Minimal Actuator Placement with Optimal Control Constraints
Abstract
We introduce the problem of minimal actuator placement in a linear control system so that a bound on the minimum control effort for a given state transfer is satisfied while controllability is ensured. We first show that this is an NP-hard problem following the recent work of Olshevsky. Next, we prove that this problem has a supermodular structure. Afterwards, we provide an efficient algorithm that approximates up to a multiplicative factor of O(logn), where n is the size of the multi-agent network, any optimal actuator set that meets the specified energy criterion. Moreover, we show that this is the best approximation factor one can achieve in polynomial-time for the worst case. Finally, we test this algorithm over large Erdos-Renyi random networks to further demonstrate its efficiency.
Cite
@article{arxiv.1503.04693,
title = {Minimal Actuator Placement with Optimal Control Constraints},
author = {Vasileios Tzoumas and Mohammad Amin Rahimian and George J. Pappas and Ali Jadbabaie},
journal= {arXiv preprint arXiv:1503.04693},
year = {2015}
}
Comments
This version includes all the omitted proofs from the one to appear in the American Control Conference (ACC) 2015 proceedings