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Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems
Yiheng Lin · Yang Hu · Guanya Shi · Haoyuan Sun · Guannan Qu · Adam Wierman

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 $O(\lambda^k T)$, where $\lambda < 1$ 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: $1 + O(\lambda^k)$. 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.

Author Information

Yiheng Lin (California Institute of Technology)
Yang Hu (Tsinghua University, Tsinghua University)
Guanya Shi (Caltech)

PhD student in machine learning and robotics

Haoyuan Sun (California Institute of Technology)
Guannan Qu (California Institute of Technology)
Adam Wierman (Caltech)

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