Set-Theoretic Approaches in Analysis, Estimation and Control of Nonlinear Systems

This paper gives an overview of recent developments in set-theoretic methods for nonlinear systems, with a particular focus on the activities in our own research group. Central to these approaches is the ability to compute tight enclosures of the range of multivariate systems, e.g. using ellipsoidal calculus or higher-order inclusion techniques based on multivariate polynomials, as well as the ability to propagate these enclosures to enclose the trajectories of parametric or uncertain differential equations. We illustrate these developments with a range of applications, including the reachability analysis of nonlinear dynamic systems; the determination of all equilibrium points and bifurcations in a given state-space domain; and the solution of set-membership parameter estimation problems. We close the paper with a discussion about on-going research in tube-based methods for robust model predictive control.