论文标题
离散时间线性随机系统的最佳协方差转向
Optimal Covariance Steering for Discrete-Time Linear Stochastic Systems
论文作者
论文摘要
在本文中，我们研究了在有限的时间范围内指导离散时间线性随机系统的状态协方差的最佳控制问题。首先，我们确定了二次成本函数的最佳控制定律的存在和独特性。然后，我们显示了最佳平均值和协方差转向问题的分离。我们还开发了有效的计算方法来解决最佳控制定律，该法被确定为半定计划的解决方案。通过数值示例证明了所提出的方法的有效性。在此过程中，我们还为矩阵riccati差异方程式获得了一些新的理论结果，这可能具有独立的兴趣。
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a quadratic cost function. Then, we show the separation of the optimal mean and the covariance steering problems. We also develop efficient computational methods to solve for the optimal control law, which is identified as the solution to a semi-definite program. The effectiveness of the proposed approach is demonstrated through numerical examples. In the process, we also obtain some novel theoretical results for a matrix Riccati difference equation, which may be of independent interest.
