Global exponential stabilization of freeway models

Abstract

This work is devoted to the construction of feedback laws, which guarantee the robust global exponential stability of the uncongested equilibrium point for general discrete-time freeway models. The feedback construction is based on a control Lyapunov function approach and exploits certain important properties of freeway models. The developed feedback laws are tested in simulation, and a detailed comparison is made with an existing feedback law reported in the literature and employed in practice. The robustness properties of the corresponding closed-loop system with respect to measurement errors are also studied.

Global exponential stabilisation of acyclic traffic networks

“…The provided results generalize some of the results provided in [13] (see Remark 5 and Remark 6 in the following sections) and can be used for ramp-metering control of freeway networks. Preliminary testing and comparison with other existing sophisticated control strategies, provided in [13], demonstrate the efficacy of the proposed methodology as a ramp metering strategy for freeways. However, the present generalized methodology can also be used as perimeter control strategy as well as for arterial (or corridor) networks with arbitrary topology that contain no cycles.…”

“…Particular emphasis is given in this study to traffic networks for which a plethora of diverse infrastructures can be addressed on the basis of a unifying modeling approach (see for example [5]- [7]). More specifically, traffic networks can be modelled as urban road networks consisting of interconnected links which are modelled as store-and-forward components [8] or cell-transmission links [9]; large urban networks consisting of smaller homogeneous sub-networks [10]; freeway networks consisting of series of links, which are modelled, e.g., via general discretized LWR (Lighthill-Whitham-Richards) models [11]- [13] or its simplified CTM (Cell Transmission Model) version [14]; large mixed (corridor) networks consisting of urban and freeway links [15].…”

Global exponential stabilization of freeway models

“…Assumption (H), has non-trivial consequences. A list of the most important consequences can be found in [15]. These consequences play a crucial role at the proof of Theorem 3.1, which is the main result of this work.…”

“…All following tests of the proposed regulator (13) A comparison of the proposed feedback regulator (13) was made with the Random Located Bottleneck (RLB) PI regulator, which was proposed in [28] and is one of the very few comparable feedback regulators that has been employed in field operations [25]. Essentially, the RLB PI regulator for system reflects the parallel operation of five bounded PI-type regulators, one for each cell (see [15] for a detailed representation of the exact equations and the selection of the parameters for RLB PI).…”

“…Due to space limitations all proofs are omitted and can be found in [15]. Definitions and Notation Throughout this manuscript, we adopt the following notation and terminology: …”