Boumediene Hamzi

Marie Curie Fellow

Department of Mathematics

Imperial College London

London SW7 2AZ

United Kingdom

Phone: +44(0)-207-594-1424

Fax: +44(0)-207-594-8517

Room: 620 Huxley Building

Welcome to my webpage. I am a Marie Curie Fellow at the Department of Mathematics of Imperial College. Before coming to Imperial, I was Research Assistant Professor at UCDavis (CA), then member of the Mathematical Sciences Research Institute in Berkeley (CA) and then Visiting Assistant Professor at Duke University (NC).

My research interests are

- Control Theory
- Deterministic Dynamical Systems
- Learning Theory
- Random Dynamical Systems

I am particularly interested in their intersection(s). More precisely, I am interested in the following problems:

- Data-Based Approaches for the Analysis of (Control and Random) Dynamical Systems: Control & Prediction, Model Reduction, Parameter Estimation.
- Dynamical Systems in Reproducing Kernel Hilbert Spaces
- Bifurcations for Control and Random Systems
- Equivalence and Ergodicity of Infinite-Dimensional SDEs and SPDEs
- Normal Forms for Control and Dynamical Systems.

**Selected Papers and Presentations**

- Preliminary Results on Control and Random Dynamical Systems in Reproducing Kernel Hilbert Spaces, Workshop on Parameter Estimation for Dynamical Systems (PEDS-II), EURANDOM, Eindhoven, Netherlands http://www.eurandom.nl/events/workshops/2012/PEDSII/Presentations/Hamzi.pdf
- Bouvrie J, B. Hamzi, Empirical Estimators for Stochastically Forced Nonlinear Systems: Observability, Controllability and the Invariant Measure, Proc. American Control Conference (ACC), 2012, http://arxiv.org/abs/1204.0563
- Bouvrie J, B. Hamzi, Model Reduction for Nonlinear Control Systems using Kernel Subspace Methods, 2011, submitted
- B. Hamzi, J. Lamb and D. Lewis. “On Normal Forms for Nonlinear Hamiltonian Control Systems”, presented at the 2011 SIAM Conference on Control and its Applications, Baltimore, Maryland, July 2011.
- J. Bouvrie and B. Hamzi. Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space, 48th Annual Allerton Conference on Communication, Control, and Computing, 2010. [arxiv]
- B. Hamzi, J. Lamb and D. Lewis. “A Simple Characterization of the Normal Forms for Nonlinear Control Systems”, presented at the 2009 SIAM Conference on Control and its Applications, Denver, Colorado, July 2009.
- B. Hamzi and A. J. Krener. " The Controlled Center Systems ", IEEE Transactions on Automatic Control, 2007, vol. 52, no11, pp. 2188-2192.
- B. Hamzi, A. J. Krener, W. Kang, The Controlled Center Dynamics of Discrete Time Control Bifurcations, Systems & Control Letters, Vol. 55, No. 7, 585-596, 2006.
- W. Kang, B. Hamzi, and A.J. Krener, On the Convergence and Behavior of Three Dimensional Normal Forms , Proc. of the 1st IFAC Conference on the Analysis and Control of Chaotic Systems, 2006.
- B. Hamzi, W. Kang and A. J. Krener, The Controlled Center Dynamics , SIAM J. Multiscale Modeling & Simulation, Vol. 3, No. 4, 2005, pp838-852.
- A.J. Krener, W. Kang, B. Hamzi, and I.A. Tall. Low codimension control singularities for single input nonlinear systems , in "New directions and applications in control and theory", 2005, vol. 321, pp. 181-192.
- B. Hamzi, W. Kang and J.-P. Barbot, Analysis and Control of Hopf Bifurcations , SIAM J. on Control and Optimization, Vol. 42, No. 6, pp. 2200-2220, 2004.
- B. Hamzi, W. Kang, and A. J. Krener, Stabilization of Discrete-Time Systems with a Fold or Period Doubling Control Bifurcation, Proc. of the 16th IFAC World Congress.
- B. Hamzi, W. Kang, and A. J. Krener, Control of Center Manifolds , Proc. of the 42nd IEEE Conference on Decision and Control, 2065 - 2070, 2003.
- B. Hamzi and A. J. Krener. " Practical Stabilization of Systems with a Fold Control Bifurcation " in New Trends in Nonlinear Dynamics and Control and their Application, W. Kang, C. Borges and M. Xiao eds., pp. 34-48, Springer, Berlin, 2003.
- B. Hamzi and W. Kang, Resonant Terms and Bifurcations of Nonlinear Control Systems with One Uncontrollable Mode, Systems and Control Letters, Vol. 49 (4), 2003, pp. 267-278.
- B. Hamzi and I. A. Tall, Normal Forms for Discrete-Time Control Systems , Proc. of the 42nd IEEE Conference on Decision and Control, 2, 1357 - 1361, 2003.
- B. Hamzi, Analysis and Stabilization of nonlinear systems with a zero-Hopf control bifurcation, Proc. of the 41st IEEE Conference on Decision and Control, 4, pp. 3912-3917, 2002.
- B. Hamzi, S. Monaco, and D. Normand-Cyrot, Quadratic stabilization of systems with period doubling bifurcation, Proc. of the 41st IEEE Conference on Decision and Control, 4, pp. 3907-3911, 2002.
- B. Hamzi, J.-P. Barbot, S. Monaco, and D. Normand-Cyrot, Nonlinear Discrete-Time Control of Systems with a Naimark-Sacker Bifurcation, Systems and Control Letters, 44, pp. 245-258, 2001.
- B. Hamzi, Quadratic Stabilization of Nonlinear Control Systems with a Double-Zero Control Bifurcation, Proc. of the 5th IFAC symposium on Nonlinear Control Systems, pp. 161-166, 2001.
- B. Hamzi, Some Results on Inverse Optimality Based Designs , Systems and Control Letters, 43, pp. 239-246, 2001.
- B. Hamzi and L. Praly, Ignored Input Dynamics and a new Characterization of Control Lyapunov Functions , Automatica, 37, pp. 831-841, 2001.

**Teaching**: Spring 2010: MAT 132S , MAT 131