Description:

This talk presents three connected topics, starting with contraction theory as a practical tool for analyzing stability using one-sided Lipschitz constants. We then discuss how time-varying contracting systems can be used to solve and track solutions of convex optimization problems, with performance linked to system properties and problem dynamics. Finally, we show how these methods can be applied to control, using real-time optimization to design feedback controllers and safety filters that ensure stability and respect constraints. The twin goals are to highlight how contraction theory provides a consistent framework linking system analysis, optimization, and control design — and to survey recent advances on contractivity as a robust, computationally efficient, and modular approach to stability in dynamical systems.

Francesco Bullo, Distinquished Professor, Department of Mechanical Engineering, University of California, Santa Barbara

Host: Arthur Montanari