Keywords: Decentralized control and large-scale systems, Multi-agent systems, Smart cities and power systems
Abstract: The gain theory surrounding the small gain theorem has been around for almost six decades, achieving tremendous success in its applications to robust control and networked control systems. Over the past six years, a phase theory has emerged and begun to flourish in many subfields of the system and control community. Serving as a long-missing companion to the well established gain theory, the phase theory has been continuously enriched by studies on matrices, operators, multivariable linear systems, nonlinear systems, and more. While these studies have largely focused on abstract monolithic models, the occasion of NecSys 25 presents an opportune moment to ask: What can the phase theory offer in the stability analysis of various dynamical networks?

The first step in answering this overarching question is to recognize the unique challenges posed by networked systems. These challenges—--such as massive scale, heterogeneity---call for general control-theoretic tools that are scalable, decentralized, and customizable to accommodate ad-hoc demands across diverse and complex network configurations. Phase theory meets these requirements by offering a quantifiable and scalable framework for analyzing network stability, generating conditions that guarantee safe plug-and-play network operations. Furthermore, its integration with the gain theory can boost its strength and reduce the conservatism of the aforementioned conditions.

In the proposed mini-workshop, we curate four presentations that address both the societal and technical challenges faced by modern dynamical networks. The speakers will offer insights into how phase theory can be harnessed for decentralized stability analysis of complex networks, by showcasing several cutting-edge applications in instances like power networks, multi-agent systems, and communication networks. Through this mini-workshop, we also aim to pave the way for further research opportunities at the intersection of phase theory and network analysis/design, as well as its application to a broader range of networked systems.

Keywords: Infinite-dimensional systems, Game theory and network games, Decentralized control and large-scale systems
Abstract: This workshop presents recent advances in dynamics, control, and games on large-scale graphs and their graph limit counterparts (including graphons and graphexes). The study of complex multi-agent systems has benefited from the abstraction of large networks via graph limits, which allow for tractable analysis and scalable control and learning algorithms. The speakers will introduce new theoretical frameworks and algorithmic tools for modeling, controlling, and learning over both dense and sparse graph sequences.

The talks will cover several key directions: new models for mean field control on sparse graphs using local weak convergence (Kai Cui), structural and probabilistic properties of graphons for Hamiltonian decompositions (Xudong Chen), Laplacian-based consensus dynamics over signed graphons (Paolo Frasca), stochastic discrete-time graphon field games with closed-form solutions (Alex Dunyak), and a unifying framework for mean field control and games over both dense and sparse networks via the graphexon formalism (Peter E. Caines and Minyi Huang). Together, these presentations highlight the evolving frontier at the intersection of control theory, network science, and game theory, with the aim of bridging local and global properties of complex systems across graph topologies.

Keywords: Smart cities and power systems, Robotics and multi-agent systems, Distributed optimization
Abstract: Advanced control and optimization methodologies are pivotal in addressing the growing complexity of practical applications. In smart cities, control and optimization algorithms reduce energy consumption, and enhance public safety through real-time monitoring and adaptive management. For aero-engines, precision control ensures stability and efficiency under dynamic flight conditions, balancing performance with stringent safety requirements. Similarly, smart grids rely on advanced control strategies to stabilize power distribution, integrate renewable energy sources, and mitigate cascading failures. These applications underscore the critical role of control theory in enabling resilient, efficient, and sustainable operations across interconnected systems.

Despite their transformative impact, scaling advanced control and optimization solutions remains challenging. In smart cities, heterogeneous sensor networks and timevarying demands necessitate robust controllers that adapt to incomplete or noisy data. Aero-engine control requires handling nonlinear dynamics and extreme operating conditions, demanding high-fidelity modeling and real-time computational efficiency. For power grids, the integration of decentralized renewable energy sources introduces stability risks, calling for distributed control and optimization architectures that ensure synchronization without centralized coordination. Future research must prioritize adaptive control frameworks, enhanced robustness to uncertainties, and scalable algorithms tailored to large-scale, multidomain systems. By addressing these challenges, advanced control will continue to drive innovation in critical industrial systems, bridging theoretical rigor with real-world practicality.

In the proposed mini-workshop, we curate four presentations that address both the theory and technical challenges in practical applications. The speakers will offer insights into how advanced control and optimization methods can be harnessed for smart city, power systems, and aerospace. The proposed mini-workshop aims to trigger new theoretical and technological advances for modern industrial systems.