Optimal parking management of connected autonomous vehicles: A control-theoretic approach

In this paper we develop a continuous-time stochastic dynamic model for the optimal parking management of connected autonomous vehicles (CAVs) in the presence of multiple parking lots within a given area. Inspired by the well-known Lotka-Volterra equations, a mathematical model is developed to explicitly incorporate the interactions among those parking garages under consideration. Time-dependent parking space availability is considered as the system state, while the dynamic price of parking is naturally used as the control input which can be properly chosen by the parking garage operators from the admissible set. By regulating parking rates, the total demand for parking can be distributed among the set of parking lots under question. Further, we formulate an optimal control problem (called Bolza problem) with the objective of maintaining the availability (managing the demand) of each parking garage at a desired level, which could potentially reduce traffic congestion as well as fuel consumption of CAVs. Based on the necessary conditions of optimality given by Pontryagin's minimum principle (PMP), we develop a computational algorithm to address the nonlinear optimization problem and formally prove its convergence. A series of Monte Carlo simulations is conducted under various scenarios and the corresponding optimization problems are solved determining the optimal pricing policy for each parking lot. Since the stochastic dynamic model is general and the control inputs, i.e., parking rates, are easy to implement, it is believed that the procedures presented here will shed light on the parking management of CAVs in the near future.