Non-recursive indefinite least squares approach to linear quadratic control for time-varying systems

An indefinite least squares 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 initial and final states are constrained to lie in affine subspaces. The output map contains a translation term, thereby enabling inclusion of linear cost terms. By hierarchical decomposition into similar small size problems defined on a suitable subdivision of the time axis, computational feasibility is provided for problems too large to be handled directly. Complete necessary and sufficient conditions for existence of a unique optimal solution are provided in terms of these smaller size problems.