NONLINEAR FEEDBACK SOLUTION TO A BOUNDED BRACHISTOCHRONE PROBLEM IN A REDUCED STATE SPACE.

Abstract

The optimal nonlinear feedback law for both an unbounded and bounded Brachistochrone problem is given. These control laws describe the Brachistochrone problem in a very simple manner. These laws are derived by using a dimensionless set of state variables which are of lower dimension than the original state space. Also using this reduced state space a two dimensional instead of three dimensional field of extremals is constructed for the bounded Brachistochrone problem. This illustrates that the state space may be reduced so that the storage of a field of extremal trajectories will not exceed the storage capacity of a practical on board computer. In this way, optimal feedback control may become a practical technique for a larger class of nonlinear systems. (Author)

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1965
Accession Number
AD0627647

Entities

People

  • Jason L. Speyer

Tags

DTIC Thesaurus Topics

  • Computers
  • Feedback
  • Geometry
  • Mathematics
  • Nonlinear Systems
  • Physical Properties
  • Three Dimensional
  • Trajectories
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Graph Algorithms and Convex Optimization.
  • Nanoscale Plasmonic Nanotechnology

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers