Nonlinear Identification and Control using Convex Optimization

Two of the basic problems in systems & control are (i) obtaining a model (e.g. system identification) and (ii) using this model to synthesize a feedback controller. For nonlinear systems both of these problems remain very challenging computationally. This talk will describe recent results on nonlinear stabilization in terms of "control contraction metrics". These results generalize well-known LMI methods for linear systems, and have a simple and appealing geometrical interpretation. We will also describe related methods for nonlinear (and linear) system identification using Lagrangian relaxation and sum-of-squares programming. Results using a specialized algorithms will be shown that significantly outperform general-purpose solvers such as Sedumi and Mosek. Extensions to scalable distributed algorithms for networked systems will be briefly discussed.