论文标题
连续时间线性随机系统具有乘法噪声的最佳协方差转向
Optimal Covariance Steering for Continuous-Time Linear Stochastic Systems With Multiplicative Noise
论文作者
论文摘要
在本文中，我们研究了有限的 - 摩尼斯最佳协方差转向问题，用于连续时线性随机系统，但均受添加剂和乘法噪声。噪声可能是连续的，也可能包含跳跃。附加噪声不取决于状态或控制，而乘法噪声的幅度与当前状态成正比。假定成本在状态和控制中都是二次的。首先，国家协方差的可控性是在温和的假设下建立的。然后，提供了转向协方差的最佳控制。最后，显示了最佳控制的存在和独特性。在此过程中，我们提供了有关矩阵riccati微分方程解决方案存在的最大间隔的独立兴趣的结果。
In this paper we study the finite-horizon optimal covariance steering problem for a continuous-time linear stochastic system subject to both additive and multiplicative noise. The noise can be continuous or it may contain jumps. Additive noise does not depend on the state or the control, whereas multiplicative noise has a magnitude proportional to the current state. The cost is assumed to be quadratic in both the state and the control. First, the controllability of the state covariance is established under mild assumptions. Then, the optimal control for steering the covariance is provided. Lastly, the existence and uniqueness of the optimal control is shown. In the process, we provide a result of independent interest regarding the maximal interval of existence of the solution to a matrix Riccati differential equation.
