We consider control from the perspective of competitive analysis. Unlike much prior work on learning-based control, which focuses on minimizing regret against the best controller selected in hindsight from some specific class, we focus on designing an online controller which competes against a clairvoyant offline optimal controller. A natural performance metric in this setting is competitive ratio, which is the ratio between the cost incurred by the online controller and the cost incurred by the offline optimal controller. Using operator-theoretic techniques from robust control, we derive a computationally efficient state-space description of the the controller with optimal competitive ratio in both finite-horizon and infinite-horizon settings. We extend competitive control to nonlinear systems using Model Predictive Control (MPC) and present numerical experiments which show that our competitive controller can significantly outperform standard $H_2$ and $H_{\infty}$ controllers in the MPC setting.

翻译：我们从竞争分析的角度来考虑控制问题。与以往许多以学习为基础的控制工作不同的是,我们侧重于尽量减少对从某个特定类别后视所选最佳控制者的遗憾,我们侧重于设计一个在线控制者,该控制者与离线最佳控制者竞争。这一背景下的自然性能衡量标准是竞争性比率,即在线控制者所产生成本与离线最佳控制者所产生成本之比。我们利用强控的操作者理论技术,得出一个计算高效的状态空间描述,对控制者进行计算,在限定的和无限的视距设置中,该控制者具有最佳的竞争比率。我们利用模型预测控制(MPC)将竞争控制扩大到非线性系统,并提出数字实验,表明我们的竞争性控制者在MPC设置中可大大超过标准$H$2美元和$Hinfty}控制者。