My current research interests are the analysis of control and random dynamical systems in Reproducing Kernel Hilbert Spaces in view of developing data-based methods for the analysis and prediction of random dynamical systems and control strategies for nonlinear systems on the basis of observed data (rather than a pre-described model). I am particularly interested in developing a qualitative theory for dynamical systems in reproducing kernel Hilbert spaces with applications to systems with critical transitions.
In general, my research interests lie at the intersection(s) of:
* Control Theory
* Deterministic Dynamical Systems
* Learning Theory/Machine Learning
* Random Dynamical Systems
with a particular emphasis on the following problems:
- Kernel Methods for Dynamical Systems (and, in general, the intersection of the fields of Machine Learning and Dynamical Systems, click here and here for more details about this research direction).
- Control Theory from a Dynamical Systems Theory point of view (Dynamical Theory of Control)
Hamzi B, Kuehn C, Mohamed S, 2019, A note on kernel methods for multiscale systems with critical transitions, Mathematical Methods in the Applied Sciences, Vol:42, ISSN:0170-4214, Pages:907-917
Bouvrie J, Hamzi B, 2017, KERNEL METHODS FOR THE APPROXIMATION OF NONLINEAR SYSTEMS, Siam Journal on Control and Optimization, Vol:55, ISSN:0363-0129, Pages:2460-2492
Hamzi B, Lamb JSW, Lewis D, 2015, A Characterization of Normal Forms for Control Systems, Journal of Dynamical and Control Systems, Vol:21, ISSN:1079-2724, Pages:273-284
Bouvrie J, Hamzi B, 2012, Empirical Estimators for Stochastically Forced Nonlinear Systems: Observability, Controllability and the Invariant Measure, Proc. American Control Conference (ACC)