Large-Scale Traffic Network Control Based on Convex Programming Coupled with B&B Strategy

Abstract

This paper presents a new framework for traffic flow control based on an integrated model description by means of a Hybrid Dynamical System (HDS). The geometrical information on the traffic network is characterized by a Hybrid Petri Net (HPN). Then, the algebraic behavior of traffic flow is transformed into a Mixed Logical Dynamical System (MLDS) form in order to introduce an optimization technique. These expressions involve both continuous evolution of traffic flow and event driven behavior of traffic light. HPN allows us to formulate the problem easily for complicated and large-scale traffic network due to its graphical understanding. MLDS enables us to optimize the control policy for traffic light by means of its algebraic manipulability and use of model predictive control framework. Since the behavior represented by HPN can be directly transformed into corresponding MLDS form, the seamless incorporation of two different modeling schemes provide a systematic design scenario for traffic flow control.

PWARX Traffic Network Hybrid Controller based on 0-1 Classification

“…Lastly the computational amounts are investigated in this subchapter. Table 6 compares the computational efforts of the results obtained by applying the proposed 0-1 classification based method and the MINLP controller reported in Kato et al [2006]. It is known that the solution method of the hybrid dynamical system is extremely burdensome, requiring exponential time of the binary variable number.…”

“…The traffic network control system is typical hybrid systems with nonlinear dynamics. In our previous study (Kato et al [2005], Kato et al [2006]), the traffic flow model was formulated based on the Mixed Integer Non-Linear Programming (MINLP) problem, where the mixed integer nonlinear traffic control problem is recast to the convex programming problem.…”

“…In this paper, we propose a new design method for the traffic network hybrid feedback controller. The method reported in Kato et al [2006] is an elaborate contrivance to avoid redundant introduction of binary variables. Since the output of the traffic network controller is the 0-1 binary signals, the control output is reproduced in this paper applying 0-1 classifications of the PWARX systems.…”