Covariance-based hardware selection-Part II: equivalence results for the sensor, actuator, and simultaneous selection problems

Recently, a number of covariance-constrained hardware selection problems have been proposed. However, underlying each is the choice of a compensating element (i.e., the state estimator for the sensor case, the feedback controller for the actuator case, and both for the simultaneous case). The subtlety is whether these compensators should be optimal or suboptimal. In this paper, we present formulations using both types of compensators and then prove that the global solution for each type of formulation is independent of the compensator assumption. However, in spite of this equivalence of solutions, the computational perspective indicates that one choice will always have an advantage. While the computational difference is minor in the sensor selection case, significant advantages can be found in the suboptimal controller version of the actuator selection problem. In particular, the suboptimal version can be used to find global solutions to the previously intractable optimal controller formulation. In the simultaneous case, similar results are presented and lead to the first global solution scheme for the covariance-based simultaneous sensor and actuator selection problem.