The geometry of Lie algebroids and its applications to optimal control

2013/02/21 by Liviu Popescu, Popescu, Liviu · 1 citation
Mathematics · Physics and Astronomy · #17B66 #49K99 #53C05 #70S05 #Advanced Differential Geometry Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1302.5212

openalex publication_date 2013/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper presents the geometry of Lie algebroids and its applications to optimal control. The first part deals with the theory of Lie algebroids, connections on Lie algebroids and dynamical systems defined on Lie algebroids (mainly Lagrangian and Hamiltonian systems). In the second part we use the framework of Lie algebroids in the study of distributional systems (drift less control affine systems) with holonomic or nonholonomic distributions.

Cited by

• Vertical and complete lifts of sections of a (dual) vector bundle and Legendre duality

Related

• Generalized Lie Algebroids - Examples by Distinguished Lie Algebroids with Applications to Optimal Control
• Mechanical control systems on Lie algebroids
• A Survey of Lagrangian Mechanics and Control on Lie algebroids and groupoids
• Optimal Control Theory on almost-Lie Algebroids
• A variational-geometric approach for the optimal control of nonholonomic\n systems