Superconvergence of Online Optimization for Model Predictive Control

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 th...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2023-03, Vol.68 (3), p.1383-1398
Main Authors: Na, Sen, Anitescu, Mihai
Format: Article
Language:English
Subjects:
Algorithms
Artificial neural networks
Convergence
dynamic programming
Heuristic algorithms
model predictive control
Newton method
Newton methods
Nonlinear dynamics
online optimization
Optimization
Perturbation
Perturbation methods
Predictive control
Sensitivity analysis
Tracking errors
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3223323