Koopman Operator Theory for Nonautonomous and Stochastic Systems (CROSBI ID 66247)
Prilog u knjizi | ostalo | međunarodna recenzija
Podaci o odgovornosti
Maćešić, Senka ; Črnjarić-Žic, Nelida
engleski
Koopman Operator Theory for Nonautonomous and Stochastic Systems
In practice, the dynamics of open systems subject to time-dependent or random forcing is much more present than the dynamics of autonomous systems. Therefore, extension of the Koopman operator theory and applications to such systems is of great importance. At the same time, it brings a new viewpoint to the existing theory of nonautonomous as well as random dynamical systems, particularly, with application of Koopman based data-driven algorithms. In this chapter, we first review the nonautonomous Koopman operator family based on the two standard nonautonomous dynamical system definitions: skew product and process. Then, we state basic properties of the operator and compare performance of the DMD and Arnoldi-type algorithms in the context of both definitions. In the case of the random dynamical systems (RDS), we introduce the associated stochastic Koopman operator family. We show that when RDS is Markovian, this family satisfies semigroup property and we present some properties for RDS generated by the stochastic differential equations. Finally, we discuss data-driven algorithms in the stochastic framework and illustrate their performance on numerical examples.
Koopman operator, nonautonomous systems, random dynamical system, stochastic Koopman operator, DMD algorithm, Arnoldi type algorithm
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
nije evidentirano
Podaci o prilogu
131-160.
objavljeno
10.1007/978-3-030-35713-9
Podaci o knjizi
The Koopman Operator in Systems and Control
Mauroy, Alexandre ; Mezic, Igor ; Susuki, Yoshihiko
Basel: Springer
2020.
978-3-030-35712-2
0170-8643
0170-8643
Povezanost rada
Matematika, Temeljne tehničke znanosti