The Lagrange multiplier rule on manifolds and optimal control of nonlinear systems

In this paper we present a differential geometric approach to the Lagrange problem and the fixed time optimal control problem for nonlinear time-invariant control systems. We restrict attention to first order conditions for optimality and present a generalized Lagrange multiplier rule for restricted...

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Bibliographic Details
Published inSIAM journal on control and optimization Vol. 22; no. 5; pp. 740 - 757
Main Author BUS, J. C. P
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.09.1984
Subjects
Applied sciences
Calculus
Calculus of variations
Computer science; control theory; systems
Control theory. Systems
Exact sciences and technology
Lagrange multiplier
Optimal control
System theory
Lagrange multiplier
Manifold
Non linear system
Optimal control
Differential geometry
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Summary:In this paper we present a differential geometric approach to the Lagrange problem and the fixed time optimal control problem for nonlinear time-invariant control systems. We restrict attention to first order conditions for optimality and present a generalized Lagrange multiplier rule for restricted variational problems. Our treatment of the optimal control problem uses a recently proposed fibre bundle approach for the definition of nonlinear systems.
ISSN:0363-0129
1095-7138
DOI:10.1137/0322047