Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems
Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems
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发表时间：
2021-06
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通讯作者：
Yiheng Lin;Yang Hu;Haoyuan Sun;Guanya Shi;Guannan Qu;A. Wierman
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作者：
Yiheng Lin;Yang Hu;Haoyuan Sun;Guanya Shi;Guannan Qu;A. Wierman
我们在动态是时变且线性的，成本是时变且良态的设定下研究预测控制。在每个时间步，控制器接收未来$k$个时间步的成本、动态和扰动的精确预测。我们表明当预测窗口$k$足够大时，预测控制是输入到状态稳定的，并实现了$O(\lambda^k T)$的动态 regret（遗憾值），其中$\lambda<1$是一个正常数。这是关于线性时变系统预测控制的第一个动态遗憾界。在关于终端成本的更多假设下，我们还表明预测控制获得了线性时变系统控制的第一个竞争界：$1 + O(\lambda^k)$。我们的结果是使用一种基于扰动界的新颖证明框架推导出来的，该扰动界描述了系统参数的微小变化如何影响最优轨迹。
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. 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: $1 + O(\lambda^k)$. 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.