Gugat M., Zuazua E. Exact penalization of terminal constraints for optimal control problems
Optimal Control Applications and Methods, Volume 37, Issue 6, November/December 2016, Pages 1329–1354, DOI: 10.1002/oca.2238
Abstract: We study optimal control problems for linear systems with prescribed initial and terminal states. We analyze the exact penalization of the terminal constraints. We show that for systems that are exactly controllable, the norm-minimal exact control can be computed as the solution of an optimization problem without terminal constraint but with a nonsmooth penalization of the end conditions in the objective function, if the penalty parameter is sufficiently large. We describe the application of the method for hyperbolic and parabolic systems of partial differential equations, considering the wave and heat equations as particular examples.