关于Hilbert空间中双线性种群动力学系统最优控制的新讨论

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Modelling and Control Pub Date : 2022-02-25 DOI:10.15388/namc.2022.27.26407

Rohit Patel, A. Shukla, J. Nieto, V. Vijayakumar, S. Jadon

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引用次数: 9

摘要

本文的目的是利用半群理论研究具有扩散的双线性种群动力学系统的最优控制问题。通过识别状态、控制和相应的函数空间，将具有非局部出生过程的双线性种群动力学模型转化为一个标准的抽象双线性控制系统。状态空间和控制空间被假定为希尔伯特空间。半群理论是从种群算子和拉普拉斯算子的性质发展起来的。然后，利用C0半群方法、不动点定理以及其他一些关于非线性项和模型中涉及的算子的简单条件，得到了系统的最优控制结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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New discussion concerning to optimal control for semilinear population dynamics system in Hilbert spaces

The objective of our paper is to investigate the optimal control of semilinear population dynamics system with diffusion using semigroup theory. The semilinear population dynamical model with the nonlocal birth process is transformed into a standard abstract semilinear control system by identifying the state, control, and the corresponding function spaces. The state and control spaces are assumed to be Hilbert spaces. The semigroup theory is developed from the properties of the population operators and Laplacian operators. Then the optimal control results of the system are obtained using the C0-semigroup approach, fixed point theorem, and some other simple conditions on the nonlinear term as well as on operators involved in the model.

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来源期刊

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.