Structure-preserving model reduction of large-scale logistics networks

Scholz‐Reiter, Bernd; Wirth, Fabian; Makuschewitz, Thomas; Schönlein, Michael; Kosmykov, Michael

doi:10.1140/epjb/e2011-10894-6

Cited by 3 publications

(8 citation statements)

References 36 publications

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“…The sequence of the application of these rules may be arbitrary or depend on some additional information about the network topology. For example, this sequence may depend on information about the most influential nodes of the network, see [39,Algorithm 1]. In this paper, we have performed initial steps in the development of a reduction approach to reduce computations for the verification of the small-gain type conditions for large-scale networks with nonlinear dynamics.…”

Section: Discussionmentioning

confidence: 99%

“…The next steps are the following: extension of the aggregation rules to other types of motifs, introduction and estimation of the error measure that compares the reduced and the original models, and the development of a numerical algorithm that performs this reduction. Further, improvement of the approach may be performed by adaptation of the ranking technique used in [40,41], and [39]. As well, we would like to mention that the proposed approach can be still useful in verification of small gain conditions for some classes of systems which are not necessarily ISS, see, for example, [42].…”

Section: Discussionmentioning

confidence: 99%

“…Conditions on the other cycles in (13) are satisfied straightforwardly. For the proof in the opposite direction we consider the cycle condition (39) and from (42) and (43) we obtain (45), that is, cycle condition for the aggregated gains Q v ,J , Q J ,v . The rest cycle conditions are satisfied straightforwardly.…”

Section: Proofmentioning

confidence: 99%

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Reduction of the small gain condition for large‐scale interconnections

Kosmykov

2013

Intl J Robust & Nonlinear

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SUMMARYThe small gain condition is sufficient for input-to-state stability (ISS) of interconnected systems. However, verification of the small gain condition requires large amount of computations in the case of a large size of the system. To facilitate this procedure we aggregate the subsystems and the gains between the subsystems that belong to certain interconnection patterns (motifs) using three heuristic rules. These rules are based on three motifs: sequentially connected nodes, nodes connected in parallel and almost disconnected subgraphs. Aggregation of these motifs keeps the main structure of the mutual influences between the subsystems in the network. Furthermore, fulfillment of the reduced small gain condition implies ISS of the large network. Thus such reduction allows to decrease the number of computations needed to verify the small gain condition. Finally, an ISS-Lyapunov function for the large network can be constructed using the reduced small gain condition. Applications of these rules is illustrated on an example.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Reduction of the small gain condition for large‐scale interconnections

Kosmykov

2013

Intl J Robust & Nonlinear

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“…investigate the problem of model reduction with a view of large-scale logistics networks [139]. Yao et al…”

Section: Logistics Networkmentioning

confidence: 99%

“…Finding: From the above 11 papers (7.3% of selected papers) [133][134][135][136][137][138][139][140][141][142][143], it can be seen that the researches on logistics network gradually expand to the completely manufacturing process. However, how to identify other aspects of robustness and complexity, how to solve the scientific problems about dynamics fuzziness, randomness, and nonlinearity in regional logistics network organization, still need to be paid much more attention.…”

Section: Logistics Networkmentioning

confidence: 99%