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

• 成果类型: Article
• 署名作者: Liu, Fengjiao; Tsiotras, Panagiotis
• 署名单位: University System of Georgia; Georgia Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3402059
• 发表日期: 2024
• 页码: 7247-7254
• 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

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.