Multiple sparsity constrained control node scheduling with application to rebalancing of mobility networks

2021/08/28 by Takuya Ikeda, Ikeda, Takuya, Kazunori Sakurama +3
Business, Management and Accounting · Engineering · #Advanced Queuing Theory Analysis #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #Traffic control and management #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2108.12624

openalex publication_date 2021/08/28 · openalex created_date 2021/09/13 · openalex updated_date 2026/07/28

Abstract

This paper treats an optimal scheduling problem of control nodes in networked systems. We newly introduce both the L0 and l0 constraints on control inputs to extract a time-varying small number of effective control nodes. As the cost function, we adopt the trace of the controllability Gramian to reduce the required control energy. Since the formulated optimization problem is combinatorial, we introduce a convex relaxation problem for its computational tractability. After a reformulation of the problem into an optimal control problem to which Pontryagin's maximum principle is applicable, we give a sufficient condition under which the relaxed problem gives a solution of the main problem. Finally, the proposed method is applied to a rebalancing problem of a mobility network.

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