Memory-dependent optimal leader-follower control for evacuation

Abstract In this paper, a novel methodology is introduced for guided evacuation scenarios, incorporating individuals’ memory and past observations. This approach employs an optimal control strategy for the leader to guide followers from predefined initial positions to safety within a specified timeframe. The effectiveness of the guiding action is evaluated based on two key factors: flocking cohesion and rescue cost. The flocking component measures both the relative distances among followers and their proximity to the leader, ensuring coordinated movement and efficient evacuation. The proposed methodology is validated through numerical simulations. Furthermore, the necessary optimality conditions are established using Pontryagin’s Maximum Principle for nonlinear fractional optimal control problems, where the differential equation involves a general fractional operator in the Caputo sense applied to the state variable with respect to time.