Passivity-Short-based Stability Analysis on Electricity Market Trading System Considering Negative Price

Muto, Keita; Namerikawa, Toru; Qu, Zhihua

doi:10.1109/ccta.2018.8511465

Cited by 4 publications

(6 citation statements)

References 13 publications

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“…The system given by (12) and (13) is passive from y a − y c to v a v c for the following storage function:…”

Section: Lemma 5 ([6])mentioning

confidence: 99%

“…This completes the proof. We are now ready for convergence analysis of the proposed dynamics, composed of (7) and (9)- (13). Due to the communication delays, the proposed method is categorized as a time delay system.…”

Section: Lemma 5 ([6])mentioning

confidence: 99%

“…Then, by using the invariance principle for delay systems [18,Theorem 4], we can prove the main result of this paper shown below. Theorem 2 Consider the system (7), (9)-(11), and the communication block (12) and (13). Assume that for all i, M i (s) has one or more stable zeros.…”

Section: Lemma 5 ([6])mentioning

confidence: 99%

“…Distributed implementation of the above optimization algorithms relies on communication technology, which poses additional issues to be addressed like delays [13]- [15], packet losses [16], and noises [17]. In this paper, we address delays in distributed optimization algorithms.…”

Section: Introductionmentioning

confidence: 99%

“…However, differently from the delay-free case, strict convexity is assumed for the cost function in the presence of delays in order to complete the convergence proof. The same is applied to [13]. Recently, the authors succeeded in eliminating the strict convexity assumption in the presence of delays, but the communication structure assumed therein is different from that in [6].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Robustification of Continuous-Time ADMM against Communication Delays under Non-Strict Convexity: A Passivity-Based Approach

Yamashita

Hatanaka

2020

SICE Journal of Control, Measurement, and System Integration

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In this paper, we address a class of distributed optimization problems with non-strictly convex cost functions in the presence of communication delays between an agent and a coordinator. To this end, we focus on a continuous-time optimization algorithm that mirrors the alternating direction method of multipliers. We first redesign the algorithm so that the dynamics ensures smoothness and a sub-block for primal optimization includes stable zeros. It is then revealed that the algorithm is composed of feedback interconnection of passive systems. We next robustify the algorithm against communication delays by applying the so-called scattering transformation. The smoothness of the dynamics allows one to use the invariance principle for delay systems, and accordingly, the state trajectories are shown to converge to an optimal solution even without the strict convexity assumption. Finally, the presented method is demonstrated via simulation of an environmental-monitoring problem.

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“…The system given by (12) and (13) is passive from y a − y c to v a v c for the following storage function:…”

Section: Lemma 5 ([6])mentioning

confidence: 99%

Section: Lemma 5 ([6])mentioning

confidence: 99%