NCSU Differential Equations/Nonlinear Analysis Seminars

Location and Time: SAS 4201, Wednesday 15:00 -16:00

Organizers: Lorena Bociu, Patrick Combettes, Ryan Murray, and Khai T. Nguyen

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Wednesday, Oct 7, 15:00-16:00, Zoom: Link

Speaker: Dante Kalise, Imperial College London
Title: Stabilising Feedback Laws for Mean-Field Control and Global Optimisation
Abstract: We look at feedback control of large systems of interacting particles. In the mean-field limit, this becomes the stabilisation of McKean–Vlasov PDEs. When the free energy is non-convex, the target states may be unstable or reached only very slowly. We linearise the Wasserstein gradient flow around the target and act on its finitely many slow or unstable modes. This gives a Riccati feedback law that locally exponentially stabilises the full nonlinear dynamics, and it can be seen as a local convexification of the free energy. The same idea applies to consensus-based optimisation (CBO), which is itself a McKean–Vlasov particle system whose target is the global minimiser. We treat global optimisation as an optimal stabilisation problem and add a stabilising feedback, obtained from the associated HJB equation, to the CBO dynamics. Convergence becomes faster and more robust, including in high dimensions.
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