Optimal Covariance Steering for Continuous-Time Linear Stochastic Systems With Multiplicative Noise

被引：2

作者：

Liu, Fengjiao ^{[1
]}

Tsiotras, Panagiotis ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Aerosp Engn, Atlanta, GA 30332 USA

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2024年 / 69卷 / 10期

关键词：

Noise; Optimal control; Mathematical models; Differential equations; Stochastic systems; Process control; Costs; Covariance control; linear stochastic systems; Riccati differential equation; state-dependent noise;

D O I：

10.1109/TAC.2024.3402059

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this article, 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. The additive noise does not depend on the state or the control, whereas the multiplicative noise has a magnitude proportional to the current state. The cost is assumed to be quadratic in both the state and the control. The optimal control for steering the covariance from some initial to some final value is provided. Furthermore, the existence and uniqueness of the optimal control is shown. In the process, we also provide a result of independent interest regarding the maximal interval of existence of the solution of a matrix Riccati differential equation.

引用

页码：7247 / 7254

页数：8

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