53 citations · 83 across the 6 of their papers we have counts for
6 papers
A note on actions of some monoids
Michal Jozwikowski, Mikolaj Rotkiewicz
Smooth actions of the multiplicative monoid of real numbers on manifolds lead to an alternative, and for some reasons simpler, definition of a vector bundle, a…
A contact covariant approach to optimal control with applications to sub-Riemannian geometry
Michał Jóźwikowski, Witold Respondek
We discuss contact geometry naturally related with optimal control problems (and Pontryagin Maximum Principle). We explore and expand the observations of [Ohsawa, 2015], providing…
Jacobi vector fields for Lagrangian systems on algebroids
Michal Jozwikowski
We study the geometric nature of the Jacobi equation. In particular we prove that Jacobi vector fields (JVFs) along a solution of the Euler-Lagrange (EL) equations are themselves s…
Optimal Control Theory on almost-Lie Algebroids
Michal Jozwikowski
We extend the Pontryagin Maximum Principle (PMP) to the geometric setting of almost-Lie (AL) algebroids -- objects which generalize Lie algebroids. The result may be understood as…
Generalized Livens theorem and constrained Hamiltonian dynamics on algebroids
Michal Jozwikowski
We generalise Livens theorem, showing that Hamiltonian equation on the vector bundle , dual to a general algebroid , can be derived by means of…
Pontryagin Maximum Principle - a generalization
Janusz Grabowski, Michal Jozwikowski
The fundamental theorem of the theory of optimal control, the Pontryagin maximum principle (PMP), is extended to the setting of almost Lie (AL) algebroids, geometrical objects gene…