summary of completed research ● projects (old and new)
The hardest thing of all is to find a black cat in a dark room, especially if there is no cat. – Confucius
Summary of completed research
Control systems and optimal control problems on Lie groups (general invariant control systems and related concepts)
"A category of control systems" (2012, 13 pages)
"Optimal control and Hamilton–Poisson formalism" (2010, 7 pages)
"Optimal control and integrability on Lie groups" (2011, 18 pages)
"On the equivalence of control systems on Lie groups" (2015, 11 pages)
"On the equivalence of cost-extended control systems on Lie groups" (2013, 6 pages)
"Cost-extended control systems on Lie groups" (2014, 23 pages)
"A note on the equivalence of control systems on Lie groups" (2017, 11 pages)
(full classification in three dimensions)
"A note on the affine subspaces of three-dimensional Lie algebras" (2012, 8 pages)
"Control affine systems on semisimple three-dimensional Lie groups" (2013, 16 pages)
"Control affine systems on solvable three-dimensional Lie groups, I" (2013, 11 pages)
"Control affine systems on solvable three-dimensional Lie groups, II" (2013, 13 pages)
"Feedback classification of invariant control systems on three-dimensional Lie groups" (2013, 6 pages)
"Control systems on three-dimensional Lie groups" (2014, 6 pages)
"Control systems on three-dimensional Lie groups: equivalence and controllability" (2014, 33 pages)
(specific low-dimensional Lie groups)
"Control and integrability on SO(3)" (2010, 6 pages)
"Integrability and optimal control" (2010, 6 pages)
"Optimal control on the rotation group SO(3)" (2012, 8 pages)
"Control and stability on the Euclidean group SE(2)" (2011, 6 pages)
"Equivalence of control systems on the Euclidean group SE(2)" (2012, 12 pages)
"Single-input control systems on the Euclidean group SE(2)" (2012, 15 pages)
"Two-input control systems on the Euclidean group SE(2)" (2013, 29 pages)
"Equivalence of control systems on the pseudo-orthogonal group SO(2,1)" (2016, 21 pages)
"Optimal control of drift-free control systems on the group of motions of the Minkowski plane" (2014, 6 pages)
"Control systems on the Heisenberg group: equivalence and classification" (2016, 18 pages)
"Control systems on nilpotent Lie groups of dimension ≤4: equivalence and classification" (2017, 16 pages)
"On the equivalence of control systems on the orthogonal group SO(4)" (2013, 6 pages)
"Control systems on the orthogonal group SO(4)" (2013, 22 pages)
(survey article)
"Invariant control systems on Lie groups: a short survey" (2017, 26 pages)
(book chapter)
"Invariant control systems on Lie groups" (2017, 55 pages) in "Lie Groups, Differential Equations, and Geometry. Advances and Surveys" (G. Falcone, editor) , Springer
Hamilton–Poisson systems (general quadratic Hamilton–Poisson systems in three dimensions)
"A classification of quadratic Hamilton–Poisson systems in three dimensions" (2013, 11 pages)
"Quadratic Hamilton–Poisson systems in three dimensions: equivalence, stability, and integration" (2017, 59 pages)
(specific quadratic Hamilton–Poisson systems)
"On some quadratic Hamilton–Poisson systems" (2013, 12 pages)
"Quadratic Hamilton–Poisson systems on so(3) *: classification and integration" (2013, 12 pages)
"On the stability and integration of Hamilton–Poisson systems on so(3) *" (2016, 42 pages)
"A few remarks on quadratic Hamilton–Poisson systems on the Heisenberg Lie–Poisson space" (2017, 7 pages)
"Quadratic Hamilton–Poisson systems on se(1,1) *: the homogeneous case" (2015, 17 pages)
"Quadratic Hamilton–Poisson systems on se(1,1) *: the inhomogeneous case" (2018, 42 pages)
Lie groups and Lie algebras
"Affine subspaces of the Lie algebra se(1,1)" (2014, 16 pages)
"Affine distributions on a four-dimensional extension of the semi-Euclidean group" (2015, 17 pages)
"Some remarks on the oscillator group" (2014, 11 pages)
"Subspaces of real four-dimensional Lie algebras: a classification of subalgebras, ideals, and full-rank systems" (2015, 53 pages)
"On the classification of real four-dimensional Lie groups" (2016, 35 pages)
Geometric mechanics on Lie groups (nonholonomic Riemannian geometry)