A spline-theoretic approach to minimum-energy control

The problem of minimum-energy control of linear systems with linear functional constraints on the output is considered from a spline-theoretic viewpoint. It is shown that constrained minimum-energy control and spline interpolation are dual projection problems: if the given system is driven by the minimum-energy control, the system output will be the spline that interpolates the output constraints. This duality result is used to obtain a simple formula for the exact optimal control under very general constraints.