Abstract
A novel freeway traffic control design framework is proposed in the chapter. The derivation is based on the parameter-dependent reformulation of the second-order macroscopic freeway model. Hard physical constraints are handled implicitly, by introducing additional scheduling parameter for controller saturation measure. The ramp metering problem is then formulated as an induced \({\mathcal{L}}_{2}\) norm minimization, where the effects of undesired traffic phenomena are attenuated on the network throughput. The solution of the resulting problem involves convex optimization methods subjected to Linear Matrix Inequalities. A numerical example is given to validate the parameter-dependent controller and evaluate its effectiveness under various traffic situations.
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Notes
- 1.
In contrast to individual user based optimum.
- 2.
For ease notations.
- 3.
E w selects the unmeasured part of the generalized disturbance d(k).
- 4.
That is where the acronym ALINEA originates from.
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Acknowledgments
This work is connected to the scientific program of the “Development of quality-oriented and harmonized R + D + I strategy and functional model at BME” project. The authors gratefully acknowledge to the support by the New Széchenyi Plan (Project ID: TÁMOP-4.2.1/B-09/1/KMR-2010-0002) and by the Hungarian scientific research fund (OTKA) through grant No. CNK 78168. This work has been partially supported by Chalmers’ new initiatives in Transportation, therefore B. Kulcsár acknowledges the support of the Area of Advance in Transportation and Aeje.
The authors would like to address special thanks to the head of Systems and Control Research Group, Professor József Bokor for his unique support of this research.
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Luspay, T., Péni, T., Kulcsár, B. (2012). Constrained Freeway Traffic Control via Linear Parameter Varying Paradigms. In: Mohammadpour, J., Scherer, C. (eds) Control of Linear Parameter Varying Systems with Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1833-7_18
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