最优控制
分段
Riccati方程
数学优化
线性二次调节器
数学
动态规划
随机微分方程
随机控制
参数统计
控制理论(社会学)
差速器(机械装置)
代数Riccati方程
微分方程
控制(管理)
计算机科学
应用数学
工程类
数学分析
统计
人工智能
航空航天工程
标识
DOI:10.1016/j.chaos.2023.114258
摘要
In recent decades, stochastic control systems have been widely used in industrial production, biomedicine, aerospace, military strategy and so on. In this paper, an approximate optimal strategy derived from a stochastic linear quadratic (SLQ) optimal control problem is considered, and a piecewise parameterization and optimization (PPAO) method is proposed. Firstly, using the principle of dynamic programming, the control form of SLQ optimal control problem is relevant to a Riccati differential equation. It is well known that the Riccati differential equation is difficult to be solved analytically. Thus, we present a PPAO method for finding an approximate optimal strategy for stochastic control problems. Here, a piecewise parameter control can be obtained by solving first-order differential equations rather than Riccati differential equations. Finally, the inventory control problems with different dimensions are used to justify the feasibility of PPAO method, and the results compared with the original optimal control are given. The results show that parametric control greatly simplifies the control form, and a small model error is ensured.
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