论文标题
基于内部模型的在线优化
Internal Model-Based Online Optimization
论文作者
论文摘要
在本文中，我们提出了一种基于模型的在线优化算法设计的方法，目的是改善解决方案轨迹（轨迹）W.R.T.的跟踪。最先进的方法。我们首先专注于具有时间变化的线性术语的二次问题，并使用数字控制工具（强大的内部模型原理）提出一种新颖的在线算法，该算法可以通过通过动力学系统对成本进行建模来实现零跟踪错误。我们证明了强烈凸和凸问题的算法的收敛性。我们进一步讨论了提出的方法对不确定性建模并量化其性能的敏感性。我们讨论了如何使用成本的近似模型将所提出的算法应用于一般（非二次）问题，并分析利用少量增益定理的收敛性。我们提出了数值结果，以证明所提出的算法的优越性能，而不是二次和非二次问题的先前方法。
In this paper we propose a model-based approach to the design of online optimization algorithms, with the goal of improving the tracking of the solution trajectory (trajectories) w.r.t. state-of-the-art methods. We focus first on quadratic problems with a time-varying linear term, and use digital control tools (a robust internal model principle) to propose a novel online algorithm that can achieve zero tracking error by modeling the cost with a dynamical system. We prove the convergence of the algorithm for both strongly convex and convex problems. We further discuss the sensitivity of the proposed method to model uncertainties and quantify its performance. We discuss how the proposed algorithm can be applied to general (non-quadratic) problems using an approximate model of the cost, and analyze the convergence leveraging the small gain theorem. We present numerical results that showcase the superior performance of the proposed algorithms over previous methods for both quadratic and non-quadratic problems.
