On the Regret of Model Predictive Control With Imperfect Inputs

Journal Article (2025)
Author(s)

C. Liu (TU Delft - Team Bart De Schutter)

S. Shi (Massachusetts Institute of Technology)

B.H.K. Schutter (TU Delft - Delft Center for Systems and Control)

Research Group
Team Bart De Schutter
DOI related publication
https://doi.org/10.1109/LCSYS.2025.3577083
More Info
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Publication Year
2025
Language
English
Research Group
Team Bart De Schutter
Volume number
9
Pages (from-to)
601-606
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Abstract

Implementing model predictive control (MPC) in practice faces many subtle but prevalent problems, including modeling errors, solver errors, and actuator faults. In essence, the real control input applied to the system always deviates from the ideal one based on a perfect controller, resulting in an imperfect controller. In this letter, we provide a general analysis to quantify the suboptimality of MPC for Lipschitz-continuous nonlinear systems due to imperfect control inputs in terms of dynamic regret. Based on a general assumption about how the imperfect controller may improve over time, sublinear regret upper bounds are established for cases where the closed-loop system under the ideal controller is Lipschitz-contractive (i.e., its Lipschitz constant is smaller than one). In addition, we also discuss how the regret scales when the closed-loop system under the oracle controller is not Lipschitz-contractive. The results provide insights into designing suitable MPC strategies, especially for learning-based MPC.