On L2 sufficient conditions for end-constrained optimal control problems with inputs in a polyhedron

An L²-local optimality sufficiency theorem proved for constrained optimal control problems is described here. This theorem applies to a class of structured infinite-dimensional nonconvex programs with constraints of the form, u∈Ω and h(u)=0, where Ω is a set of Lebesgue measurable essentially bounded vector-valued functions u(·):[0, 1]→R^m with range in a polyhedron U, and h is a smooth map of the space of essentially bounded functions u(·) into R^k. The theorem is based on formal counterparts of the finite-dimensional Karush-Kuhn-Tucker sufficient conditions in a Cartesian product of polyhedra, a strengthened variant of Pontryagin´s necessary condition, and structure/continuity conditions on the first and second differentials of the objective function and equality constraint functions. Its sufficient conditions are directly applicable to nonconvex continuous-time Bolza optimal control problems with control-quadratic Hamiltonians, affine inequality constraints on the control inputs, and equality constraints on the terminal state vector, or equivalent isoperimetric constraints