Generalized pseudo-inverse based nested discrete-time LQ-control with indefinite cost

A generalized pseudo-inverse approach to discrete-time finite horizon linear quadratic control with final state constraint is considered. Necessary and sufficient conditions for existence of a unique optimal solution are provided. Both the test for existence of a solution, as well as the computation of it, decompose, via a nesting procedure, into problems of successively smaller size, thus rendering computational feasibility for problems too large to be handled directly.