Optimal Periodic Sensor Scheduling in Networks of Dynamical Systems

TL;DR

This paper develops an ADMM-based method to design optimal periodic sensor schedules for discrete-time dynamical systems, balancing estimation accuracy and sensor resource constraints.

Contribution

It formulates a novel combinatorial optimization problem linking sensor activation to estimator gain structure and solves it using ADMM for the first time.

Findings

Effective sensor scheduling balancing accuracy and resource use.

Outperforms existing algorithms in numerical comparisons.

Provides a practical approach for resource-constrained sensor networks.

Abstract

We consider the problem of finding optimal time-periodic sensor schedules for estimating the state of discrete-time dynamical systems. We assume that {multiple} sensors have been deployed and that the sensors are subject to resource constraints, which limits the number of times each can be activated over one period of the periodic schedule. We seek an algorithm that strikes a balance between estimation accuracy and total sensor activations over one period. We make a correspondence between active sensors and the nonzero columns of estimator gain. We formulate an optimization problem in which we minimize the trace of the error covariance with respect to the estimator gain while simultaneously penalizing the number of nonzero columns of the estimator gain. This optimization problem is combinatorial in nature, and we employ the alternating direction method of multipliers (ADMM) to find its locally optimal solutions. Numerical results and comparisons with other sensor scheduling algorithms in the literature are provided to illustrate the effectiveness of our proposed method.