Lagrangian duality between constrained estimation and control

We show that the Lagrangian dual of a constrained linear estimation problem is a particular nonlinear optimal control problem. The result has an elegant symmetry, which is revealed when the constrained estimation problem is expressed as an equivalent nonlinear optimisalion problem. The results extend and enhance known connections between the linear quadratic regulator and linear quadratic state estimation problems. (c) 2005 Elsevier Ltd. All rights reserved.