论文标题
线性随机汉密尔顿系统通过互连进行最佳最佳控制
Mean Square Optimal Control by Interconnection for Linear Stochastic Hamiltonian Systems
论文作者
论文摘要
本文涉及遭受随机外力的线性随机哈密顿（LSH）系统。它们的动力学是由线性随机微分方程建模的，该方程是通过刚度，质量，阻尼和耦合矩阵参数化的。使用Inerter，Springs和Dampers讨论了此类系统的一类物理耦合。我们考虑了在两个LSH系统互连的耦合参数上最小化稳态二次成本功能的问题，其中一个扮演模拟控制器的作用。对于此均方根的最佳控制划分的最佳控制设置，我们概述了最佳的一阶必需条件，这些条件采用了以前针对约束线性二次高斯控制问题开发的变异方法。
This paper is concerned with linear stochastic Hamiltonian (LSH) systems subject to random external forces. Their dynamics are modelled by linear stochastic differential equations, parameterised by stiffness, mass, damping and coupling matrices. A class of physical couplings is discussed for such systems using inerters, springs and dampers. We consider a problem of minimising a steady-state quadratic cost functional over the coupling parameters for the interconnection of two LSH systems, one of which plays the role of an analog controller. For this mean square optimal control-by-interconnection setting, we outline first-order necessary conditions of optimality which employ variational methods developed previously for constrained linear quadratic Gaussian control problems.
