Superconvergence of Online Optimization for Model Predictive Control

• 成果类型: Article
• 署名作者: Na, Sen; Anitescu, Mihai
• 署名单位: University of Chicago; United States Department of Energy (DOE); Argonne National Laboratory
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3223323
• 发表日期: 2023
• 页码: 1383-1398
• 关键词: convergence; optimization; Perturbation methods; Artificial neural networks; Heuristic algorithms; Predictive control; sensitivity analysis; dynamic programming; model predictive control; Newton method; online optimization

摘要

We develop a one-Newton-step-per-horizon, online, lag-L, model predictive control (MPC) algorithm for solving discrete-time, equality-constrained, nonlinear dynamic programs. Based on recent sensitivity analysis results for the target problems class, we prove that the approach exhibits a behavior that we call superconvergence; that is, the tracking error with respect to the full-horizon solution is not only stable for successive horizon shifts, but also decreases with increasing shift order to a minimum value that decays exponentially in the length of the receding horizon. The key analytical step is the decomposition of the one-step error recursion of our algorithm into algorithmic error and perturbation error. We show that the perturbation error decays exponentially with the lag between two consecutive receding horizons, whereas the algorithmic error, determined by Newton's method, achieves quadratic convergence instead. Overall this approach induces our local exponential convergence result in terms of the receding horizon length for suitable values of L. Numerical experiments validate our theoretical findings.