Document Type

Conference Proceeding

Publication Date

2007

Publication Title

IEEE Conference on Intelligent Transportation Systems

Publisher

Institute of Electrical and Electronics Engineers

First page number:

379

Last page number:

384

Abstract

This paper presents design of a time-optimal controller for a model representing evacuation dynamics in one dimension. The model presented here is based on the law of conservation of mass. The model is the classical one equation model for a traffic flow based on conservation of mass with a prescribed relationship between density and velocity. The equations of motion are described by nonlinear partial differential equations. We address the optimal control problem for the space discretized dynamics thus making use of nonlinear ordinary differential equations. The objective is to synthesize a nonlinear open loop controller that evacuates people in minimum time. Necessary conditions for time-optimal solution are derived. Pontryagin's minimum principle is used to arrive at a bang-bang form for optimal control.

Keywords

Control theory; Evacuation of civilians; Mathematical models; Traffic flow

Comments

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

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