Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

Li, Yanning; Canepa, Edward; Claudel, Christian

doi:10.1109/tcns.2014.2304152

Cited by 42 publications

(36 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Suppose (q 1 (j), q 2 (j)) , ∀j ∈ J is the optimal solution to CP (29), then there exists a set of multipliers {λ i } that satisfies KKT. We now show that, the set of multipliers {λ i } also satisfies ∪ jmax j=1 KKT j .…”

Section: Discussionmentioning

confidence: 99%

“…Note that there are other related approaches that also do not require discretiza-tion of the time-space domain, including our earlier result on optimal traffic control on networks [29] and a recent continuous-time solver of traffic dynamics on the network [18]. Our earlier work [29] investigates control of the HJ PDE on a network and assumes all junctions are fully signalized by traffic actuators. Therefore, it does not require a model of the traffic dynamics at the junction and consequently it cannot be used to solve the HJ PDE on a network when the junction dynamics are prescribed.…”

mentioning

confidence: 99%

See 1 more Smart Citation

A Convex Formulation of Traffic Dynamics on Transportation Networks

Claudel

Piccoli³

et al. 2017

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

This article proposes a numerical scheme for computing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton-Jacobi (HJ) partial differential equation (PDE), which is an equivalent form of the Lighthill-Whitham-Richards PDE. The main contribution of this article is the construction of a single convex optimization program which computes the traffic flow at a junction over a finite time horizon and decouples the PDEs on connecting links. Compared to discretization schemes which require the computation of all traffic states on a time-space grid, the proposed convex optimization approach computes the boundary flows at the junction using only the initial condition on links and the boundary conditions of the network. The computed boundary flows at the junction specify the boundary condition for the HJ PDE on connecting links, which then can be separately solved using an existing semi-explicit scheme for single link HJ PDE. As demonstrated in a numerical example of ramp metering control, the proposed convex optimization approach also provides a natural framework for optimal traffic control applications.

show abstract

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

A Convex Formulation of Traffic Dynamics on Transportation Networks

Claudel

Piccoli³

et al. 2017

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the third group of traffic strategies adopting simplifications in the traffic model we can mention the following: the Traffic responsive Urban Control (TUC) strategy (Aboudolas et al 2010), which solves a linearquadratic problem based on a store-and-forward simplification of the traffic flow; the DISCO or mixedinteger linear program approaches where traffic is modeled after the cell-transmission model (Lo, Chang, and Chan 2001;Lo 2001); model predictive control strategies based on the simplified S-model (Lin et al 2012); and gating feedback regulators derived via a simplified dynamic model based on the network fundamental diagram of traffic flow (Keyvan-Ekbatani et al 2012). We conclude this nonexhaustive overview by mentioning recently emerging approaches for optimal control of the transportation network (Han, Szeto, and Friesz 2015;Li, Canepa, and Claudel 2014): these methods rely on a Lighthill-Whitham-Richards traffic flow model and characterize the optimal solution by the Lax-Hopf formula. The advantage is that no specific approximations nor discretization are required; however, one limitation is currently the lack of computational tractability, when the problem size scales up.…”

Section: Introductionmentioning

confidence: 99%

A Simulation-Based Traffic Signal Control for Congested Urban Traffic Networks

Baldi

Michailidis

Ntampasi

et al. 2019

Transportation Science

View full text Add to dashboard Cite

Traffic congestion in urban networks may lead to strong degradation in the utilization of the network infrastructure, which can be mitigated via suitable control strategies. This paper studies and analyzes the performance of an adaptive traffic-responsive strategy that controls the traffic light parameters in an urban network to reduce traffic congestion. A nearly optimal control formulation is adopted to avoid the curse of dimensionality occurring in the solution of the corresponding Hamilton–Jacobi–Bellman (HJB) optimal control problem. First, an (approximate) solution of the HJB is parametrized via an appropriate Lyapunov function; then, the solution is updated at each iteration in such a way to approach the nearly optimal solution, using a close-to-optimality index and information coming from the simulation model of the network (simulation-based design). Simulation results obtained using a traffic simulation model of the network Chania, Greece, an urban traffic network containing many varieties of junction staging, demonstrate the efficiency of the proposed approach, as compared with alternative traffic strategies based on a simplified linear model of the traffic network. It is shown that the proposed strategy can adapt to different traffic conditions and that low-complexity parametrizations of the optimal solution, a linear and a bimodal piecewise linear strategy, respectively, provide a satisfactory trade-off between computational complexity and network performance.

show abstract

“…Gas dynamic-based two species traffic models with the two species being cars and trucks have also been defined [16], [17]. There have also been papers on analysis of stability in traffic flows [22], [23], and control methods for PDE traffic models [24].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Automotive Cyber-Attacks on Highways Using Partial Differential Equation Models

Ghanavati

Chakravarthy

Menon

2018

IEEE Trans. Control Netw. Syst.

View full text Add to dashboard Cite

Abstract-This paper considers scenarios wherein a group of malicious vehicles on a highway perform a cooperative attack with the motive of creating undesirable wave effects among other vehicles on the highway. The two species of vehicles -malicious vehicles and normal vehicles, and their associated interaction effects, are modeled using Partial Differential Equations (PDEs). The malicious vehicles, which may be arbitrarily distributed on the highway, perform a sequence of velocity changes with the objective of making the density/velocity profile on the highway, track a reference profile. This reference profile (chosen by the malicious vehicles) has the property that once generated, it spontaneously evolves into a shock wave that propagates along the highway. Analytical expressions governing the velocity inputs of the malicious vehicles with which they can generate such waves are determined, for perfect as well as imperfect information scenarios. Simulation results are presented to validate the theory.

show abstract

Optimal Control of Scalar Conservation Laws Using Linear/Quadratic Programming: Application to Transportation Networks

Cited by 42 publications

References 32 publications

A Convex Formulation of Traffic Dynamics on Transportation Networks

A Convex Formulation of Traffic Dynamics on Transportation Networks

A Simulation-Based Traffic Signal Control for Congested Urban Traffic Networks

Analysis of Automotive Cyber-Attacks on Highways Using Partial Differential Equation Models

Contact Info

Product

Resources

About