Bio: Giovanni Fantuzzi is an EPSRC Doctoral Prize Fellow in the Department of Aeronautics, Imperial College London, from which he received an MEng degree in 2014 and a PhD in 2018. During his PhD he developed optimization-based methods and software for studying stability and time-averaged properties of dynamical systems, with applications to fluid flows. In 2015 he was awarded a Geophysical Fluid Dynamics Fellowship from Woods Hole Oceanographic Institution and was subsequently a Research Assistant at the University of Oxford, where he worked on fast algorithms for structured semidefinite programmes and sum-of-squares optimization. His current research spans fluid dynamics and convex optimization, and he is especially interested in scalable convex approaches to hydrodynamic analysis.

Beyond numerical integration: studying nonlinear dynamics with polynomial optimization

Systems characterized by complex nonlinear dynamics lie at the heart of 21st century technology. Examples are turbulent flows in the transport and aviation industries, smart energy networks, and models of cell dynamics used in synthetic biology. Quantitative analysis of such systems using direct numerical simulations sometimes requires prohibitively large computational resources even when one is interested only in some average properties, such as mean power consumption, because all time and length scales across which the system evolves must be resolved. In addition, while numerical simulations offer detailed information starting from a specific initial state, they cannot provide safety-critical performance or stability guarantees that hold for all possible initial states. In this talk, I will describe an alternative approach to studying nonlinear systems with polynomial dynamics, which combines ideas from Lyapunov’s stability theory with recent numerical tools for polynomial optimization. In particular, I will present a range of examples that demonstrate how this optimization-based method enables the efficient algorithmic construction of stability certificates and the computation of rigorous bounds on performance-related system properties. Other applications, including optimal control and disturbance amplification analysis, will be discussed along with open problems and future research directions.