论文标题
对线性约束反馈综合的子策略的策略优化
Policy Optimization over Submanifolds for Linearly Constrained Feedback Synthesis
论文作者
论文摘要
在本文中，我们研究了对Schur稳定控制器的多种限制的政策优化，配备了Riemannian指标，该指标在最佳控制问题的背景下自然出现。我们提供对通用受约束的平滑成本功能的外部分析，随后促进将任何此类受限问题纳入此框架中。通过研究该歧管的二阶几何形状，我们提供了一种牛顿型算法，该算法不依赖指数映射或撤回，同时确保局部收敛保证。该算法取决于开发的稳定证书和约束的线性结构。然后，我们将方法应用于两个众所周知的约束最佳控制问题。最后，几个数值示例展示了所提出的算法的性能。
In this paper, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic analysis of a generic constrained smooth cost function, that subsequently facilitates subsuming any such constrained problem into this framework. By studying the second order geometry of this manifold, we provide a Newton-type algorithm that does not rely on the exponential mapping nor a retraction, while ensuring local convergence guarantees. The algorithm hinges instead upon the developed stability certificate and the linear structure of the constraints. We then apply our methodology to two well-known constrained optimal control problems. Finally, several numerical examples showcase the performance of the proposed algorithm.
