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

Liviu Popescu, Daniel Militaru and Gabriel Tică
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Liviu Popescu: Department of Statistics and Economic Informatics, University of Craiova, 200585 Craiova, Romania
Daniel Militaru: Independent Researcher, 200585 Craiova, Romania
Gabriel Tică: Department of Statistics and Economic Informatics, University of Craiova, 200585 Craiova, Romania

Mathematics, 2022, vol. 10, issue 4, 1-19

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.

Keywords: control affine systems; controllability; optimal control; Hamilton–Jacobi–Bellman equations; Lie geometric methods; holonomic distribution; economic applications (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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