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Optimal Control and Maximum Principle in (B)-Spaces. Examples for PDE in (H)-Spaces and ODE in $${{\mathbb{R}}^{n}}$$
Doklady Mathematics ( IF 0.6 ) Pub Date : 2019-11-01 , DOI: 10.1134/s1064562419060048
A. I. Prilepko

Observation and control problems in Banach (B)-spaces are investigated. A criterion for controllability and optimal controllability is formulated on the basis of the BUME method and the monotone mapping method. An inverse controllability problem is introduced, and an abstract maximum principle is formulated in (B)-spaces. For PDE in Hilbert (H)-spaces and for ODE in $${{\mathbb{R}}^{n}}$$, an integral maximum principle is proved and an optimality system is presented.

中文翻译:

(B)-空间中的最优控制和最大原理。(H)-Spaces 中的 PDE 和 $${{\mathbb{R}}^{n}}$$ 中的 ODE 示例

研究了 Banach (B) 空间中的观测和控制问题。在BUME方法和单调映射方法的基础上,制定了可控性和最优可控性的判据。引入了逆可控性问题,并在(B)空间中制定了抽象的最大值原理。对于希尔伯特(H)-空间中的偏微分方程和$${{\mathbb{R}}^{n}}$$中的常微分方程,证明了积分极大值原理并给出了一个最优系统。
更新日期:2019-11-01
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