On distributed computation of optimal control of traffic flow over networks

Ba, Qin; Savla, Ketan

doi:10.1109/allerton.2016.7852358

Cited by 8 publications

(13 citation statements)

References 13 publications

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“…The parameters of the optimal feedback control law in (11) are obtained by setting the exogenous input λ k to zero. Then, the feasibility of the optimal control action in guaranteed for any feasible nonzero λ k .…”

Section: Remarkmentioning

confidence: 99%

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On Structural Properties of Optimal Feedback Control of Traffic Flow under the Cell Transmission Model

Jafari

Savla

2019

2019 American Control Conference (ACC)

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In this paper, we investigate the structure of the finite-time optimal feedback control for freeway traffic networks modeled by the Cell Transmission Model. Piecewise affine supply and demand functions are considered and optimization with respect to a general linear objective function is studied. Using the framework of multi-parametric linear programming, we show that the optimal feedback control can be represented in a closed-form by a piecewise affine function on polyhedra of the network traffic density. The resulting optimal feedback control law, however, has a centralized structure and requires instantaneous access to the state of the entire network that may lead to prohibitive communication requirements in large-scale complex networks. We subsequently examine the design of a decentralized optimal feedback controller with a one-hop information structure, wherein the optimum outflow rate from each segment of the network depends only on the density of that segment and the density of the segments immediately downstream. The decentralization is based on the relaxation of constraints that depend on state variables that are unavailable according to the information structure. The resulting decentralized control scheme has a simple closed-form representation and is scalable to arbitrary large networks; moreover, we demonstrate that, with respect to certain meaningful linear performance indexes, the performance loss due to decentralization is zero; namely, the centralized optimal controller has a decentralized realization with a one-hop information structure and is obtained at no computational cost.

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Section: Remarkmentioning

confidence: 99%

“…Hence, to design a feedback control law, we retain only the first equation in (30) and discard the rest of them. Therefore, in (11), the parameters of the optimal feedback controller at time k = 0 are given by…”

Section: Appendixmentioning

confidence: 99%

On Structural Properties of Optimal Feedback Control of Traffic Flow under the Cell Transmission Model

Jafari

Savla

2019

2019 American Control Conference (ACC)

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“…In [13], another algorithm inspired by ADMM for solving the DTA problem distributively is presented. Our approach solves the same problem and is also inspired by ADMM, but differs significantly from the one in [13]. There, the constraints on the decision variables are not included in the Lagrangian, and must be handled when solving the distributed subproblems.…”

Section: Distributed Algorithmmentioning

confidence: 99%

“…Another distributed algorithm for solving the considered DTA problem is proposed in [13]. Except for that both methods are inspired by ADMM, the approaches are quite different.…”

Section: Introductionmentioning

confidence: 99%

“…Except for that both methods are inspired by ADMM, the approaches are quite different. In [13], the constraints on the decision variables are not included in the Lagrangian, and must thus instead be taken into account when solving the distributed subproblems. This allows for dividing the the decision variables into two groups and performing the Lagrangian minimization in two steps.…”

Section: Introductionmentioning

confidence: 99%

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On Distributed Optimal Control of Traffic Flows in Transportation Networks

Rosdahl

Nilsson

Como

2018

2018 IEEE Conference on Control Technology and Applications (CCTA)

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We propose and analyze distributed computation algorithms for finite-horizon optimal control problems in transportation networks. We model traffic flow dynamics by the cell-transmission model and focus on two problems: systemoptimum dynamic traffic assignment (where the routing is part of the optimization) and freeway network control (where the routing is exogenous and the optimization is confined to speed limits and ramp-metering controls). While these are non-convex problems, we focus on some recently proposed provably exact convex relaxations and apply Alternating Direction Method of Multipliers techniques. We present fully distributed iterative algorithms and implement them on some transportation network testbeds, testing their convergence speed and accuracy.

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