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

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. Because of their nature being able to transport discontinuities of initial or boundary conditions into the domain on which the solution lives or even to develop discontinuities in the presence of smooth data, these problems 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 while analytical solutions are known here. 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 proble...

• Type: Journal
• Year: 2008
• Where: MCS
• Authors: Matthias Gerdts, Günter Greif, Hans Josef Pesch
• Keywords: Hyperbolic Equations, MCS 2008, Optimal Control, Optimal Control Problem, Pattern Recognition