Numerical optimal control of the wave equation: Optimal boundary control of a string to rest in finite time

DOI10.1016/j.matcom.2008.02.014zbMath1162.65358OpenAlexW2134431133MaRDI QIDQ1010018

Matthias Gerdts, Günter Greif, Hans Josef Pesch

Publication date: 3 April 2009

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2008.02.014

zbMATH Keywords

optimal controlwave equationnumerical examplesfinite differenceshyperbolic equationdiscretization methodnonlinear programming problem

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Numerical methods based on nonlinear programming (49M37) Existence theories for optimal control problems involving partial differential equations (49J20) Discrete approximations in optimal control (49M25)

Related Items

Optimal control of longitudinal motion of an elastic rod using boundary forces, A Fast and Stable Preconditioned Iterative Method for Optimal Control Problem of Wave Equations, Optimal control in a bounded domain for wave propagating in the whole space: coupling through boundary integral equations, Substructure exploitation of a nonsmooth Newton method for large-scale optimal control problems with full discretization, A Preconditioned MINRES Method for Optimal Control of Wave Equations and its Asymptotic Spectral Distribution Theory, Crank–Nicolson finite difference schemes for parabolic optimal Dirichlet boundary control problems, A Parallel-In-Time Block-Circulant Preconditioner for Optimal Control of Wave Equations, A minimum effort optimal control problem for the wave equation, Modeling and optimizing the turn of a loaded elastic rod controlled by an electric drive, Two fast finite difference schemes for elliptic Dirichlet boundary control problems, Norm-minimal Neumann boundary control of the wave equation, Exponential Stabilization of the Wave Equation by Dirichlet Integral Feedback, Distributed feedback design for systems governed by the wave equation, Optimal feedback control for undamped wave equations by solving a HJB equation

Cites Work

• Modeling, analysis and control of dynamic elastic multi-link structures
• Domain decomposition of optimal control problems for dynamic networks of elastic strings
• Analytic solutions of \(L^{\infty}\) optimal control problems for the wave equation
• Solutions of \(L^p\)-norm-minimal control problems for the wave equation
• Wave propagation, observation and control in 1-\(d\) flexible multi-structures.
• Optimal boundary control of a string to rest in finite time with continuous state
• A Sensitivity and Adjoint Calculus for Discontinuous Solutions of Hyperbolic Conservation Laws with Source Terms
• Dynamic Domain Decomposition in Approximate and Exact Boundary Control in Problems of Transmission for Wave Equations
• L^p-Optimal Boundary Control for the Wave Equation
• Propagation, Observation, and Control of Waves Approximated by Finite Difference Methods
• Suboptimal control of a 2D molten carbonate fuel cell PDAE model
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item