Optimal Sensor and Actuator Selection using Balanced Model Reduction
For control engineers dealing with high-dimensional systems, this work provides a tractable method for sensor/actuator placement that was previously computationally infeasible.
The paper addresses optimal sensor and actuator selection in high-dimensional systems by using balanced model reduction and greedy optimization, achieving linear runtime scaling with state dimension and approximating known optimal placements on the Ginzburg-Landau system.
Optimal sensor and actuator selection is a central challenge in high-dimensional estimation and control. Nearly all subsequent control decisions are affected by these sensor/actuator locations, and optimal placement amounts to an intractable brute-force search among the combinatorial possibilities. In this work, we exploit balanced model reduction and greedy optimization to efficiently determine sensor and actuator selections that optimize observability and controllability. In particular, we determine locations that optimize scalar measures of observability and controllability via greedy matrix QR pivoting on the dominant modes of the direct and adjoint balancing transformations. Pivoting runtime scales linearly with the state dimension, making this method tractable for high-dimensional systems. The results are demonstrated on the linearized Ginzburg-Landau system, for which our algorithm approximates known optimal placements computed using costly gradient descent methods.