Speaker: Vincent Roulet

Title: Complexity Bounds of Iterative Linearization Algorithms for Discrete-Time Nonlinear Control

Abstract: We revisit the nonlinear optimization approach to discrete-time nonlinear control and optimization algorithms based on iterative linearization. While widely popular in many domains, these algorithms have mainly been analyzed from an asymptotic viewpoint. We establish non-asymptotic complexity bounds and global convergence for a class of generalized Gauss-Newton algorithms relying on iterative linearization of the nonlinear control problem, henceforth calling iterative linear quadratic regulator or differential dynamic programming algorithms as subroutines. The sufficient conditions for global convergence are examined for multi-rate sampling schemes given the existence of a feedback linearization scheme. We illustrate the algorithms in synthetic experiments and provide a software library based on reverse-mode automatic differentiation to reproduce the numerical results.