Optimal Control Problems on Riemannian Manifolds: Theory and Applications

Abstract

Any air vehicle can be thought of as evolving on Riemannian manifold with the total kinetic energy as the metric. In this paper, we first derive first-order necessary conditions for a Boiza-type optimal control problem on a Riemannian manifold. Then we apply this theory to a rotating rigid body, by obtaining expressions for the Riemannian connection and curvature tensor via Cartan's formalism.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 2002
Accession Number
ADA408334

Entities

People

  • David Doman
  • Ram Venkataraman
  • Raymond Holsapple

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Aircrafts
  • Boundary Value Problems
  • Calculus Of Variations
  • Control Systems
  • Curvature
  • Differential Equations
  • Differential Geometry
  • Equations
  • Geometric Forms
  • Geometry
  • Kinetic Energy
  • Lie Groups
  • Lines (Geometry)
  • Mathematics
  • Vehicles

Readers

  • Fluid Dynamics.
  • Graph Algorithms and Convex Optimization.