NDLI: Reduction of Euler Lagrange problems for constrained variational problems and relation with optimal control problems

Content Provider	IEEE Xplore Digital Library
Author	Bloch, A.M. Croach, P.E.
Copyright Year	1994
Description	Author affiliation: Dept. of Math., Ohio State Univ., Columbus, OH, USA (Bloch, A.M.)
Abstract	Considers the relation between the optimal control problem and the classical calculus of variations problem with constraints. Some variational problems concerning control systems modeled on a state space of dimension n may be attacked by either formulation. The Pontryagin maximum principle gives rise to necessary conditions formulated in terms of a system of 2n Hamiltonian equations, while the Euler-Lagrange equations describing the necessary conditions in the classical calculus of variations formulation give rise to more equations. Clearly, in this case, the classical Legendre condition does not link the two formulations. The authors describe a technique to reduce the Euler-Lagrange equations to a system of 2n equations and describe the transformation which links the resulting system with the corresponding Hamiltonian equations. The authors describe some examples in detail and specifically address the situation where the equations describing the necessary conditions may be reduced due to the presence of symmetries.<>
Starting Page	2584
Ending Page	2590
File Size	551164
Page Count	7
File Format	PDF
ISBN	0780319680
DOI	10.1109/CDC.1994.411534
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1994-12-14
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Lagrangian functions Equations Optimal control State-space methods Calculus Constraint theory Control system synthesis Systems engineering and theory Cost function Control systems
Content Type	Text
Resource Type	Article

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