A pseudo-inverting nested indefinite quadratic control for time-varying systems

A generalized pseudo-inverse based approach to discrete-time, finite horizon, linear quadratic control of time-varying systems is presented. The cost functional is a general sign-indefinite quadratic form, and the final state is constrained. Necessary and sufficient conditions for existence of a unique optimal solution are provided. Both the test for existence of a solution, as well its computation, decompose hierarchically to small size problems defined on a suitable subdivision of the time axis, thus rendering computational feasibility for problems too large to be handled directly.