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This paper presents a methodology for the computation of optimal feedback flow rates (flow velocities and flow discharges) for pedestrian evacuation from a network of corridors using network-wide pedestrian congestion data. The pedestrian flow is defined in a macroscopic sense, wherein ordinary differential equations (ODEs) for each corridor and node are obtained using the conservation of pedestrian mass. The effect of congestion on the flow velocities and discharges in the corridor and the corridor intersections is explicitly modeled. Collectively, these corridor and node equations define the state-space model of the pedestrian flow in the network. The state variables signify the congestion in a corridor or an intersection, whereas the control variables directly affect the flow velocities and the flow discharges. For this model, an optimization-based control algorithm is developed to ensure a maximum total instantaneous input discharge that is subject to tracking the optimal congestion state and boundedness of the control variables. A comparison of the simulation results in the controlled and uncontrolled scenarios shows superior performance in the controlled case due to convergence to the optimal congestion state and consistently high network input and exit discharges.Index Terms-Conservation of mass, feedback linearization, linear programming, pedestrian evacuation, traffic flow model.

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Abstract-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.