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

TL;DR

This paper proposes a novel control node scheduling method using sparsity constraints and convex relaxation, applied to rebalancing mobility networks to optimize control energy and efficiency.

Contribution

It introduces a combined L0 and l0 sparsity constraint framework with convex relaxation for control node scheduling in networked systems.

Findings

Effective control node selection reduces control energy.

Convex relaxation provides computationally feasible solutions.

Application to mobility networks demonstrates practical utility.

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.