Minimal Input Selection for Robust Control

TL;DR

This paper presents a method for selecting the smallest set of input nodes to ensure the stability of uncertain networked systems with delays, using submodular optimization techniques for efficiency.

Contribution

It introduces a novel approach to input selection that accounts for uncertainties and delays, providing polynomial-time algorithms with provable optimality bounds.

Findings

Applicable to various uncertainties including additive, multiplicative, and delays.

Provides polynomial-time algorithms with optimality guarantees.

Validated on IEEE 39-bus power system case study.

Abstract

This paper studies the problem of selecting a minimum-size set of input nodes to guarantee stability of a networked system in the presence of uncertainties and time delays. Current approaches to input selection in networked dynamical systems focus on nominal systems with known parameter values in the absence of delays. We derive sufficient conditions for existence of a stabilizing controller for an uncertain system that are based on a subset of system modes lying within the controllability subspace induced by the set of inputs. We then formulate the minimum input selection problem and prove that it is equivalent to a discrete optimization problem with bounded submodularity ratio, leading to polynomial-time algorithms with provable optimality bounds. We show that our approach is applicable to different types of uncertainties, including additive and multiplicative uncertainties in the system matrices as well as uncertain time delays. We demonstrate our approach in a numerical case study on the IEEE 39-bus test power system.