Let M be a σ-compact C∞ manifold of dimension n≥ 2 and consider a single-input control
system: x˙(t)= X (x (t))+ u (t) Y (x (t)), where X, Y are C∞ vector fields on M. We prove that …

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely
discussed and used as a method to solve optimal control problems in medicine, robotics …

2-Dimensional almost-Riemannian structures are generalized Riemannian structures on
surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of …

arxiv:0812.1334v1 [math.DG] 7 Dec 2008 Page 1 arxiv:0812.1334v1 [math.DG] 7 Dec 2008
Acta Applicandae Mathematicae manuscript No. (will be inserted by the editor) Feedback …

arxiv:0812.1351v1 [math.DG] 7 Dec 2008 Page 1 arxiv:0812.1351v1 [math.DG] 7 Dec 2008
Feedback Equivalence of 1-dimensional Control Systems of the 1-st Order Valentin Lychagin …

Motivated by control-affine systems in optimal control theory, we introduce the notion of a
point-affine distribution on a manifold X–ie, an affine distribution F together with a …

Рассмотрена проблема классификации гамильтоновых систем со скалярным
управляющим параметром относительно преобразований обратной связи. Построены …

A geometric method is described to characterize the different kinds of extremals in optimal
control theory. This comes from the use of a presymplectic constraint algorithm starting from …

In the famous 1910 “cinq variables” paper Cartan showed in particular that for maximally
nonholonomic rank 2 distributions in ℝ5 with non-zero covariant binary biquadratic form the …

The problem is considered of the classification of Hamiltonian systems with a scalar control
parameter relative to feedback transformations. Differential invariants of these systems …