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Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems

Lin, Yiheng and Hu, Yang and Shi, Guanya and Sun, Haoyuan and Qu, Guannan and Wierman, Adam (2021) Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems. In: Advances in Neural Information Processing Systems 34 (NeurIPS 2021). Advances in Neural Information Processing Systems , pp. 1-12. ISBN 9781713845393.

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We study predictive control in a setting where the dynamics are time-varying and linear, and the costs are time-varying and well-conditioned. At each time step, the controller receives the exact predictions of costs, dynamics, and disturbances for the future k time steps. We show that when the prediction window k is sufficiently large, predictive control is input-to-state stable and achieves a dynamic regret of O(λ^kT), where λ < 1 is a positive constant. This is the first dynamic regret bound on the predictive control of linear time-varying systems. We also show a variation of predictive control obtains the first competitive bound for the control of linear time-varying systems: 1 + O(λ^k). Our results are derived using a novel proof framework based on a perturbation bound that characterizes how a small change to the system parameters impacts the optimal trajectory.

Item Type:Book Section
Related URLs:
URLURL TypeDescription ItemDiscussion Paper
Lin, Yiheng0000-0001-6524-2877
Shi, Guanya0000-0002-9075-3705
Sun, Haoyuan0000-0002-6203-0198
Qu, Guannan0000-0002-5466-3550
Wierman, Adam0000-0002-5923-0199
Additional Information:Yiheng Lin, Yang Hu, Haoyuan Sun, Guanya Shi, and Guannan Qu contributed equally to this work. This work was supported by NSF grants CNS-2106403, NGSDI-2105648, and AitF-1637598, with additional support from Amazon AWS, PIMCO, and the Resnick Sustainability Insitute. Yiheng Lin was supported by Kortschak Scholars program.
Group:Resnick Sustainability Institute
Funding AgencyGrant Number
Amazon Web ServicesUNSPECIFIED
Resnick Sustainability InstituteUNSPECIFIED
Kortschak Scholars ProgramUNSPECIFIED
Record Number:CaltechAUTHORS:20221012-231545995
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:117377
Deposited By: George Porter
Deposited On:13 Oct 2022 18:40
Last Modified:13 Oct 2022 18:40

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