Title: Sensing-Constrained LQG Control,
Abstract: Linear-Quadratic-Gaussian (LQG) control is concerned with the design of an
optimal controller and estimator for linear Gaussian systems with imperfect
state information. Standard LQG assumes the set of sensor measurements, to be
fed to the estimator, to be given. However, in many problems, arising in
networked systems and robotics, one may not be able to use all the available
sensors, due to power or payload constraints, or may be interested in using the
smallest subset of sensors that guarantees the attainment of a desired control
goal. In this paper, we introduce the sensing-constrained LQG control problem,
in which one has to jointly design sensing, estimation, and control, under
given constraints on the resources spent for sensing. We focus on the realistic
case in which the sensing strategy has to be selected among a finite set of
possible sensing modalities. While the computation of the optimal sensing
strategy is intractable, we present the first scalable algorithm that computes
a near-optimal sensing strategy with provable sub-optimality guarantees. To
this end, we show that a separation principle holds, which allows the design of
sensing, estimation, and control policies in isolation. We conclude the paper
by discussing two applications of sensing-constrained LQG control, namely,
sensing-constrained formation control and resource-constrained robot
navigation.