A STUDY OF THE OPTIMAL CONTROL OF DYNAMIC SYSTEMS

Abstract

In this report, we study the problem of controlling the behavior of a general dynamic system subject to various physical constraints. The class of dynamic systems considered is assumed to obey the linear vector differential equation x equals Fx + Du , x(0) equals c where x is an n-vector called the state vector, F is a nxn matrix of constant elements, D is a nxr matrix of constant elements, u is a r-vector called the control vector. The constraints stipulated are, u(t) equals u(iT) for iT is less than or equal to t which is less than (i + 1)T and the absolute value of u(t) is less than or equals to 1 for t greater than or equal to i.e., the control vector is constrained to be piecewise constant and amplitude limited. We are interested in the determination of u(t) subject to (ii) or (iii) of both such that the state vector x(t) attains the value zero in minimum time or the integral of some measure of the vector is a minimum over a period of time. A well-known example of this class of problems is the so-called bang-bang control problem. (Author)

Document Details

Document Type
Technical Report
Publication Date
Feb 10, 1961
Accession Number
AD0261851

Entities

People

  • Yu-chi Ho

Organizations

  • Harvard University

Tags

DTIC Thesaurus Topics

  • Amplitude
  • Differential Equations
  • Equations
  • Integrals
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Linear Algebra
  • Operations Research