An ADMM algorithm for optimal sensor and actuator selection

We consider the problem of the optimal selection of a subset of available sensors or actuators in large-scale dynamical systems. By replacing a combinatorial penalty on the number of sensors or actuators with a convex sparsity-promoting term, we cast this problem as a semidefinite program. The solution of the resulting convex optimization problem is used to select sensors (actuators) in order to gracefully degrade performance relative to the optimal Kalman filter (Linear Quadratic Regulator) that uses all available sensing (actuating) capabilities. We employ the alternating direction method of multipliers to develop a customized algorithm that is well-suited for large-scale problems. Our algorithm scales better than standard SDP solvers with respect to both the state dimension and the number of available sensors or actuators.