161 research outputs found
LAGRANGE-HAMILTON MODEL FOR CONTROL AFFINE SYSTEMS WITH POSITIVE HOMOGENEOUS COST
In this paper we give a new technique to obtain the Hamiltonian function in order to solve the driftless control affine systems (distributional systems) with positive homogeneous costs. The method consists by using the Lagrange multipliers and Legendre transformation associated to a singular Lagrangian. This method could be an alternative to the classical Pontryagin Maximum Principle.control affine systems, positive homogeneous cost, Lagrange-Hamilton formalism, Pontryagin Maximum Principle
A complete characterization of exponential stability for discrete dynamics
For a discrete dynamics defined by a sequence of bounded and not necessarily
invertible linear operators, we give a complete characterization of exponential
stability in terms of invertibility of a certain operator acting on suitable
Banach sequence spaces. We connect the invertibility of this operator to the
existence of a particular type of admissible exponents. For the bounded orbits,
exponential stability results from a spectral property. Some adequate examples
are presented to emphasize some significant qualitative differences between
uniform and nonuniform behavior.Comment: The final version will be published in Journal of Difference
Equations and Application
Geometrical structures on the cotangent bundle
In this paper we study the geometrical structures on the cotangent bundle
using the notions of adapted tangent structure and regular vector fields. We
prove that the dynamical covariant derivative on fix a nonlinear
connection for a given -regular vector field. Using the Legendre
transformation induced by a regular Hamiltonian, we show that a
semi-Hamiltonian vector field on corresponds to a semispray on if
and only if the nonlinear connection on is just the canonical nonlinear
connection induced by the regular Lagrangian.Comment: International Journal of Geometric Methods in Modern Physics, 201
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