Lie Geometric Methods in the Study of Driftless Control Affine Systems with Holonomic Distribution and Economic Applications

Abstract

In the present paper, two optimal control problems are studied using Lie geometric methods and applying the Pontryagin Maximum Principle at the level of a new working space, called Lie algebroid. It is proved that the framework of a Lie algebroid is more suitable than the cotangent bundle in order to find the optimal solutions of some driftless control affine systems with holonomic distributions. Finally, an economic application is given.

Preface to the Special Issue on “Advances in Differential Dynamical Systems with Applications to Economics and Biology”

“…In the paper by Popescu et al [7], the Pontryagin Maximum Principle and Lie geometric methods are employed to study two optimal control problems at the level of the Lie algebroid. It is demonstrated that the cotangent bundle is not the best framework for finding the best solutions to some driftless control affine systems with holonomic distributions.…”