Seminar Details
2020-03-03 (14:00) : Koopman operator-based identification of nonlinear ODEs and PDEs
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Mauroy, Alexandre
Abstract :
The Koopman operator provides a linear description of nonlinear systems. In this talk, we will exploit this description in the context of nonlinear identification and parameter estimation. Since the generator of the semigroup of Koopman operators is directly connected to the underlying dynamics, we will exploit the key idea that identifying the linear generator is equivalent to identifying the nonlinear dynamics. Using this systematic approach, we will report on two dual linear techniques. These techniques will be illustrated with several examples and complemented with convergence properties derived from the theory of strongly continuous linear semigroups. Finally, the proposed identification framework will be extended to nonlinear PDEs by considering Koopman operator semigroups acting on a space of nonlinear functionals.