Complexity Bounds of Iterative Linear Quadratic Optimization Algorithms for Discrete Time Nonlinear Control
Abstract
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many domains, such an approach has mainly been analyzed locally. We observe that global convergence guarantees can be ensured provided that the linearized discrete time dynamics are surjective and costs on the state variables are strongly convex. We present how the surjectivity of the linearized dynamics can be ensured by appropriate discretization schemes given the existence of a feedback linearization scheme. We present complexity bounds of algorithms based on linear quadratic approximations through the lens of generalized GaussNewton methods. Our analysis uncovers several convergence phases for regularized generalized GaussNewton algorithms.
 Publication:

arXiv eprints
 Pub Date:
 April 2022
 DOI:
 10.48550/arXiv.2204.02322
 arXiv:
 arXiv:2204.02322
 Bibcode:
 2022arXiv220402322R
 Keywords:

 Mathematics  Optimization and Control;
 68Q25;
 49M37;
 G.1.6