Superconvergence of Online Optimization for Model Predictive Control

Na, Sen; Anitescu, Mihai

doi:10.1109/tac.2022.3223323

Superconvergence of Online Optimization for Model Predictive Control

Journal Article · Fri Nov 18 00:00:00 EST 2022 · IEEE Transactions on Automatic Control

DOI:https://doi.org/10.1109/tac.2022.3223323· OSTI ID:2335712

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Univ. of Chicago, IL (United States)
Argonne National Laboratory (ANL), Argonne, IL (United States)

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, while 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. In conclusion, numerical experiments validate our theoretical findings.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 2335712

Journal Information:: IEEE Transactions on Automatic Control, Journal Name: IEEE Transactions on Automatic Control Journal Issue: 3 Vol. 68; ISSN 0018-9286

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

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