Minimal actuator placement with optimal control constraints

V. Tzoumas, M. A. Rahimian, G. J. Pappas, A. Jadbabaie
2015 2015 American Control Conference (ACC)  
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 [1]. 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(log n), where n is the size of the
more » ... e 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 Erdős-Rényi random networks to further demonstrate its efficiency.
doi:10.1109/acc.2015.7171040 dblp:conf/amcc/TzoumasRPJ15 fatcat:qimx35vsevajpbmswkzkjy3xcu