Superconvergence of Online Optimization for Model Predictive Control

نویسندگان

چکیده

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 the target problems class, we prove that approach exhibits behavior call superconvergence ; is, tracking error with respect to full-horizon solution is not only stable successive horizon shifts, but also decreases increasing shift order minimum value decays exponentially in length of receding horizon. The key analytical step decomposition one-step recursion our into xmlns:xlink="http://www.w3.org/1999/xlink">algorithmic error and xmlns:xlink="http://www.w3.org/1999/xlink">perturbation . show perturbation lag between two consecutive horizons, whereas algorithmic error, determined by Newton's method, achieves quadratic convergence instead. Overall this induces local exponential result terms suitable values Numerical experiments validate theoretical findings.

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ژورنال

عنوان ژورنال: IEEE Transactions on Automatic Control

سال: 2023

ISSN: ['0018-9286', '1558-2523', '2334-3303']

DOI: https://doi.org/10.1109/tac.2022.3223323