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arXiv · 1503.04693

Minimal Actuator Placement with Optimal Control Constraints

Vasileios Tzoumas·Mohammad Amin Rahimian·George J. Pappas·Ali Jadbabaie
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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.

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Vasileios Tzoumas, Mohammad Amin Rahimian, George J. Pappas, Ali Jadbabaie. 2015-03-16. Minimal Actuator Placement with Optimal Control Constraints. https://arxiv.org/abs/1503.04693

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