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We study predictive control in a setting where the dynamics are time-varyingand linear, and the costs are time-varying and well-conditioned. At each timestep, the controller receives the exact predictions of costs, dynamics, anddisturbances for the future $k$ time steps. We show that when the predictionwindow $k$ is sufficiently large, predictive control is input-to-state stableand achieves a dynamic regret of $O(\lambda^k T)$, where $\lambda < 1$ is apositive constant. This is the first dynamic regret bound on the predictivecontrol of linear time-varying systems. Under more assumptions on the terminalcosts, we also show that predictive control obtains the first competitive boundfor the control of linear time-varying systems: $1 + O(\lambda^k)$. Our resultsare derived using a novel proof framework based on a perturbation bound thatcharacterizes how a small change to the system parameters impacts the optimaltrajectory.

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