Periodic Reporting for period 4 - COSMOS (Game theoretic Control for Complex Systems of Systems)
Okres sprawozdawczy: 2023-08-01 do 2025-01-31
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.
Within COSMOS, significant progress was made in developing distributed algorithms and control strategies for equilibrium seeking in multi-agent systems governed by game-theoretic interactions. A foundational contribution was the design of fully distributed equilibrium-seeking algorithms for generalized Nash games with coupling constraints. These algorithms employ fixed-step proximal point methods with operator-theoretic foundations, providing linear convergence guarantees under strong monotonicity conditions. The introduction of inertial acceleration and over-relaxation variants further enhanced convergence speed, surpassing classical projected-gradient approaches. COSMOS also developed continuous-time primal-dual controllers enabling multi-integrator agents to converge to equilibria using only local information and partial knowledge of others’ decisions. These controllers were extended to nonlinear feedback-linearizable dynamics, broadening practical applicability. To address uncertainty and stochasticity in real-world applications, the project introduced the first distributed algorithms for stochastic generalized Nash equilibrium problems. These methods combine proximal splitting with pseudogradient sampling, ensuring almost sure convergence to stochastic generalized Nash equilibria despite noisy or incomplete data. A major advance was the creation of derivative-free learning algorithms inspired by extremum-seeking control theory. These enable agents to reach generalized Nash equilibria using only noisy cost measurements, without requiring gradient information, a key capability for practical systems with limited sensing or unknown models. The algorithms were validated in diverse application contexts, including distributed energy management in smart grids under renewable generation uncertainty, decentralized traffic merging scenarios, and heterogeneous multi-robot coordination using local sensing and communication. Numerical simulations and case studies demonstrated robustness, scalability, and practical viability. Dissemination activities included numerous publications in top-tier journals such as IEEE Trans. Automatic Control and Automatica, and presentations at international conferences. These efforts fostered collaborations with academic partners, enhancing impact and opening avenues for technology transfer.
COSMOS made significant advances beyond the existing state of the art in distributed equilibrium seeking for multi-agent systems. Prior methods often required two-layer iterative schemes with diminishing step sizes or global parameter knowledge, limiting scalability and practical deployment. COSMOS replaced these with single-layer, fixed-step proximal algorithms providing linear convergence guarantees, representing a notable theoretical and practical improvement. The project pioneered the first distributed algorithms for stochastic generalized Nash equilibrium problems under mere monotonicity assumptions. This filled a crucial gap by enabling agents to operate reliably under uncertainty and stochastic disturbances with minimal information requirements. In addition, COSMOS introduced derivative-free equilibrium seeking methods based on extremum-seeking control, allowing agents to learn equilibria using only function evaluations without gradient access. This approach expanded applicability to systems with unknown dynamics or partial model information, a capability absent in previous work. Furthermore, COSMOS extended equilibrium-seeking algorithms to time-varying communication networks, developing dynamic tracking proximal-gradient methods that maintain convergence despite changing network topology, addressing practical challenges in real-world multi-agent coordination. Overall, these contributions enhanced robustness, scalability, and adaptability of distributed equilibrium-seeking methods, bridging theory and practice and opening new research directions at the intersection of control, optimization, and learning.