Probabilistic and infinite dimensional control via optimization and kernels – PIVOINE

This project aims to control systems with high model complexity, emerging from physics (PDEs) or from uncertainty quantification (stochastic processes), or both.
Motivation: A common denominator to the environmental crisis and the aritificial intelligence (AI) revolution lies in the need for safely controlling our technologies, and is well illustrated by two examples involving high model complexity control systems: (i) on the environmental side, the energy transition is key, but involves fluctuating renewable energy sources subject to uncertainties, as well as safety-critical nuclear plants; new methodologies are needed to prevent power networks overloads and support new technologies; (ii) on the AI front, fighting fake news is crucial and is mostly rooted in decisions at the level of recommendation and learning algorithms; interpreting learning and optimization algorithms as uncertain dynamical systems opens a rich field of research, at the interface between control and learning.
Approach: Project PIVOINE proposes to address these challenges by building on the concept of infinite embedding, i.e. convexification of problems by recasting them in infinite dimensional feature spaces, while keeping finite dimensional representations of solutions. Such strategy is used in moment-SoS optimization, in kernel learning and in Koopman operator control. These methods are particularly useful to address nonlinear control problems, especially when considering uncertainties and PDEs. In particular, probabilistic behaviors are well-captured in moment spaces, while PDEs are often well-posed in Hilbert spaces. Importantly, infinite embeddings appear in both model-based and data-driven control, so that they can be used on dynamic systems represented with either models or data (or both).
PIVOINE will leverage synergy between various infinite embeddings to control dynamic systems with realistic representations.