A Control-Theoretic Approach for Scalable and Robust Traffic Density Estimation Using Convex Optimization

Nugroho, Sebastian A.; Taha, Ahmad F.; Claudel, Christian

doi:10.1109/tits.2019.2953023

Cited by 12 publications

(12 citation statements)

References 48 publications

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“…Next in Section III, we present a robust observer framework developed using the concept of L ∞ stability for discrete-time Lipschitz nonlinear systems. This observer extends our prior work [14], which presents a similar observer for continuous-time Lipschitz nonlinear systems. In Section IV, we demonstrate the performance of our observer for performing density estimation on a simple highway and compare it with Unscented Kalman Filter (UKF).…”

Section: Introductionsupporting

confidence: 68%

“…Our goal is to achieve asymptotic estimation error for estimation error dynamics given above. In our prior work [14], we present a robust observer using the concept of L ∞ stability for traffic density estimation assuming nonlinear continuous-time traffic dynamics model. The L ∞ stability theory is previously developed in [15] for feedback control purpose, which is then used in [16] to develop a robust observer for nonlinear discretetime systems which nonlinearities satisfy incremental quadratic constraint.…”

Section: A Robust Observer Frameworkmentioning

confidence: 99%

“…Nonetheless in this paper, the observer is designed specifically for Lipschitz nonlinearity instead of incremental quadratic nonlinearity. Albeit incremental quadratic nonlinearity comprises a large class of nonlinear functions including Lipschitz nonlinearity, the use of condition (14) will return much simpler matrix inequality formulations-for example, see [14]. To that end, we utilize the definition of L ∞ stability presented in [15], [16].…”

Section: A Robust Observer Frameworkmentioning

confidence: 99%

See 2 more Smart Citations

Asymmetric Cell Transmission Model-Based, Ramp-Connected Robust Traffic Density Estimation under Bounded Disturbances

Vishnoi

Nugroho

Taha

et al. 2020

2020 American Control Conference (ACC)

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In modern transportation systems, traffic congestion is inevitable. To minimize the loss caused by congestion, various control strategies have been developed most of which rely on observing real-time traffic conditions. As vintage traffic sensors are limited, traffic density estimation is very helpful for gaining network-wide observability. This paper deals with this problem by first, presenting a traffic model for stretched highway having multiple ramps built based on asymmetric cell transmission model (ACTM). Second, based on the assumption that the encompassed nonlinearity of the ACTM is Lipschitz, a robust dynamic observer framework for performing traffic density estimation is proposed. Numerical test results show that the observer yields a sufficient performance in estimating traffic densities having noisy measurements, while being computationally faster the Unscented Kalman Filter in performing real-time estimation.

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Section: Introductionsupporting

confidence: 68%

Section: A Robust Observer Frameworkmentioning

confidence: 99%

Section: A Robust Observer Frameworkmentioning

confidence: 99%

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Asymmetric Cell Transmission Model-Based, Ramp-Connected Robust Traffic Density Estimation under Bounded Disturbances

Vishnoi

Nugroho

Taha

et al. 2020

2020 American Control Conference (ACC)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since the presence of unknown inputs will not make the estimation error to be exactly zero, a robustness metric, referred to as and L ∞ stability, is employed. The purpose of this metric is to provide numerical assurance on the behavior of performance output z against nonzero, time-varying unknown inputs w. Our prior work [53] deals with a robust observer design using the concept of L ∞ stability for traffic density estimation purpose assuming nonlinear continuous-time traffic dynamics model corresponding with the Greenshield's model. Furthermore, our recent work [47] develops a robust L ∞ observer for the discretetime model corresponding with the ACTM.…”

Section: A Robust Observer For State Estimationmentioning

confidence: 99%

Where Should Traffic Sensors Be Placed on Highways?

Nugroho¹,

Vishnoi²,

Taha³

et al. 2021

Preprint

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This paper investigates the practical engineering problem of traffic sensors placement on stretched highways with ramps. Since it is virtually impossible to install bulky traffic sensors on each highway segment, it is crucial to find placements that result in optimized network-wide, traffic observability. Consequently, this results in accurate traffic density estimates on segments where sensors are not installed. The substantial contribution of this paper is the utilization of control-theoretic observability analysis-jointly with integer programming-to determine traffic sensor locations based on the nonlinear dynamics and parameters of traffic networks. In particular, the celebrated asymmetric cell transmission model is used to guide the placement strategy jointly with observability analysis of nonlinear dynamic systems through Gramians. Thorough numerical case studies are presented to corroborate the proposed theoretical methods and various computational research questions are posed and addressed. The presented approach can also be extended to other models of traffic dynamics.

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“…2 nd -order swing equation x i := [δi ωi] δi: rotor angle, ωi: rotor speed Highway traffic [19] ρi Epidemic outbreaks [22] ṗi = −δpi…”

Section: Type Of Systems Nonlinear Dynamics Model Descriptionmentioning

confidence: 99%

Towards Understanding Sensor and Control Nodes Selection in Nonlinear Dynamic Systems: Lyapunov Theory Meets Branch-and-Bound

Nugroho¹,

Taha²

2020

Preprint

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Sensor and actuator selection problems (SASP) are some of the core problems in dynamic systems design and control. These problems correspond to determining the optimal selection of sensors (measurements) or actuators (control nodes) such that certain estimation/control objectives can be achieved. While the literature on SASP is indeed inveterate, the vast majority of the work focuses on linear(ized) representation of the network dynamics, resulting in the placements of sensors or actuators (SA) that are valid for confined operating regions. As an alternative, herein we propose a new general framework for addressing SASP in nonlinear dynamic systems (NDS), assuming that the inputs and outputs are linearly coupled with the nonlinear dynamics. This is investigated through (i) classifying and parameterizing the NDS into various nonlinear function sets, (ii) utilizing rich Lyapunov theoretic formulations, and (iii) designing a new customized branch-and-bound (BnB) algorithm that exploits problem structure of the SASP. The newly designed BnB routines are computationally more attractive than the standard one and also directly applicable to solve SASP for linear systems. In contrast with contemporary approaches from the literature, our approach is suitable for finding the optimal SA combination for stable/unstable NDS that ensures stabilization of estimation error and closed-loop dynamics through a simple linear feedback control policy.

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A Control-Theoretic Approach for Scalable and Robust Traffic Density Estimation Using Convex Optimization

Cited by 12 publications

References 48 publications

Asymmetric Cell Transmission Model-Based, Ramp-Connected Robust Traffic Density Estimation under Bounded Disturbances

Asymmetric Cell Transmission Model-Based, Ramp-Connected Robust Traffic Density Estimation under Bounded Disturbances

Where Should Traffic Sensors Be Placed on Highways?

Towards Understanding Sensor and Control Nodes Selection in Nonlinear Dynamic Systems: Lyapunov Theory Meets Branch-and-Bound

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