Existence and Optimal Control Results for Second-Order Semilinear System in Hilbert Spaces

被引：37

作者：

Shukla, Anurag ^{[1
]}

Patel, Rohit ^{[1
]}

机构：

[1] Rajkiya Engn Coll Kannauj, Dept Appl Sci, Kannauj 209732, India

来源：

CIRCUITS SYSTEMS AND SIGNAL PROCESSING | 2021年 / 40卷 / 09期

关键词：

Mild solution; Second-order system; Sine and cosine family; Optimal control; EVOLUTION-EQUATIONS;

D O I：

10.1007/s00034-021-01680-2

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

The article provides sufficient conditions for the existence of optimal control for second-order semilinear control system in Hilbert spaces. We consider the integral cost function as J(z, v) "= integral(T)(0) L(tau,zv(tau), v(tau)dt, subject to the equations z ''(tau) = Az(tau) + Bv(tau) + g(tau, z(tau)): 0 < tau <= T z(0) = z(0) z'(0) = z(0) Next, we discuss the existence and the uniqueness of mild solutions for the above proposed problem using Banach fixed point theorem. The stated Lagrange's problem admits at least one optimal control pair under certain assumptions. Finally, the validation of theoretical results is provided through an example.

引用

页码：4246 / 4258

页数：13

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