Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems
Abstract
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.
Additional Information
Yiheng Lin, Yang Hu, Haoyuan Sun, Guanya Shi, and Guannan Qu contributed equally to this work.
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Additional details
- Eprint ID
- 109905
- Resolver ID
- CaltechAUTHORS:20210716-225843457
- Created
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2021-07-16Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field