Finite difference schemes and partial differential equations
Finite difference schemes and partial differential equations
SIAM Journal on Control and Optimization
Domain Decomposition of Optimal Control Problems for Dynamic Networks of Elastic Strings
Computational Optimization and Applications
Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures
Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures
Optimal Control of Distributed Parameter Systems
Optimal Control of Distributed Parameter Systems
SIAM Journal on Control and Optimization
Lp-Optimal Boundary Control for the Wave Equation
SIAM Journal on Control and Optimization
Penalty Techniques for State Constrained Optimal Control Problems with the Wave Equation
SIAM Journal on Control and Optimization
Semismooth Newton Methods for Optimal Control of the Wave Equation with Control Constraints
SIAM Journal on Control and Optimization
A minimum effort optimal control problem for the wave equation
Computational Optimization and Applications
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In many real-life applications of optimal control problems with constraints in form of partial differential equations (PDEs), hyperbolic equations are involved which typically describe transport processes. Since hyperbolic equations usually propagate discontinuities of initial or boundary conditions into the domain on which the solution lives or can develop discontinuities even in the presence of smooth data, problems of this type constitute a severe challenge for both theory and numerics of PDE constrained optimization. In the present paper, optimal control problems for the well-known wave equation are investigated. The intention is to study the order of the numerical approximations for both the optimal state and the optimal control variables for problems with known analytical solutions. The numerical method chosen here is a full discretization method based on appropriate finite differences by which the PDE constrained optimal control problem is transformed into a nonlinear programming problem (NLP). Hence, we follow here the approach 'first discretize, then optimize', which allows us to make use not only of powerful methods for the solution of NLPs, but also to compute sensitivity differentials, a necessary tool for real-time control.