Related papers: The geometry of Lie algebroids and its application…

In this paper, we consider a geometric formalism for optimal control of underactuated mechanical systems. Our techniques are an adaptation of the classical Skinner and Rusk approach for the case of Lagrangian dynamics with higher-order…

Left-invariant optimal control problems on Lie groups form an important class of problems with big symmetry group. They are interesting from the theoretical point of view since they often can be completely studied, and general features can…

Motivated by the ubiquity of control-affine systems in optimal control theory, we investigate the geometry of point-affine control systems with metric structures in dimensions two and three. We compute local isometric invariants for…

After recalling the notion of Lie algebroid, we construct these structures associated with contact forms or systems. We are then interested in particular classes of Lie Rinehart algebras.

In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we…

This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to…

Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie…

Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…

In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…

Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome while minimizing some cost function. For a controlled…

We consider the class of control systems where the differential equation, state and control system are described by polynomials. Given a set of trajectories and a class of Lagrangians, we are interested to find a Lagrangian in this class…

This paper develops the notion of implicit Lagrangian systems on Lie algebroids and a Hamilton--Jacobi theory for this type of system. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We…

This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain…

The Lie algebroids are generalization of the Lie algebras. They arise, in particular, as a mathematical tool in investigations of dynamical systems with the first class constraints. Here we consider canonical symmetries of Hamiltonian…

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spaces. In the setup, we assume only that the drift and control…

For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…

The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…

This paper studies (single-time and multitime) optimal control problems on a nonholonomic manifold (described either by the kernel of a Gibbs-Pfaff form or by the span of appropriate vector fields). For both descriptions we analyse:…

In this work, we will investigate the question of optimal control for bilinear systems with constrained endpoint. The optimal control will be characterized through a set of unconstrained minimization problems that approximate the former.…