Optimal Sensor and Actuator Selection Using Balanced Model Reduction

Krithika Manohar,Steven L Brunton,J Nathan Kutz

doi:10.1109/tac.2021.3082502

Abstract

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 and actuator locations. In this article, 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 using 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.

Highlights

Complex System TimeSpace5 0 -5 -10 -15 -20 ActuatorsOptimal Feedback Control SensorsBalanced Sensor/Actuator Selection Offline learningOptimizing the selection of sensors and actuators is one of the foremost challenges in feedback control [1]
We propose a greedy algorithm for sensor and actuator selection based on jointly maximizing observability and controllability in linear timeinvariant systems
We show that it is possible to apply our framework to closed loop systems, demonstrating near optimal sensor and actuator selection in comparison with more expensive iterative closed loop H2 optimization

Summary

Introduction

Optimizing the selection of sensors and actuators is one of the foremost challenges in feedback control [1]. Determining optimal selections with respect to a desired objective is an NP-hard selection problem, and in general can only be solved by enumerating all possible configurations. This combinatorial growth in complexity is intractable; the placement of sensors and actuators are typically chosen according to heuristics and intuition. We propose a greedy algorithm for sensor and actuator selection based on jointly maximizing observability and controllability in linear timeinvariant systems. Our approach (see Fig. 1) exploits low-rank transformations that balance the observability and controllability gramians to bypass the combinatorial search, enabling favorable scaling for high-dimensional systems

Objectives

Results

Conclusion