Frontiers in Optimal Control: Geometry, Complexity, and Learning

Frontiers in Optimal Control: Geometry, Complexity, and Learning is a research program centered on the theory, computation, and emerging data-driven extensions of optimal control. The program focuses on how optimal decisions can be modeled, analyzed, and computed for complex dynamical systems subject to uncertainty, nonlinearity, constraints, and large-scale interactions. Rooted in the classical foundations of the field the program highlights optimal control as a unifying mathematical language for decision-making across engineering, finance, energy systems, robotics, transportation, and computational biology.

A central objective of the program is to advance optimal control beyond its traditional boundaries by connecting it with geometric, probabilistic, and learning-based methods. Particular emphasis will be placed on optimal transport and Schrödinger bridge formulations, mean-field games and control, infinite-dimensional stochastic control, dual control, PAC-Bayes perspectives on learning-based control, and the geometric and computational analysis of singular optimal control. Across these themes, the program addresses some of the field’s most pressing challenges: scalability in high dimensions, control under uncertainty, decentralized decision-making in networks, and the development of computational methods that retain rigorous performance guarantees.

By bringing together researchers from control theory, optimization, probability, numerical analysis, and machine learning, the program aims to strengthen the mathematical foundations of modern optimal control while fostering new approaches to computation and feedback design. Through research talks, thematic discussions, and focused workshops, it will create an interdisciplinary environment for developing the next generation of optimal control theory and algorithms.