Sensor and actuator placement for large-scale systems: A projection-based formulation

The problem of sensor and actuator placement aims at achieving near-optimal control performance with only a small number of sensors or actuators. In this paper we present a new formulation and design for the problem of sensor and actuator placement as a structural-constrained mathcal{H}{2} optimization. The structural constraint is defined by two projections which indicate the placement of sensors and actuators respectively. The advantage of this formulation is that the associated structural constraint always satisfies quadratic invariance condition, and allows convex reformulation for the constrained mathcal{H}{2} optimization in model matching form. We provide an optimality gap between the constrained mathcal{H}{2} problem with selected sensors and actuators and the unconstrained mathcal{H}{2} problem with full feedback, and subsequently propose the minimization problem to tighten the gap. The overall computational complexity for our proposed design is shown to be mathcal{O}(n-{3}), which can be very scalable for large-scale applications. We illustrate our design with simulations of a IEEE prototype power system model