Duality of Linear Discrete Time Systems with Constraints

This correspondence considers the duality of linear estimation and control with constraints for discrete time systems. By using Bellman´s principle of optimality, two important problems in estimation-namely, constrained energy and multiplicative noise¿are shown to be duals of linear regulator problems with constraints on the control and states, respectively, with boundary conditions specified at opposite ends of the extremals in time. Algorithms are presented to establish the duality concept.