This book is a comprehensive, self-contained guide to generalized Nash equilibrium (GNE) seeking methods for population games focused on optimizing the control of large-scale complex systems (LSCSs). It equips readers with the tools needed to model and solve non-cooperative multi-agent interactions using GNE methods. This provides a novel framework for tackling real-world problems like congestion management, energy systems, and dynamic resource allocation. The approaches in this book will benefit both researchers and practitioners because, by framing optimization-based control tasks as GNE problems and relying on the population games framework, they enable more robust, scalable solutions to challenges involving LSCSs.

The book is structured to guide readers from foundational concepts such as variational inequalities and dissipativity theory, to advanced topics like the design of evolutionary and payoff dynamics models for distributed systems. The clear progression from theory to application is enhanced by numerous hands-on examples and fully documented Python code allowing readers to replicate and customize the book's simulations for deeper understanding. Features of the text include:

• detailed illustrations of theoretical concepts,
• solutions to practical problems and
• a unique focus on integrating game theory with optimization-based control.
  This blend of rigorous theory and practical application makes this book a valuable resource for both students and professionals in the field of control systems and multi-agent decision-making.

Guides readers from the basics of theory to advanced applications Presents self-contained introduction to generalized Nash equilibrium problems in large-scale multi-agent systems Provides hands-on numerical examples with Python code for easy validation, replication, and customization

Autorentext

Doctor Juan Martinez-Piazuelo has made notable contributions to the research and development of optimization-based control strategies for large-scale complex systems using game-theoretical approaches. His expertise spans evolutionary game theory, generalized Nash equilibrium problems, and distributed optimization, all focused on large-scale, non-cooperative multi-agent systems with real-world applications. His research has been widely published in high-impact scientific journals and presented at prestigious international conferences. Professor Carlos Ocampo-Martinez has been deeply engaged in research and development in the management and control of large-scale complex systems, particularly in the domains of water and energy. His work spans evolutionary game theory, model predictive control, and distributed optimization techniques for managing complex networks. With a strong focus on real-world applications, he has published over a hundred of high-impact journal articles, covering topics such as decentralized control for urban water and energy systems, predictive control of complex networks, and the management of clean energy production. Additionally, he has authored and edited several influential books with Springer, focusing on advanced control strategies for large-scale systems. Professor Nicanor Quijano is an expert in the modeling and control of distributed network optimization systems, particularly those that are utilized in the fields of agriculture, energy, and urban drainage systems. His research has mostly concentrated on topics such as real-time management of urban drainage and irrigation systems, dynamic population games for optimal dispatch in hierarchical microgrid control, and the dispatch of distributed generators employing population dynamics. His knowledge in these areas provides relevant insights into the issues and solutions connected with integrating energy vectors as well as the water-energy-food nexus, which is paramount in this sort of research problem. His work has been published in a number of peer-reviewed journals.

Inhalt

Introduction.- Delta Dissipative Dynamical Systems.- Population Games, GNE Problems, and Dynamics.- On the Design of EDM-PDM Pairs for GNE Seeking.- An Analogy-Based Approach to Dynamic Resource Allocation Problems.- Appendices.