A Posteriori Error Estimates in Time-Domain Decomposition of Final Value Optimal Control of the Acoustic Wave Equation

Abstract. We consider a boundary optimal control problem for the acoustic wave equation with a final value cost criterion. A time-domain decomposition procedure for the corresponding optimality system is introduced, which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. The process is inherently parallel and is suitable for real-time control applications. Convergence of the local solutions and controls to the global ones was established in an earlier publication. In this paper, a posteriori error estimates of the difference between the local solutions and the global one are obtained in terms of the mismatch of the n th iterates, or of successive iterates, across the time-domain break points.