One Critical Case in Singularly Perturbed Control Problems

8th Workshop on Multi-Rate Processes and Hysteresis;HSFS Workshop (Hysteresis and Slow-Fast Systems)

Sobolev, Vladimir^1

Samara National Research University, Moskovskoye shosse, 34, Samara

443086, Russia^1

关键词: Control problems;    Critical case;    Integral manifold;    Optimal control problem;    Singularly perturbed;    Singularly perturbed problem;    Standard theories;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/811/1/012017/pdf
DOI  :  10.1088/1742-6596/811/1/012017

来源: IOP

【 摘 要 】

The aim of the paper is to describe the special critical case in the theory of singularly perturbed optimal control problems. We reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory. We illustrate our approach by an example of control problem.