Optimal Control of Pedestrian Evacuation in a Corridor

The problem of optimal control of pedestrian evacuation from a corridor has been addressed. The corridor has been treated as a one dimensional link in the building network from which the pedestrians have to be evacuated. The governing flow equations are derived from the discretized continuity equation and a flow density relation for the pedestrian flow. Necessary conditions for the optimal control of these differential equations are developed using the calculus of variations method. The necessary conditions constitute a 2 point boundary value problem that has to be solved for the state, the co-state and the optimal control. Method of steepest descent is used to solve this problem. Numerical results are presented in the end for a test case.