Research

My research has two main ingredients: Multi-timescale dynamical systems theory and control theory. I am further interested in their applications to, for example, engineering, biochemistry, neuroscience, etc.

Many complex phenomena have intrinsically many different timescales. A usual system’s approach to understand them is to separate the processes at each timescale, hoping that information of each subprocess will provide enough insight on the overall dynamics. Sometimes this approach works well, especially when the timescale separation is, in some sense, global. There are instances, however, where such an approach is not suitable. In this latter situation, the timescale separation does not persist across the phase-space and trajectories that initially evolve slowly can suddenly jump to another state. The goal of my research is to understand systems with the aforementioned behaviour and to control them. Most of the following articles show work in that direction.

Preprints, work in progress and submitted works:
  • On fast-slow consensus networks with a dynamic weight,
    HJK and Christian Kuehn.
  • A survey on the blow-up method for fast-slow systems [arXiv],
    HJK and Christian Kuehn.

  • Geometric desingularization of a biochemical oscillator,
    Hadi Tafgvafarad, HJK, Peter Szmolyan and Ming Cao.
Journals (peer-reviewed):

*CDC-XX = The contents of this paper were also selected by CDC XX Program Committee for presentation at the Conference

  1. Stabilization of a class of slow-fast control systems at non-hyperbolic points [Preprint]
    HJK
    , Jacquelien M.A. Scherpen, and D. del Puerto-Flores.
    Automatica, vol. 99, pp. 13-21, 2019.
  2. Improving the region of attraction of a non-hyperbolic point in slow-fast systems with one fast direction [Preprint]
    HJK
    and Jacquelien M.A. Scherpen.
    IEEE Control Systems Letters, vol. 2, no. 2, pp. 403-408, 2018.
  3. Parameter-robustness analysis for a biochemical oscillator model describing the social-behavior transition phase of myxobacteria
    Hadi Tafgvafarad, HJK, and Ming Cao.
    Proceedings of the Royal Society A, 2018.
  4. Model order reduction and composite control for a class of slow-fast systems around a non-hyperbolic point [Preprint]
    HJK
    and Jacquelien M.A. Scherpen.
    The IEEE Control Systems Letters, 2017.
  5. Limit sets within curves where trajectories converge to
    Pouria Ramazi, HJK and Ming Cao.
    Applied Mathematics Letters, 2017.
  6. Vibrational Stabilization by Reshaping Arnold Tongues: A Numerical Approach
    Joaquín Collado, HJK.
    Applied Mathematics, 2016.
  7. Analysis of a slow fast system near a cusp singularity [arXiv]
    HJK
    , Henk W. Broer and R. Roussarie.
    Journal of Differential Equations, 2016.
  8. Formal normal form of Ak slow-fast systems [arXiv]
    HJK.
    Comptes Rendus Mathematique, 2015.
  9. Bifurcations of a non-gravitational interaction problem
    X. Liu and HJK.
    Applied Mathematics and Computation, 2015.
  10. Polynomial normal forms of Constrained Differential Equations with three parameters [arXiv]
    HJK
    and Henk W. Broer.
    Journal of Differential Equations, 2014.
Conference proceedings (peer-reviewed):
  1. Nonlinear adaptive stabilization of a class of planar slow-fast systems at a non-hyperbolic point
    HJK
    , Jacquelien M.A. Scherpen and D. del Puerto-Flores.
    American Control Conference 2017.
  2. Stabilization of a planar slow-fast system at a non hyperbolic point
    HJK
    and Jacquelien M.A. Scherpen.
    MTNS 2016.
  3. Model order reduction of a flexible-joint robot: a port-Hamiltonian approach
    HJK
    , M. Munoz-Arias and Jacquelien M.A. Scherpen.
    NOLCOS 2016.
Others: