A dual pair of optimization-based formulations for estimation and control

Abstract

A finite-horizon optimal estimation problem for discrete-time linear systems is formulated and solved. The formulation is a natural extension of that which yields a deadbeat observer. The resultant observer is the dual of the controller produced by the finite-horizon minimum energy control problem with terminal equality constraint. Nonlinear extensions of this dual pair are also considered and sufficient conditions are provided for stability and convergence.