Freeway ramp metering: An LPV set theoretical analysis

Luspay, Tamás; Kulcsár, Balázs; Péni, Tamás; Varga, István

doi:10.1109/acc.2011.5991406

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…4. Construct a convex polytope of matrix functions in (18), which can be performed by applying numerical methods. For the case of the PW model, the method of tensor-product transformation [28] has been used.…”

Section: Representation Of Dynamical Systemsmentioning

confidence: 99%

“…The proposed methodology is independent of the selected control decision algorithm and adjustable for different problem configurations. A preliminary version of the paper has been published in [18]. The current version is an extension of [18] in terms of methodological description, theoretical focus (t-step, reachability set), case study, and the depth of evaluation.The paper is structured in the following frame.…”

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confidence: 99%

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Set‐theoretic analysis of the isolated ramp metering problem

Luspay

Kulcsár

Péni

2015

Intl J Robust & Nonlinear

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Analysis of ramp metering, as an effective freeway traffic control solution, is focused in the paper. The studied traffic control problem is discussed in a set-theoretic context in order to quantitatively characterize its effectivenes. The notions of maximal robust controlled invariant set, as well as t-step robust controllable set are defined and used for analyzing the ramp metering problem independently of the control policy applied. Algorithms are developed to compute these sets, with special attention to their practical interpretations. Numerical examples with graphical representation of the proposed methodology are given to examine local ramp metering and conclude implications to control strategies. 1247The ramp metering control problem has been investigated in [5] and [10] by using optimal control considerations. The first-order macroscopic freeway model of and Richards [12] was used for representing dynamics, and the total time spent (TTS) objective is minimized subject to the dynamical equations. The mathematical analysis of the constrained optimization showed that it is not beneficial to meter ramps when the freeway is either uniformly congested or uniformly uncongested. At the same time, under mixed traffic conditions, ramp metering is proved to improve network performance. Based on a first-order description, Gomes and Horowitz [13,14] provided a similar analysis of the optimal control problem. Freeway dynamics were represented by the asymmetric cell transmission model (CTM) [15], and numerical conditions were derived for the equivalent linear formulation of the non-linear optimization problem. As a consequence, a nearglobal optimal ramp metering law has also been established. The characterization of the equilibrium solutions of the CTM and its implication for ramp metering have been carried out in [16]. By exploring the equilibrium of the model, it has been shown that discharge flow can be increased by applying ramp metering. In the case of an initially congested freeway, the existence of a ramp metering law, which dissolves congestion and improves network efficiency, has been derived. Furthermore, it has been shown that the TTS objective can be minimized by controlling the on-ramp volume even when the congestion cannot be resolved completely. Recently, Wang et al. [17] provided a control theoretic analysis of the local ramp metering problem. Specific ramp control laws of ALINEA and PI-ALINEA have been considered and analyzed by using linear and non-linear stability techniques. Design conditions for the feedback gains were concluded from the results of the analysis.Within this line of research, this paper contributes to the mathematical analysis of the ramp metering problem. The presence of controlled and uncontrolled variables with physical bounds implies a set-theoretic setup for investigating the effect of ramp metering. For this purpose, a systematic, settheoretic framework is proposed and developed throughout the paper. First, the non-linear model is embedded into a linear parameter varying (LP...

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Section: Representation Of Dynamical Systemsmentioning

confidence: 99%

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confidence: 99%

Set‐theoretic analysis of the isolated ramp metering problem

Luspay

Kulcsár

Péni

2015

Intl J Robust & Nonlinear

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“…Computational complexity relaxation of the TP model transformation for higher dimensional cases is proposed in . Further key applications of the TP model transformation are presented in , . Applications of the TP model transformation in conjunction with sliding‐mode control are presented in .…”

Section: Introductionmentioning

confidence: 99%

TP Model Transformation as a Manipulation Tool for QLPV Analysis and Design

Bárányi¹

2015

Asian Journal of Control

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The main motivation of the TP model transformation is that modern identification and control analysis, along with design methodologies, are based on various kinds of different representations that have different benefits and drawbacks in terms of identification and modeling effort and structure, however, the link between these representations is in many cases difficult to establish, especially if the model components are not given by closed formulae but rather by various soft-computing-based or black box models. This paper shows that the TP model transformation can serve as a gateway between different representations by bridging to a widely adopted polytopic representation. Further, it is capable of readily manipulating the resulting polytopic representation for further design requirements, which in many cases has a strong effect on the resulting control performance and the conservativeness of the solution. The paper discusses how the TP model transformation can be used as a final step of modeling and, at the same time, as a preprocessing step in polytopic model based design approaches. The paper introduces the generalized TP model transformation, which is a tractable, non-heuristic numerical tool that can be executed on sets of functions. Different manipulation techniques are investigated to show the benefits of the generalized TP model transformation. Finally, a stability verification technique is proposed for cases where system components are available in different representations.Key Words: qLPV and polytopic system based control design, TP model transformation, linear matrix inequality based design.

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A Parameter Identification Scheme for Second-Order Highway Traffic Model Based on Differential Algebraic Methodology

Zhao

2013

Intelligent Computing for Sustainable Energy and Environment

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Freeway ramp metering: An LPV set theoretical analysis

Cited by 5 publications

References 10 publications

Set‐theoretic analysis of the isolated ramp metering problem

Set‐theoretic analysis of the isolated ramp metering problem

TP Model Transformation as a Manipulation Tool for QLPV Analysis and Design

A Parameter Identification Scheme for Second-Order Highway Traffic Model Based on Differential Algebraic Methodology

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