论文标题
连续时间线性随机系统具有加性噪声的最佳协方差转向
Optimal Covariance Steering for Continuous-Time Linear Stochastic Systems With Additive Noise
论文作者
论文摘要
在本文中，我们研究了如何在有限的时间间隔内最佳地指导一般连续时间线性系统的状态协方差的问题。这里的最佳性意味着使用最小的控制能达到目标状态协方差。附加噪声可能包括白色高斯噪声和突然的“跳跃噪声”的组合，这些噪声是不连续的。我们首先建立了状态协方差对线性时变随机系统的可控性。然后，我们转向最佳控制的推导，该控制需要解决两个动态耦合矩阵普通微分方程（ODE），并具有分裂边界条件。我们显示了对这些耦合矩阵ODE的解决方案的存在和唯一性，从而表明了最佳对照的耦合矩阵ODE。
In this paper, we study the problem of how to optimally steer the state covariance of a general continuous-time linear stochastic system over a finite time interval subject to additive noise. Optimality here means reaching a target state covariance with minimal control energy. The additive noise may include a combination of white Gaussian noise and abrupt "jump noise" that is discontinuous in time. We first establish the controllability of the state covariance for linear time-varying stochastic systems. We then turn to the derivation of the optimal control, which entails solving two dynamically coupled matrix ordinary differential equations (ODEs) with split boundary conditions. We show the existence and uniqueness of the solution to these coupled matrix ODEs, and thus those of the optimal control.
