Research Interests:

Analysis and Classification of Nonlinear Phenomena in Non Smooth Systems
The classification of bifurcations in piecewise smooth systems, such as C-bifurcations or border-collisions and grazing bifurcations, is the subject of much on-going research. These systems are used to model a large variety of engineering systems, such as power electronic circuits and vibro-impacting machines. Hence, the understanding of the role played by nonsmooth phenomena such as sliding and grazing in organising their dynamics be of immediate relevance in several engineering applications. My research is oriented towards both the theoretical classification of bifurcations in nonsmooth systems and applications to engineering systems such as Power Converters and Relay Feedback Systems.

Sliding and Multisliding Bifurcations
We have recently discovered a novel class of bifurcations in nonsmooth dynamical systems which give rise to periodic solutions lying partly within the system discontinuity set. The analysis of these phenomena is currently under investigation. For further details, please download the relevant preprints from this publication list.

Control and Synchronization of Continuous-Time Chaotic Systems
We are currently working on the application of modified model reference adaptive controllers (MRAC) to the control and synchronization of chaotic systems. The main idea is to exploit some features of chaos in order to increase the performance of the control scheme. Good results have been obtained by exploiting the boundedness of chaotic attractor (for more information look here).

MCS (Minimal Control Synthesis) Control of Nonlinear Systems
 MCS control was first introduced in 1990 by Prof. D. P. Stoten and Dr. H. Benchoubane at the Department of Mechanical Engineering of the University of Bristol, UK. This strategy has been successfully applied to the control of several systems (electrical motors, robotic manipulators etc.). An extension of it to nonlinear systems is currently under investigation as well as its performance in controlling and synchronizing chaotic systems.

Applications of Nonlinear Dynamics to Power Electronics
The analysis of DC-DC converters as well as that of many power electronics systems have shown that, under certain conditions, they can exhibit many different complex behaviours. An investigation of the different bifurcations and regimes is not a simple task to perform due to the fact that these systems are PWL (Piece-Wise Linear). Using a rigourous nonlinear dynamics approach, we are studying new ways of controlling and analysing their dynamical behaviour and while outlining the important role played by nonsmooth phenomena in organising their dynamical behaviour (for more info see my article on UK-NLN News or refer to my publications).

Bifurcation Tailoring and application to Aircraft flight dynamics
Together with my colleagues Mark Lowenberg (Dept of Aerospace Engineering, Bristol) and David Stoten (Dept of Mechanical Engineering, Bristol), I am currently involved on a research project aimed at developing new advanced control schemes for the control of bifurcations in aircraft flight dynamics. Guy Charles (PG) and Dr Xiaofan Wang (Research Assistant) are currently actively involved in this project (for further details have a look at the AeroChaos Group Website).

Current PhD students and PostDocs