论文标题
部分可观测时空混沌系统的无模型预测
Douglas--Rachford algorithm for control-constrained minimum-energy control problems
论文作者
论文摘要
由于其简单性和效率，分裂和投影类型算法已应用于许多优化问题，但是将这些算法应用于最佳控制并不常见。在本文中，我们利用道格拉斯 - - rachford（DR）算法来解决控制受控制的最小能源最佳控制问题。我们不是传统的方法将问题离散并使用大规模有限维数值优化技术解决问题，而是将问题分为两个子问题，并使用博士算法在这两个子问题的解决方案集的相交中找到一个最佳点，从而为原始问题提供了解决方案。我们得出了投影的一般表达方式，并提出了一种数值方法。我们获得了纯，不足，严重和过度抑制的谐波振荡器的投影仪的分析闭合形式表达式。我们说明了我们的方法不仅解决这些示例问题，而且还解决了一个具有挑战性的机床操纵器问题。通过数值案例研究，我们探索并提出了算法参数值的理想范围，该算法参数产生较少数量的迭代。
Splitting and projection-type algorithms have been applied to many optimization problems due to their simplicity and efficiency, but the application of these algorithms to optimal control is less common. In this paper we utilize the Douglas--Rachford (DR) algorithm to solve control-constrained minimum-energy optimal control problems. Instead of the traditional approach where one discretizes the problem and solves it using large-scale finite-dimensional numerical optimization techniques we split the problem in two subproblems and use the DR algorithm to find an optimal point in the intersection of the solution sets of these two subproblems hence giving a solution to the original problem. We derive general expressions for the projections and propose a numerical approach. We obtain analytic closed-form expressions for the projectors of pure, under-, critically- and over-damped harmonic oscillators. We illustrate the working of our approach to solving not only these example problems but also a challenging machine tool manipulator problem. Through numerical case studies, we explore and propose desirable ranges of values of an algorithmic parameter which yield smaller number of iterations.
