Slow Integral Manifolds and Control Problems in Critical and Twice Critical Cases

7th International Workshop on MUlti-Rate Processes & HYSteresis; 2nd International Workshop on Hysteresis and Slow-Fast Systems

Sobolev, Vladimir^1

Department of Technical Cybernetics, Samara State Aerospace University (SSAU), 34, Moskovskoye shosse, Samara

443086, Russia^1

关键词: Control problems;    Differential systems;    Integral manifold;    Normally hyperbolic;    Perturbation problems;    Singularly perturbed;    Singularly perturbed problem;    Standard theories;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/727/1/012017/pdf
DOI  :  10.1088/1742-6596/727/1/012017

来源: IOP

【 摘 要 】

We consider singularly perturbed differential systems in cases where the standard theory to establish a slow integral manifold existence does not work. The theory has traditionally dealt only with perturbation problems near normally hyperbolic manifold of singularities and this manifold is supposed to isolated. Applying transformations 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 several examples.