On the Bilinear Regulator Problem with a Pursuit-Evasion Application.

Abstract

The purpose of this work is to formulate and analyze the quadratic cost problem associated with a bilinear system. The existence of optimal controls to this problem is established. A class of commutative bilinear systems and the minimum energy problem associated with it are investigated. It is shown that optimal controls for this problem are in constant form which are determined by the boundary conditions. Sufficient conditions for uniqueness of optimal controls are also derived for this problem. This system is shown to be reachable to a given state by a constant input if and only if it is reachable to by a time-varying input. This gives the control engineer a great deal of flexibility in the design of a feasible easily-implemented controller. Application to a two-dimensional pursuit-evasion problem is considered in which the minimum energy problem with terminal constraint is solved analytically. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jun 09, 1976
Accession Number
ADA032876

Entities

People

  • Allan E. Pearson
  • Kuang-chung Wei

Organizations

  • Brown University

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Communities of Interest

  • Weapons Technologies

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Control Systems Engineering
  • Control Theory
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  • Equations
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Fields of Study

  • Mathematics

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  • Control Systems Engineering.
  • Mathematical Modeling and Probability Theory.