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

Lin, Yiheng and Hu, Yang and Sun, Haoyuan and Shi, Guanya and Qu, Guannan and Wierman, Adam (2021) Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems. . (Unpublished)

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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. Under more assumptions on the terminal costs, we also show that 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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper ItemBook Chapter
Lin, Yiheng0000-0001-6524-2877
Sun, Haoyuan0000-0002-6203-0198
Shi, Guanya0000-0002-9075-3705
Qu, Guannan0000-0002-5466-3550
Additional Information:Yiheng Lin, Yang Hu, Haoyuan Sun, Guanya Shi, and Guannan Qu contributed equally to this work.
Record Number:CaltechAUTHORS:20210716-225843457
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109905
Deposited By: George Porter
Deposited On:16 Jul 2021 23:22
Last Modified:12 Oct 2022 23:24

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