Multitime optimal control with second order PDEs constraints
In this paper we study a simplified version of multitime optimal control problem for linear second-order partial differential equations (PDE). The multitime multiple integral functional is of Lagrange type. Necessary optimality conditions of multitime maximum principle type are derived. The multitime optimal control with second-order PDE constraints can be analyzed in three ways: as problems governed by (i) explicit m-flows, (ii) implicit m-flows, and (iii) second-order PDEs. All directions lead to variants of multitime maximum principle. The theoretical results are confirmed by solving two significant problems.
multitime PDE constrained optimization, multitime optimal control problems, multitime optimal principle, duality