Analysis of the optimization landscape of Linear Quadratic Gaussian (LQG) control
Analysis of the optimization landscape of Linear Quadratic Gaussian (LQG) control
复制标题
线性二次高斯 (LQG) 控制的优化景观分析
作者：
Yang Zheng;Yujie Tang;Na Li
本文从现代优化的角度回顾了经典的线性二次型高斯(LQG)控制。我们分析了LQG优化问题的两个方面：(1)镇定控制器集的连通性数学{C}_n$$Cn；(2)固定点的结构。众所周知，相似变换不会改变动态控制器的输入输出行为或LQG成本。这种通过相似变换所固有的对称性使LQG的景观非常丰富。证明了(1)镇定控制器集{C}n$Cn至多有两个路径连通分支，且它们在相似变换定义的映射下是微分同胚的；(2)在{C}n$Cn上的LQG代价函数可能存在许多不能控制和不可观测的严格次优驻点；(3)所有可控和可观测的驻点都是全局最优的，并且它们在相似变换下是相同的.这些结果对求解LQG问题的直接政策梯度方法的性能分析具有一定的指导意义。
This paper revisits the classical Linear Quadratic Gaussian (LQG) control from a modern optimization perspective. We analyze two aspects of the optimization landscape of the LQG problem: (1) Connectivity of the set of stabilizing controllers $$mathcal {C}_n$$ C n ; and (2) Structure of stationary points. It is known that similarity transformations do not change the input-output behavior of a dynamic controller or LQG cost. This inherent symmetry by similarity transformations makes the landscape of LQG very rich. We show that (1) The set of stabilizing controllers $$mathcal {C}_n$$ C n has at most two path-connected components and they are diffeomorphic under a mapping defined by a similarity transformation; (2) There might exist many strictly suboptimal stationary points of the LQG cost function over $$mathcal {C}_n$$ C n that are not controllable and not observable; (3) All controllable and observable stationary points are globally optimal and they are identical up to a similarity transformation. These results shed some light on the performance analysis of direct policy gradient methods for solving the LQG problem.
影响因子：
8.7
作者：
Maryam Fazel;Rong Ge;S. Kakade;M. Mesbahi
通讯作者：
Maryam Fazel;Rong Ge;S. Kakade;M. Mesbahi
影响因子：
2.2
作者：
Feng, Han;Lavaei, Javad
通讯作者：
Lavaei, Javad
影响因子：
6.8
作者：
Hesameddin Mohammadi;A. Zare;M. Soltanolkotabi;M. Jovanovi'c
通讯作者：
Hesameddin Mohammadi;A. Zare;M. Soltanolkotabi;M. Jovanovi'c