Minimum energy control and ARMA splines

This paper considers the problem of exact minimum energy control of linear systems with linear functional constraints on the output. An explicit correspondence is established between constrained minimum energy control and interpolation with ARMA (autoregressive-moving average) splines, and then used to obtain a formula for the optimal control. The control-spline correspondence is an input-output duality: if the system is driven by the optimal control, the output will be the appropriate spline.