Symmetry between constrained reference tracking and constrained state estimation

This paper exposes a symmetry relationship between constrained output reference tracking and constrained state estimation problems. The symmetry, which is different from the traditional duality relationship between control and estimation, is provided by means of two tables that give a complete translation of all variables of one problem into the variables of the other. An example is provided to illustrate the behaviour of the optimal solutions to the reference tracking and state estimation problems. The symmetry relationship leads to interesting interpretations of several of the resulting trajectories