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arXiv 1503.04693eess.SYcs.SIcs.SYmath.OC
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最小执行器布置与最优控制约束

Minimal Actuator Placement with Optimal Control Constraints

University of Pennsylvania(宾夕法尼亚大学)

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

AI总结:

研究最小执行器布置问题,确保状态转移的控制努力有界,证明问题NP难,具有超模结构,提出近似算法,达到O(logn)的逼近因子,验证算法在大规模网络中的效率。

摘要:

我们引入了一个问题:在线性控制系统中,最小化执行器布置,使得给定状态转移的最小控制努力有界,同时确保可控性。我们首先证明该问题NP难,依据Olshevsky最近的工作。接着证明该问题具有超模结构。然后提供一个高效的算法,能以O(logn)的乘法因子近似任何满足指定能量标准的最优执行器集。此外,我们证明在多项式时间内,最坏情况下的最佳逼近因子即为O(logn)。最后,我们在大规模Erdos-Renyi随机网络上测试该算法,进一步展示其效率。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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