4 Presentations

• 
  03:30 PM - 03:55 PM

  Mean field games and model predictive control for charging electric vehicles in solar powered parking lots

  • Samuel M. Muhindo, presenter, Polytechnique Montréal
  • Roland Malhamé, GERAD - Polytechnique Montréal
  • Geza Joos, McGill University

  We propose a strategy, with concepts from Mean Field Games and Model Predictive Control, to coordinate the charging of a large population of battery electric vehicles in a parking lot powered by solar energy and managed by an aggregator. An autoregressive–moving average model is used for solar forecasting, while a Poisson distribution (with finite population) model of vehicle arrivals and departures is assumed. Both model forecasts are updated as
  fresh observations become available. Standard Mean Field Game theory cannot be applied in view of the fluctuating number of interacting agents. For this reason, a novel heuristic strategy is developed based on the computation of a fictitious initial mean state of charge effectively resulting in part of the solar energy being reserved for incoming vehicles. The goal is to share the solar energy so as to minimize the standard deviation of the state of charge of batteries when vehicles leaving the parking lot, while maintaining some fairness and decentralization criteria. Numerical results are reported.

• 
  03:55 PM - 04:20 PM

  Mean field regrets in discrete time games

  • Ziteng Cheng, presenter, University of Toronto
  • Sebastian Jaimungal, University of Toronto

  We use mean field games (MFGs) to investigate approximations of $N$-player games with uniformly symmetrically continuous heterogeneous closed-loop actions. Centered around the notion of regret, we conduct non-asymptotic analysis on the approximation capability of MFGs from the perspective of state-action distributions without requiring the uniqueness of equilibria. Under suitable assumptions, we first show that scenarios in the $N$-player games with large $N$ and small average regrets can be well approximated by approximate solutions of MFGs with relatively small regrets. We then show that $\delta$-mean field equilibria can be used to construct $\varepsilon$-equilibria in $N$-player games. If time permits, we will discuss the incorporation of risk aversion into MFGs.

• 
  04:20 PM - 04:45 PM

  A Scalable Dynamic Collective Choice Model with Congestion Effects

  • Noureddine Toumi, presenter,
  • Roland Malhamé, GERAD - Polytechnique Montréal
  • Jérôme Le Ny, GERAD - Polytechnique Montréal

  In today's world, understanding the mechanisms behind collective decision-making holds significant importance across various domains, including public opinion shaping and commuter route selection within transportation networks. However, analyzing decision-making may be challenging, particularly in large-scale systems. In this context, we introduce a new scalable and analytically tractable dynamic collective choice model with congestion effects. Our model involves a group of agents choosing between multiple destinations and cooperating to minimize a common quadratic average cost. By exploiting the model structure, we transform the solution search problem into a parametric optimization problem over feasible agent-to-destination proportions. This reduces the computational complexity when compared to the exhaustive solution search, which entails solving an exponentially increasing number of linear quadratic regulator problems. We also define an appropriate system of limiting equations, whose solution can be used to efficiently approximate the optimal solution as the number of agents increases. This approximate solution further reduces the amount of computation and information exchange needed by agents to compute their control strategies, which is a valuable asset for practical applications.

• 
  04:45 PM - 05:10 PM

  Multi-Marginal Optimal Transport for the Coverage Control Problem with Mobile Robot Teams

  • Jérôme Le Ny, presenter, GERAD - Polytechnique Montréal

  In mobile robotics, the coverage control problem involves deploying a group of robots and distributing tasks in the environment to each robot. We consider an extension of this problem to scenarios where tasks are handled by teams of robots from different classes, potentially with constraints on each robot's utilization rate. Leveraging a connection with the theory of multi-marginal optimal transport, we show that the optimization of the assignment maps and utilization rates are convex problems, which can be addressed by finite-dimensional deterministic or stochastic optimization methods. The last subproblem of optimizing the robot states or locations is in general non convex, but local optimization techniques like deterministic or stochastic gradient descent, akin to Lloyd's method used for the standard coverage control problem, can be applied. Numerical simulations will showcase the formulation and some features of the proposed algorithms.