Imperial College London
Dr Boumediene Hamzi

DrBoumedieneHamzi

Faculty of Natural Sciences, Department of Mathematics

Visiting Reader
 
 
 
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Contact

 

+44 (0)20 7594 1424b.hamzi Website

 
 
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Location

 

654Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

59 results found

Bouvrie J, Hamzi B, 2010, Balanced reduction of nonlinear control systems in reproducing kernel Hilbert space, Pages: 294-301

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where balanced truncation may be carried out implicitly. This leads to a nonlinear reduction map which can be combined with a representation of the system belonging to a reproducing kernel Hilbert space to give a closed, reduced order dynamical system which captures the essential input-output characteristics of the original model. Empirical simulations illustrating the approach are also provided. ©2010 IEEE.

Conference paper

Bouvrie J, Hamzi B, 2010, Balanced Reduction of Nonlinear Control Systems in Reproducing Kernel Hilbert Space

We introduce a novel data-driven order reduction method for nonlinear controlsystems, drawing on recent progress in machine learning and statisticaldimensionality reduction. The method rests on the assumption that the nonlinearsystem behaves linearly when lifted into a high (or infinite) dimensionalfeature space where balanced truncation may be carried out implicitly. Thisleads to a nonlinear reduction map which can be combined with a representationof the system belonging to a reproducing kernel Hilbert space to give a closed,reduced order dynamical system which captures the essential input-outputcharacteristics of the original model. Empirical simulations illustrating theapproach are also provided.

Conference paper

Hamzi B, Krener AJ, 2007, The Controlled Center Systems, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 52, Pages: 2188-2192, ISSN: 0018-9286

Journal article

Hamzi B, Krener AJ, Kang W, 2006, The controlled center dynamics of discrete time control bifurcations, SYSTEMS & CONTROL LETTERS, Vol: 55, Pages: 585-596, ISSN: 0167-6911

Journal article

Krener AJ, Kang W, Hamzi B, Tall Iet al., 2006, Control singularities of codimensions one and two, Pages: 245-250, ISSN: 1474-6670

In this paper, we classify singularities of control systems of codimension one and two.

Conference paper

Kang W, Hamzi B, Krener AJ, 2006, On the Convergence and Behavior of Three Dimensional Normal Forms, 1st IFAC Conference on the Analysis and Control of Chaotic Systems

Conference paper

Hamzi B, Krener AJ, 2006, The controlled center systems, 45th IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 6414-6418, ISSN: 0743-1546

Conference paper

Hamzi B, Kang W, Krener AJ, 2005, Stabilization of discrete time systems with a fold or period doubling control bifurcations, Pages: 240-245, ISSN: 1474-6670

For nonlinear control systems with uncontrollable linearization around an equilibrium, the local asymptotic stability of the linear controllable directions can be easily achieved by linear feedback. Therefore we expect that the stabilizability of the whole system should depend on a reduced order model whose stabilizability depends on the linearly uncontrollable directions. The controlled center dynamics technique, introduced by the authors in a previous article, formalizes this intuition. in this paper we apply this approach to stabilize discrete-time systems with a fold or period-doubling control bifurcations. Copyright © 2005 IFAC.

Conference paper

Krener AJ, Kang W, Hamzi B, Tall Iet al., 2005, Low codimension control singularities for single input nonlinear systems, Conference in Honor of Clyde Martins 60th Birthday on New Directions and Applications in Control Theory, Publisher: SPRINGER-VERLAG BERLIN, Pages: 181-192, ISSN: 0170-8643

Conference paper

Hamzi B, Kang W, Krener AJ, 2005, The controlled center dynamics, MULTISCALE MODELING & SIMULATION, Vol: 3, Pages: 838-852, ISSN: 1540-3459

Journal article

Krener AJ, Kang W, Hamzi B, Tall IAet al., 2005, Low codimension control singularities for single input nonlinear systems, Publisher: Springer Verlag, ISBN: 9783540239536

This volume contains a collection of papers in control theory and applications presented at a conference in honor of Clyde Martin on the occasion of his 60th ...

Book

Hamzi B, Kang W, Krener AJ, 2004, The Controlled Center Dynamics of discrete time control bifurcations, Pages: 669-674, ISSN: 1474-6670

In this paper we introduce the "Controlled Center Dynamics" for nonlinear discrete time systems with control bifurcations. Then we use this approach to stabilize discrete-time systems with a transcontrollable bifurcation.

Conference paper

Hamzi B, Kang W, Barbot JP, 2004, Analysis and control of Hopf bifurcations, SIAM JOURNAL ON CONTROL AND OPTIMIZATION, Vol: 42, Pages: 2200-2220, ISSN: 0363-0129

Journal article

Hamzi B, Kang W, 2003, Resonant terms and bifurcations of nonlinear control systems with one uncontrollable mode, SYSTEMS & CONTROL LETTERS, Vol: 49, Pages: 267-278, ISSN: 0167-6911

Journal article

Hamzi B, Krener AJ, 2003, Practical stabilization of systems with a fold control bifurcation, Symposium on New Trends in Nonlinear Dynamics and Control, and Their Applications, Publisher: SPRINGER-VERLAG BERLIN, Pages: 37-48, ISSN: 0170-8643

Conference paper

Hamzi B, Tall IA, 2003, Normal forms for nonlinear discrete time control systems, 42nd IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 1357-1361

Conference paper

Hamzi B, Kang W, Krener AJ, 2003, Control of center manifolds, 42nd IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 2065-2070

Conference paper

Hamzi B, 2002, Quadratic stabilization of nonlinear control systems with a double-zero bifurcation, 5th IFAC Symposium on Nonlinear Control Systems, Publisher: PERGAMON-ELSEVIER SCIENCE LTD, Pages: 161-166, ISSN: 0962-9505

Conference paper

Hamzi B, Barbot JP, Monaco S, Normand-Cyrot Det al., 2002, Normal forms versus Naimark-Sacker bifurcation control, 5th IFAC Symposium on Nonlinear Control Systems, Publisher: PERGAMON-ELSEVIER SCIENCE LTD, Pages: 167-172, ISSN: 0962-9505

Conference paper

Hamzi B, 2002, Analysis and stabilization of nonlinear systems with a zero-Hopf control bifurcation, 41st IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 3912-3917, ISSN: 0191-2216

Conference paper

Hamzi B, Monaco S, Normand-Cyrot D, 2002, Quadratic stabilization of systems with period doubling bifurcation, 41st IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 3907-3911, ISSN: 0743-1546

Conference paper

Hamzi B, Barbot JP, Monaco S, Normand-Cyrot Det al., 2001, Nonlinear discrete-time control of systems with a Naimark-Sacker bifurcation, SYSTEMS & CONTROL LETTERS, Vol: 44, Pages: 245-258, ISSN: 0167-6911

Journal article

Hamzi B, 2001, Some results on inverse optimality based designs, SYSTEMS & CONTROL LETTERS, Vol: 43, Pages: 239-246, ISSN: 0167-6911

Journal article

Hamzi B, Praly L, 2001, Ignored input dynamics and a new characterization of control Lyapunov functions, AUTOMATICA, Vol: 37, Pages: 831-841, ISSN: 0005-1098

Journal article

Hamzi B, Kang W, 2001, Resonant terms in a class of systems with stationary bifurcations, 40th IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 722-727, ISSN: 0191-2216

Conference paper

Hamzi B, Kang W, Barbot JP, 2000, On the control of Hopf bifurcations, 39th IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 1631-1636, ISSN: 0743-1546

Conference paper

Hamzi B, Barbot JP, Kang W, 1999, Bifurcation for discrete time parameterized systems with uncontrollable linearization, Pages: 684-688, ISSN: 0191-2216

In this paper we study bifurcation problems for discrete time parameterized nonlinear control systems which possess one uncontrollable mode in their linearization. First, we classify equilibrium sets, then we study controllability and stabilizability near bifurcation points.

Conference paper

Hamzi B, Barbot JP, Kang W, 1999, Normal forms for discrete time parameterized systems with uncontrollable linearization, Pages: 2035-2038, ISSN: 0191-2216

In this paper we determine quadratic normal forms for discrete time parameterized nonlinear control systems which possess one uncontrollable mode in their linearization. These normal forms are the simplest elements of the equivalence class of the group of transformations by quadratic change of coordinates and quadratic feedback.

Conference paper

Hamzi B, Barbot JP, Kang W, 1998, Bifurcation and topology of equilibrium sets for nonlinear discrete time control systems, IFAC Symposium on Nonlinear Control Systems Design, Publisher: PERGAMON PRESS LTD, Pages: 31-35

Conference paper

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