Optimal control of freeway networks based on the Link Node Cell transmission model

Muralidharan, Ajith; Horowitz, Roberto

doi:10.1109/acc.2012.6315236

Cited by 48 publications

(48 citation statements)

References 7 publications

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“…subject to (5), where N is a fixed final time. In this paper, we are interested in cost functions wherein ψ k (x k , u k ) is a linear function of x k and u k , and ψ N (x N ) is a linear function of x N , that is…”

Section: Problem Formulationmentioning

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 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: Problem Formulationmentioning

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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“…Other works concerned with optimal control of the CTM [11,18,3] assume in addition concavity of the demand and supply functions to keep the resulting optimization problems tractable. Note that the former two references assume the classical triangular fundamental diagram, whose demand and supply functions are both monotonic and concave.…”

Section: Problem Formulationmentioning

confidence: 99%

Sufficient optimality conditions for distributed, non-predictive ramp metering in the monotonic cell transmission model

Schmitt¹,

Ramesh²,

Lygeros³

2017

Transportation Research Part B: Methodological

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We consider the ramp metering problem for a freeway stretch modeled by the Cell Transmission Model. Assuming perfect model knowledge and perfect traffic demand prediction, the ramp metering problem can be cast as a finite horizon optimal control problem with the objective of minimizing the Total Time Spent, i.e., the sum of the travel times of all drivers. For this reason, the application of Model Predictive Control (MPC) to the ramp metering problem has been proposed. However, practical tests on freeways show that MPC may not outperform simple, distributed feedback policies. Until now, a theoretical justification for this empirical observation was lacking. This work compares the performance of distributed, non-predictive policies to the optimal solution in an idealised setting, specifically, for monotonic traffic dynamics and assuming perfect model knowledge. To do so, we suggest a distributed, non-predictive policy and derive sufficient optimality conditions for the minimization of the Total Time Spent via monotonicity arguments. In a case study based on real-world traffic data, we demonstrate that these optimality conditions are only rarely violated. Moreover, we observe that the suboptimality resulting from such infrequent violations appears to be negligible. We complement this analysis with simulations in non-ideal settings, in particular allowing for model mismatch, and argue that Alinea, a successful, distributed ramp metering policy, comes close to the ideal controller both in terms of control behavior and in performance.

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“…In order to control large freeway networks, some distributed MPC algorithms have been developed (see for instance Ferrara et al (2014), Majid et al (2014)). In other approaches, in order to reduce the complexity of the MPC schemes and hence to develop solutions to be applied on-line in large networks, the nonlinear optimization problems are properly relaxed to be linear, as done for instance by Muralidharan and Horowitz (2012) who adopt the so-called Link-Node Cell Transmission Model.…”

Section: Introductionmentioning

confidence: 99%

Event-triggered model predictive schemes for freeway traffic control

Ferrara

Sacone²,

Siri³

2015

Transportation Research Part C: Emerging Technologies

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Optimal control of freeway networks based on the Link Node Cell transmission model

Cited by 48 publications

References 7 publications

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

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

Sufficient optimality conditions for distributed, non-predictive ramp metering in the monotonic cell transmission model

Event-triggered model predictive schemes for freeway traffic control

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