The COSMOS project tackled a fundamental challenge in control theory and engineering: designing scalable, reliable, and adaptive control for large-scale multi-agent systems where agents interact, compete, or cooperate under limited information and communication constraints. Such systems are common in emerging technologies such as smart energy grids, autonomous transportation, robotic swarms, and decentralized markets. COSMOS aimed to enable autonomous agents, each with limited knowledge, to collectively reach stable and efficient equilibria despite coupling constraints and environmental uncertainty. Centralized control methods are unsuitable due to computational bottlenecks, privacy issues, and communication overhead. Thus, COSMOS focused on distributed, model-based equilibrium-seeking and control strategies that adapt in real time. This challenge is vital for society as it supports the digital transformation of critical infrastructures and sustainable development goals. Examples include decentralized demand-response in smart grids integrating renewable energy, autonomous vehicle coordination to reduce congestion and emissions, and collaborative robotic systems. Robust and scalable control in these areas enables safer, more efficient, and cleaner systems. The overall objectives of COSMOS were to: (i) develop a rigorous framework for distributed control and learning in multi-agent systems with partial information and coupling constraints; (ii) design computationally efficient algorithms enabling agents to seek equilibria using only local information and limited communication; (iii) bridge control theory and learning to allow systems to adapt to changing environments and uncertainty; and (iv) validate these methods in realistic case studies in energy, mobility, and robotics. COSMOS delivered scientific breakthroughs, including novel equilibrium-seeking algorithms for generalized and aggregative games, guaranteeing convergence even under partial decision information and network uncertainty. The project introduced fast algorithms improving convergence rates compared to existing methods, including inertial acceleration techniques. Further advances addressed stochastic environments by developing distributed algorithms for stochastic generalized Nash equilibrium problems, enabling agents to reach equilibria despite randomness in cost functions and measurements. COSMOS also pioneered derivative-free equilibrium seeking inspired by extremum-seeking control, allowing agents to learn optimal strategies using only noisy cost observations, a breakthrough for systems lacking gradient information. These theoretical contributions were demonstrated on real-world-inspired benchmarks, such as distributed energy dispatch with demand uncertainty, game-theoretic automated lane merging, and multi-robot coordination. COSMOS outcomes were disseminated extensively through high-impact journals (e.g. IEEE Transactions on Automatic Control, Automatica) and top conferences, fostering interdisciplinary collaboration across control, optimization, and machine learning. In conclusion, COSMOS substantially advanced the control of large-scale, networked cyber-physical systems, providing scalable and adaptive solutions with strong theoretical guarantees. Its results support critical European priorities in digitalization, sustainability, and resilient infrastructure design, laying a foundation for next-generation intelligent systems.
