly article
title: Receding horizon control for the stabilization of the wave equation
zbMATH Open document ID: 1380.49053
author: Behzad Azmi
author: Karl Kunisch
published in: Discrete and Continuous Dynamical Systems
publication date: 2017-11-14T00:00:00Z
review text: For stabilizing the wave equation, the equation is inserted into an optimal feedback control problem with an infinite horizon, a quadratic objective function, some boundary conditions and having a control input \(u=u(t)\), \(0 \leq t \leq + \infty\), acting with a control input operator \(B\) on the right hand side of the wave equation \(\ddot y - \Delta y = Bu\) (distributed control) or acting on parts of the boundary of the problem (Dirichlet, Neumann control, resp.). The given problems can be converted then into first order linear-quadratic control problems in a certain Hilbert space. An approximate optimal feedback control is constructed by the open-loop feedback control method which is also used in model predictive control/receding horizon control: Measuring the state \(z(t)\) of the problem at certain sampling time points \(t_k = \Delta k\), \(k=0,1,\dots\), optimal open-loop controls are determined at each finite time interval \([t_k,t_k + T]\) with a given time horizon \(T\). Sufficient conditions are provided for the suboptimality and exponential stability of the proposed approximate optimal feedback control procedure. Moreover, numerical simulations are given.
reviewed by: Kurt Marti
Mathematics Subject Classification ID: 49N35
Mathematics Subject Classification ID: 49N10
Mathematics Subject Classification ID: 93B07
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 93C20
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 49M25
zbMATH DE Number: 6806955
zbMATH Keywords: receding horizon control
zbMATH Keywords: model predictive control
zbMATH Keywords: asymptotic stability
zbMATH Keywords: observability
zbMATH Keywords: optimal control
zbMATH Keywords: infinite-dimensional systems
MaRDI profile type: Publication
full work available at URL: dcds.2018021
OpenAlex ID: W2766867245
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DOI: 10.3934/DCDS.2018021
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