Sophie Hall

Automatic Control Laboratory, ETH Zürich

Monday, November 25, 2024, 10:30

SR-02-012 Building 102

Sophie Hall from ETH Zurich will introduce game theory for control systems and present her latest research results.

Timeline:

1. 10:30-12:00 Tutorial
2. 12:30-13:30 Lunch at IPM 
3. 13:30-14:30 Scientific Talk

Tutorial: From Prisoner’s Dilemma to Generalized Nash Equilibrium Problems – An Introduction to Game Theory in Control

Part 1 (10:30-11:15): High-level overview of fundamental Game Theory concepts

It gives a high-level overview of the fundamental game theory concepts relevant to control engineers, such as best response dynamics, Nash equilibrium, hierarchy in games, and classification of games such as zero-sum, potential, and aggregative games.

Part 2 (11:15-12:00): Introduction to Generalized Nash Equilibrium Problems (GNEPs) 

How do we model the self-interest of agents in control problems? How do we legislate temperance in control? We will discuss Generalized Nash Equilibrium Problems, how to solve them, their theoretical properties, and how they allow us to model three different couplings that may arise in control: 

1. Cost coupling (i.e., resource pricier with higher usage)

2. Dynamic coupling (i.e., shared infrastructure)

3. Constraint coupling (i.e., shared resources are finite).  Finally, we will compare GNEPS played in receding horizon to MPC. 

    

Scientific Talk (13:30 - 14:30): Stability Guarantees for Receding Horizon Games

Game-theoretic MPC (or Receding Horizon Games) is an emerging control methodology for multi-agent systems that generates control actions by solving a dynamic game with coupling constraints in a receding-horizon fashion. This control paradigm has recently received increasing attention in various application fields, including robotics, autonomous driving, traffic networks, and energy grids, due to its ability to model the competitive nature of self-interested agents with shared resources while incorporating future predictions, dynamic models, and constraints into the decision-making process.

 In this talk, we will present two different approaches to formally prove the stability of Receding Horizon Games. The first approach relies on a potential structure of the game, corresponding to symmetric pricing, and ensures practical stability and recursive feasibility relying on tools from economic MPC. The second approach is the first formal stability analysis, which also holds for non-potential games and is based on dissipativity and monotone operator theory. Specifically, we derive LMI-based certificates that ensure the asymptotic stability of the Receding Horizon Game and are numerically verifiable.