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Explore a novel measure-theoretic approach to deterministic control in this 48-minute research seminar that reinterprets classical nonlinear control problems through the lens of optimal transport theory. Discover how transport theory, traditionally used for controlling probability distributions in multi-agent systems and generative modeling, can be leveraged in reverse to provide fresh insights into fundamental control concepts. Learn about new transport-based characterizations that offer linear global tests for controllability and stabilizability, while addressing classical obstructions like Brockett's condition through innovative approaches. Examine computational methods that bridge modern machine learning techniques in generative modeling with traditional control tools, demonstrating the practical applications of this theoretical framework. Gain understanding of how this lifted, measure-theoretic formulation opens new avenues for analyzing and solving deterministic control problems, with implications for uncertainty propagation and multi-agent control systems.
