Algorithms for Joint Sensor and Control Nodes Selection in Dynamic Networks

TL;DR

This paper develops and compares optimal, search-based, and heuristic algorithms for selecting sensors and control nodes in linear dynamic networks to ensure stability with minimal resources.

Contribution

It introduces three methods—mixed-integer nonlinear programming, binary search, and heuristics—for joint sensor and actuator selection, including optimal and suboptimal solutions.

Findings

Optimal solutions depend on parameter tuning.

Binary search provides parameter-free optimal solutions.

Heuristics offer faster, suboptimal solutions.

Abstract

The problem of placing or selecting sensors and control nodes plays a pivotal role in the operation of dynamic networks. This paper proposes optimal algorithms and heuristics to solve the simultaneous sensor and actuator selection problem in linear dynamic networks. In particular, a sufficiency condition of static output feedback stabilizability is used to obtain the minimal set of sensors and control nodes needed to stabilize an unstable network. We show the joint sensor/actuator selection and output feedback control can be written as a mixed-integer nonconvex problem. To solve this nonconvex combinatorial problem, three methods based on (1) mixed-integer nonlinear programming, (2) binary search algorithms, and (3) simple heuristics are proposed. The first method yields optimal solutions to the selection problem---given that some constants are appropriately selected. The second method requires a database of binary sensor/actuator combinations, returns optimal solutions, and necessitates no tuning parameters. The third approach is a heuristic that yields suboptimal solutions but is computationally attractive. The theoretical properties of these methods are discussed and numerical tests on dynamic networks showcase the trade-off between optimality and computational time.