Hierarchical decision making problems, such as bilevel programs and Stackelberg games, are attracting increasing interest in both the engineering and machine learning communities. Yet, existing solution methods lack either convergence guarantees or computational efficiency, due to the absence of smoothness and convexity. In this work, we bridge this gap by designing a first-order hypergradient-based algorithm for Stackelberg games and mathematically establishing its convergence using tools from nonsmooth analysis. To evaluate the hypergradient, namely, the gradient of the upper-level objectve, we develop an online scheme that simultaneously computes the lower level equilibrium and its Jacobian. Crucially, this scheme exploits and preserves the original hierarchical and distributed structure of the problem, which renders it scalable and privacy-preserving. We numerically verify the computational efficiency and scalability of our algorithm on a large-scale hierarchical demand-response model.

Urban traffic congestion remains a pressing chal-lenge in our rapidly expanding cities, despite the abundance of available data and the efforts of policymakers. By leveraging behavioral system theory and data-driven control, this paper exploits the Data-enabled Predictive Control (DeePC) algorithm in the context of urban traffic control performed via dynamic traffic lights. To validate our approach, we consider a high-fidelity case study using the state-of-the-art simulation software package Simulation of Urban MObility (SUMO). Preliminary results indicate that DeePC outperforms existing approaches across various key metrics, including travel time and CO₂ emissions, demonstrating its potential for effective traffic management.

We study the problem of routing plug-in electric and conventional fuel vehicles on a city scale using incentives. In our model, commuters selfishly aim to minimize a local cost that combines travel time and the financial expenses of using city facilities, i.e., parking and service stations. The traffic authority can influence the commuters' routing choice via personalized discounts on parking tickets and on the energy price at service stations. We formalize the problem of optimally designing these monetary incentives to induce traffic decongestion as a large-scale bilevel game, where constraints arise at both levels due to the finite capacities of city facilities and incentives budget. Then, we develop an efficient scalable solution scheme with convergence guarantees based on BIG Hype, a recently-proposed hypergradient-based algorithm for bilevel games. Finally, we validate our approach via numerical simulations over the Anaheim's traffic network, showcasing its advantages in terms of traffic decongestion and scalability.

The electric power system is currently undergoing a period of unprecedented changes. Environmental and sustainability concerns lead to replacement of a significant share of conventional fossil fuel-based power plants with renewable energy sources. As a result of this energy transition, centralized bulk generation based on fossil fuel and interfaced with synchronous machines is substituted by distributed generation based on renewables and interfaced with power electronic converters. Accordingly, the entire operation of power systems is undergoing several major paradigm shifts: from decentralized device-level control, over distributed coordination of energy sources, to real-time system-level optimization, and open markets involving demand response and energy storage. In this article, we give a tutorial introduction to new and emerging thrusts in analysis, control, and optimization of future, smart, and cyber-enabled power systems. The solutions that we present tap into some recent methodological advances in control and optimization, with a focus on the analysis of multiagent decision scenarios and on the design of decentralized and networked control strategies. We cover the topics of decentralized control of power converters in low-inertia power systems, real-time control of distribution grids, optimal and distributed frequency control of transmission grids, and coordination of energy supply and demand. Throughout the article we also present worthwhile open directions for future research.