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Towards Scale-Free Control of large-scale traffic networks

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The talk discuss new research lines addressing the optimal control of time-varying dynamic large-scale traffic networks. The driving idea consists in aggregating the whole network in sub-networks having some suitable control properties, allowing the optimal games to be more tractable. The talk starts with a recall of controllability and observability properties in 1-D traffic networks and provide a detailed example of how to partition the systems and how to solve the associated time-varying optimal games [1]. Then we discuss recent work on how such ideas can be extended to 2-D graphs in relation with the problem of games played over networks and focus our attention on the importance of the topology of communication between nodes. We analyze the topology of the graph and its importance in the structure of the game. We show that, by condensing the strongly connected components of the control graph into super-nodes, it is possible to give a hierarchical interpretation to the network game. According to this analysis, we assign to each node a level of priority and define a sequential procedure to steer the response of the network to a Nash equilibrium. Given a certain topology, this equilibrium is unique and it depends on the particular topology and the set of local cost function (Ref.2). The talk finishes by discussing new avenues for organizing such large-scale complex networks, by proposing a new aggregation procedure that combines, complexity reduction (scale-free graph structure), physical preservation properties, and control targets [3]. In connection with this goal, some preliminary results [3] will be presented.

[1] D. Pisarski and C. Canudas-de-Wit. “Nash Game Based Distributed Control Design for Balancing of Traffic Density over Freeway Networks. IEEE Transactions on Control of Network Systems, IEEE , 2016, 3 (2), pp.149-161.

[2] G. Casadei, C. Canudas De-Wit. Networks Games: Condensation of the Graph as a Hierarchical interpretation of the Game, IFAC WC ’17. Toulouse, France.

[3] N. Martin, C. Canudas-de-Wit, and P. Frasca. “Large-scale network reduction towards scale-free structure”. To be presented at the 6th Int. Conference on Complex Networs and their applications, Lyon, Dec. 2017.

This talk is part of the CUED Control Group Seminars series.

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