Progress has been made along all main directions of the proposal, and in two cases breakthrough results have been achieved:
1) Scalable methods for control synthesis in infrastructure networks:
New scalable control‐synthesis methods have been developed by mathematically exploiting properties of symmetry and monotonicity. After successfully addressing several important special cases, a major breakthrough in 2024 demonstrated that all these cases can be unified within a single framework built around the concept of positive cones. Classical linear–quadratic control theory appears as a special case, while additional exploitation of symmetry and sign constraints yields further subclasses with significantly more efficient algorithms.
2) Learning and adaptation under adversarial disturbances:
Methods for learning and adaptation have been developed under the assumption of adversarial disturbances. This led to a notable breakthrough in 2020, where the standard Riccati equation for optimal robust control was extended to produce rigorous bounds for the robustness and performance of adaptive feedback loops. The result was presented at the field’s main venue, the L4DC (Learning for Dynamics and Control) Symposium 2021. Follow-up work explored several directions, including optimality, scalability, regret analysis, and state estimation. In particular, a refinement of the initial result showed how randomized control laws naturally emerge as mixed strategies in minimax dynamic games.
3) Decomposable certificates for robustness verification:
The study of decomposable certificates for robustness verification was conducted in synergy with a project funded by the European Space Agency, where machine-learning-based components for space missions must be certified before launch. New certificates based on Integral Quadratic Constraints were developed for neural-network components used within dynamic feedback systems.
4) Applications in district heating networks:
Applications in district heating have been investigated to inspire and create synergies with the theoretical research. The main focus has been on networks operating close to their capacity limits. It is widely recognized that under such conditions, consumers located far from production sites are more likely to experience losses due to insufficient capacity—manifested as reduced indoor temperatures. To address this problem, we developed updated control methodologies that distribute available capacity more fairly, resulting in drastically reduced temperature losses for individual customers. Experimental verification was carried out on a test facility at Aalborg University.
Exploitation and dissemination:
Results have been published in the main conferences and journals of the field. A highlight was the plenary lecture at the IEEE Conference on Decision and Control in Singapore 2023. Another one was a keynote at the Chinese Conference on Decision and Control in Xiamen 2025. An invited review article is currently being prepared as a follow-up.
