Simultaneous Sensor and Actuator Selection/Placement through Output Feedback Control

TL;DR

This paper addresses the challenge of selecting minimal sensors and actuators in dynamic networks to achieve stable output feedback control, formulating it as a complex optimization problem and proposing two computational approaches.

Contribution

It introduces a novel formulation of the joint sensor and actuator selection problem as a mixed-integer nonlinear matrix inequality optimization and provides two solution methods.

Findings

The proposed methods effectively identify minimal SaA sets for stability.

Numerical experiments demonstrate the approaches' performance and computational feasibility.

Abstract

In most dynamic networks, it is impractical to measure all of the system states; instead, only a subset of the states are measured through sensors. Consequently, and unlike full state feedback controllers, output feedback control utilizes only the measured states to obtain a stable closed-loop performance. This paper explores the interplay between the selection of minimal number of sensors and actuators (SaA) that yield a stable closed-loop system performance. Through the formulation of the static output feedback control problem, we show that the simultaneous selection of minimal set of SaA is a combinatorial optimization problem with mixed-integer nonlinear matrix inequality constraints. To address the computational complexity, we develop two approaches: The first approach relies on integer/disjunctive programming principles, while the second approach is a simple algorithm that is akin to binary search routines. The optimality of the two approaches is also discussed. Numerical experiments are included showing the performance of the developed approaches.