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

TL;DR

This paper introduces a dual pair of optimization-based methods for estimation and control in discrete-time linear systems, extending to nonlinear cases with stability conditions.

Contribution

It presents a novel dual formulation linking finite-horizon estimation and control, including nonlinear extensions with stability guarantees.

Findings

Derived a finite-horizon optimal estimator as a dual to minimum energy control

Extended the dual pair to nonlinear systems with stability conditions

Provided conditions for stability and convergence of the nonlinear extensions

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.