On the Complexity of Minimum-Cost Networked Estimation of Self-Damped Dynamical Systems

TL;DR

This paper addresses the complex problem of designing cost-efficient networked estimators for self-damped dynamical systems, offering polynomial-time solutions for key subproblems under specific conditions.

Contribution

It introduces a polynomial-order solution for the minimum-cost networked estimation problem in self-damped systems, reducing complexity for certain network configurations.

Findings

Polynomial-time solution for sensor selection in self-damped systems

Polynomial complexity for bidirectional communication networks

Illustrative example demonstrating the methodology

Abstract

In this paper, we consider the optimal design of networked estimators to minimize the communication/measurement cost under the networked observability constraint. This problem is known as the minimum-cost networked estimation problem, which is generally claimed to be NP-hard. The main contribution of this work is to provide a polynomial-order solution for this problem under the constraint that the underlying dynamical system is self-damped. Using structural analysis, we subdivide the main problem into two NP-hard subproblems known as (i) optimal sensor selection, and (ii) minimum-cost communication network. For self-damped dynamical systems, we provide a polynomial-order solution for subproblem (i). Further, we show that the subproblem (ii) is of polynomial-order complexity if the links in the communication network are bidirectional. We provide an illustrative example to explain the methodologies.