Greedy Sensor and Actuator Placement Using Balanced Model Reduction

Optimal sensor and actuator placement is one of the foremost challenges in the estimation and control of high-dimensional complex systems. For high-dimensional systems it is impractical to monitor or actuate every state, and the determination of a few optimal sensors and actuators amounts to a brute-force combinatorial search across all possible placements. In this work, we exploit balanced model reduction to efficiently determine sensor and actuator placements to maximize the observability and controllability of the reduced system. In particular, we choose sensors and actuators that maximize the volume of the associated observability and controllability ellipsoids in the balanced transform coordinates. The placements are then determined using a greedy matrix pivoting algorithm on the direct and adjoint balancing modes. The pivoting procedure scales linearly with the state dimension, making this method extremely tractable for high-dimensional systems. Our scalable sensor and actuator placement algorithm is demonstrated on the linearized Ginzburg-Landau system, resulting in the well-known optimal placements computed via gradient descent methods, at a fraction of the cost.