Positively invariant manifolds: concept and applications

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

Sazhin, Sergei S.^1 ; Shchepakina, Elena^2 ; Sobolev, Vladimir^3

Sir Harry Ricardo Laboratories, Advanced Engineering Centre, School of Computing, Engineering and Mathematics, University of Brighton, Brighton

BN2 4GJ, United Kingdom^1

Department of Technical Cybernetics, Samara National Research University, Moskovskoye shosse, 34, Samara

443086, Russia^2

Department of Differential Equations and Control Theory, Samara National Research University, Moskovskoye shosse, 34, Samara

443086, Russia^3

关键词: Combustion pro-cess;    Conventional theory;    Integral manifold;    Invariant manifolds;    Lipschitzian;    Order reduction;    Singular perturbed system;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/811/1/012015/pdf
DOI  :  10.1088/1742-6596/811/1/012015

来源: IOP

【 摘 要 】

In many applications of the system order reduction models, including those focused on spray ignition and combustion processes, it is assumed that all functions in corresponding differential equations are Lipschitzian. This assumption has not been checked in most cases and the cases when these functions were non-Lipschitzian have sometimes been overlooked. This allows us to question the results of application of the conventional theory of integral manifolds to some such systems. The aim of this paper is to demonstrate that even in the case of singular perturbed systems with non-Lipschitzian nonlinearities the order reduction can be performed, using a new concept of positively invariant manifolds. This is illustrated by several examples including the problem of heating, evaporation, ignition and combustion of Diesel fuel sprays.