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Advanced nonlinear control concepts for freeway traffic networks

Kontorinaki Maria

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Summary

The continuously increasing number of vehicles in industrial countries is a major problem, which triggers congestion phenomena having negative impacts such as increased travel times and fuel consumption as well as reduced safety. Useful tools for the investigation of the congestion problem are Traffic Flow Modeling and Traffic Control. Traffic Flow Modeling targets the accurate representation of the network and traffic flow characteristics, while Traffic Control aims at improving the traffic conditions of the network and mitigating the problem of traffic congestion.Despite the continuous advances in the field of Nonlinear Systems and Control, the design and deployment of efficient control algorithms, originated from this field that can be applied for Traffic Control, remains a significant objective. Literature, so far, generally lacks methods for traffic control emanated from systematic and rigorous mathematical derivations. This is mainly due to the complexity and the strong nonlinearities of traffic flow dynamics. Practical control design approaches are often based on simplified models of the system dynamics, leading to traffic systems with suboptimal performance; nevertheless, for complex control system applications, the use of more complex models is virtually unavoidable.This thesis is one of the first attempts towards this direction. More specifically, it introduces a general class of acyclic first-order models that can be used to represent a wide variety of traffic networks, such as freeways, interconnection of freeways, urban networks and corridors; appropriate specifications on the parameter selection of these models are proposed in order to end up with models representing specific traffic networks. More specifically, the developed models correspond to large-scale discrete space-time dynamical systems that are highly nonlinear and uncertain. The assumptions surrounding the proposed modeling framework are mild enough to render the models capable of reproducing traffic flow phenomena of high interest, such as the capacity drop phenomenon and more; phenomena which cannot be represented by the classical formulation of first-order models.As a next step, this thesis investigates potential specifications that can be accommodated within the developed models so as to be able to reproduce correctly the desired traffic pattern at an active bottleneck due to on-ramp merging and the related capacity drop phenomenon. Despite the increasing interest from the research community in integrating capacity drop in first-order models, a limited number of effective approaches have been proposed, and only a few are actually tested using real traffic data to evaluate their behavior in case a bottleneck is activated. To this end, this thesis aims to fill this gap, gathering the state-of-the-art related to capacity drop modeling within first-order models, contributing also with further insights about their implications. The collected models are tested in calibration and validation using real traffic data from a freeway site in U.K.Having tested the accuracy of a part of the developed model, the overall modeling framework is utilized in order to develop a general robust model-based methodology for Traffic Control. In particular, this thesis proposes a rigorous methodology that provides explicit feedback control laws for the robust global exponential stability of any selected uncongested equilibrium point of the above networks. The stabilization is achieved by means of either vector or single Lyapunov Function criteria and Graph Theory tools and exploits several important properties of the network models. The achieved stabilization is robust with respect to the overall uncertain nature of network models when congestion phenomena are present and the uncertainty stemming from the fundamental diagram selection. Potential applications of the developed control methodology include urban and peri-urban signal control, perimeter control, ramp metering and mainline metering.Finally, by exploiting tools from the Adaptive Control field, this thesis proposes a general methodology for the development of generic adaptive control schemes, which have limited requirements with respect to the knowledge of system parameters. The application of the proposed control schemes guarantees the robust global exponential attractivity of the desired and unknown uncongested equilibrium point for the closed-loop freeway systems. The proposed adaptive control schemes are then tested with respect to their ability to be used as a real-time ramp-metering control strategy. Testing this strategy with sufficiently accurate traffic flow models, different than the ones used for its design, is deemed as an indispensable step towards potential application of the proposed methodology in the field. Appropriate realistic traffic control scenarios are constructed involving local and coordination control actions.

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