LQG Control and Sensing Co-Design

We investigate a linear-quadratic-Gaussian (LQG) control and sensing codesign problem, where one jointly designs policies. focus on the realistic case design is selected among finite set of available sensors, each sensor associated with different cost (e.g., power consumption). consider two dual problem instances: sensing-constrained LQG control, maximizes performance subject to budget, minimum-sensing minimizes constraints. prove that no polynomial time algorithm guarantees across all instances constant approximation factor from optimal. Nonetheless, we present first algorithms per-instance suboptimality guarantees. To this end, leverage separation principle, which partially decouples control. Then, frame as optimization approximately supermodular functions; develop novel solve problems; original results establish connections between their control-theoretic quantities. conclude article by discussing applications, namely, formation resource-constrained robot navigation.