Optimal Control, Geometry, and Mechanics

V. Jurdjevic

Chapter 7 in Mathematical Control Theory, 1999, pp 227-267 from Springer

Abstract: Abstract This essay highlights the contributions of geometric control theory to the calculus of variations. The Maximum Principle is recognized as a covariant necessary condition of optimality valid for variational problems defined on subsets C of the tangent bundle of the ambient manifold, rather than the entire tangent bundle, as was commonly assumed by the classical theory. Control-theoretic interpretations provide a uniform framework for variational problems with non-holonomic constraints and reveal the significance of controllability theory for such problems. The merits of this theory are then illustrated through solutions of variational problems on Lie groups having either left or right invariance. By focusing on problems fromm geometry and mechanics, the essay visibly demonstrates the innovative ideas that geometric control brings to the calculus of variations.

Keywords: Vector Field; Symmetric Space; Heisenberg Group; Elastic Problem; Hamiltonian Vector Field (search for similar items in EconPapers)
Date: 1999
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1416-8_7

Ordering information: This item can be ordered from
http://www.springer.com/9781461214168

DOI: 10.1007/978-1-4612-1416-8_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().