Time-Optimal Control for One Dimensional Evacuation System

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.