论文标题
可行和巨大的动态输出反馈控制的连通性以及稳健性约束
Connectivity of the Feasible and Sublevel Sets of Dynamic Output Feedback Control with Robustness Constraints
论文作者
论文摘要
本文认为，使用$ \ Mathcal {H} _ \ Infty $ robustness约束的线性动态输出反馈控制的优化景观。我们考虑所有稳定的全订单动力控制器的可行集，该集合满足了额外的$ \ MATHCAL {H} _ \ infty $ robustness约束。我们表明，这个$ \ MATHCAL {H} _ \ infty $约束的集合最多具有两个路径连接的组件，这些组件在通过相似性转换定义的映射下是差异的。我们的证明技术利用了$ \ Mathcal {H} _ \ infty $ Control中的变量的经典变化来建立一个主观映射，该映射是从凸影投影到$ \ MATHCAL {H} _ \ infty $ contration $ contration set的集合。此证明想法也可以用来建立严格的Sublevel线性二次高斯（LQG）控制和最佳$ \ MATHCAL {H} _ \ infty $ CONTROM的相同拓扑属性。我们的结果为基于梯度的政策搜索而言为强大的控制问题带来了积极的消息。
This paper considers the optimization landscape of linear dynamic output feedback control with $\mathcal{H}_\infty$ robustness constraints. We consider the feasible set of all the stabilizing full-order dynamical controllers that satisfy an additional $\mathcal{H}_\infty$ robustness constraint. We show that this $\mathcal{H}_\infty$-constrained set has at most two path-connected components that are diffeomorphic under a mapping defined by a similarity transformation. Our proof technique utilizes a classical change of variables in $\mathcal{H}_\infty$ control to establish a subjective mapping from a set with a convex projection to the $\mathcal{H}_\infty$-constrained set. This proof idea can also be used to establish the same topological properties of strict sublevel sets of linear quadratic Gaussian (LQG) control and optimal $\mathcal{H}_\infty$ control. Our results bring positive news for gradient-based policy search on robust control problems.
