My interests

My interests include mostly geometric structures related to Physics and Control Theory, in particular, Lie algebroids and their generalizations. My results in this field include: developing Optimal Control Theory in the framework of almost-Lie algebroids [1,2], describing Jacobi vector fields for Lagrangian and Hamiltonian systems on algebroids [3] and developing an algebroid framework for higher-order Lagrangian mechanics and variational calculus [4,7,13]. I also applied an algebroid-inspired approach to the problem of comparison of constraints dynamics in classical mechanics obtaining new results for Chaplygin systems [8,14]. I am also interested in geometry of graded bundles [9,11].

Recently I switched my interest back to classical Control Theory, developing a contact-theoretic version of the Pontryagin Maximum Principle [10]. Now my efforts concentrate on applications of this approach to sub-Riemannian geodesic problems [10,12,B,C].

I collaborate mostly with prof. Janusz Grabowski (IM PAN), prof. Witold Respondek (INSA Rouen) and dr Mikołaj Rotkiewicz (University of Warsaw).

Preprints

Publications

  1. M. Jóźwikowski, W. Respondek
    A comparison of vakonomic and nonholonomic dynamics with applications to non-invariant Chaplygin systems
    J. Geom. Mech. 11 (2019) pp. 77-122; arxiv link

  2. M. Jóźwikowski, M. Rotkiewicz
    Higher-Order Analogs of Lie Algebroids via Vector Bundle Comorphisms
    SIGMA Symmetry Integrability Geom. Methods Appl. 14 (2018), 135; arxiv link
  3. M. Jóźwikowski, W. Respondek
    Why are normal sub-Riemannian extremals locally minimizing?
    Differential Geom. Appl. 60 (2018) pp. 174-189; arxiv link; YT presentation
  4. J. Grabowski, M. Jóźwikowski, M. Rotkiewicz
    Duality for graded bundles
    Rep. Math. Phys. 80 (2017) pp. 115-41; arxiv link
  5. M. Jóźwikowski, W. Respondek
    A contact covariant approach to optimal control with applications to sub-Riemannian geometry
    Math. Control Signals Systems 28 (2016) pp. 1-47; arxiv link; YT presentation part 1 and part 2
  6. M. Jóźwikowski, M. Rotkiewicz
    A note on actions of some monoids
    Differential Geom. Appl. 47 (2016) pp. 212-245; arxiv link; audioslides
  7. M. Jóźwikowski, W. Respondek
    A comparison of vakonomic and nonholonomic dynamics for systems on Lie groups
    IFAC-PapersOnLine 48 (2015) pp. 81-86
  8. M. Jóźwikowski, M. Rotkiewicz
    Models for higher algebroids
    J. Geom. Mech. 7 (2015) pp. 317-359; arxiv link(extended version)
  9. J. Tafel, M. Jóźwikowski
    New solutions of initial conditions in general relativity
    Class. Quantum Gravity 31 (2014) 115001; arxiv link
  10. A.M. Pyziel, A.W. Demiaszkiewicz, M. Jóźwikowski
    Coccidia (Apicomplexa: Eimeriidae) of the lowland Europeanbison Bison bonasus bonasus (L.)
    Vet. Par. 202 (2014) pp. 138-144
  11. M.Jóźwikowski, M. Rotkiewicz
    Bundle-theoretic methods for higher-order variational calculus
    J. Geom. Mech. 6 (2014) pp. 99-120; arxiv link
  12. M. Jóźwikowski
    Jacobi vector fields for Lagrangian systems on algebroids
    Int. J. Geom. Meth. Mod. Phys 10 (2013) 1350012; arxiv link
  13. M. Jóźwikowski
    Optimal Control Theory on almost Lie algebroids
    PhD thesis (2011); arxiv link
  14. J. Grabowski, M. Jóźwikowski
    Pontryagin maximum principle on almost Lie algebroids
    SIAM J. Contr. Opt. 49 (2011), pp. 1306-1357; arxiv link(extended version)




(C) Michał Jóźwikowski, 2016-2020