Journal of Dynamical and Control Systems 

About: Journal of Dynamical and Control Systems is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Mathematics & Optimal control. It has an ISSN identifier of 1079-2724. Over the lifetime, 906 publications have been published receiving 11177 citations.

The dynamic interpolation problem: On Riemannian manifolds, Lie groups, and symmetric spaces

Abstract: We consider the dynamic interpolation problem for nonlinear control systems modeled by second-order differential equations whose configuration space is a Riemannian manifoldM. In this problem we are given an ordered set of points inM and would like to generate a trajectory of the system through the application of suitable control functions, so that the resulting trajectory in configuration space interpolates the given set of points. We also impose smoothness constraints on the trajectory and typically ask that the trajectory be also optimal with respect to some physically interesting cost function. Here we are interested in the situation where the trajectory is twice continuously differentiable and the Lagrangian in the optimization problem is given by the norm squared acceleration along the trajectory. The special cases whereM is a connected and compact Lie group or a homogeneous symmetric space are studied in more detail.

Qualitative properties of trajectories of control systems: A survey

Abstract: We present a unified approach to a complex of related issues in control theory, one based to a great extent on the methods of nonsmooth analysis. The issues include invariance, stability, equilibria, monotonicity, the Hamilton-Jacobi equation, feedback synthesis, and necessary conditions.

On problems related to growth, entropy, and spectrum in group theory

Abstract: We review some known results and open problems related to the growth of groups. For a finitely generated group Γ, given whenever necessarytogether with a finite generating set, we discuss the notions of

Exponential mappings for contact sub-Riemannian structures

Abstract: On sub-Riemannian manifolds any neighborhood of any point contains geodesics which are not length minimizers; the closures of the cut and the conjugate loci of any pointq containq. We study this phenomenon in the case of a contact distribution, essentially in the lowest possible dimension 3, where we extract differential invariants related to the singularities of the cut and the conjugate loci nearq and give a generic classification of these singularities.

Sub-Riemannian structures on 3D lie groups

Abstract: We give a complete classification of left-invariant sub-Riemannian structures on three-dimensional Lie groups in terms of the basic differential invariants. As a consequence, we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups SL(2) and A +( $ \mathbb{R} $ )?×?S 1, where A +( $ \mathbb{R} $ ) denotes the group of orientation preserving affine maps on the real line.