AMPLITUDE-LIMITED CONTROL OF LINEAR, DISCRETE SYSTEMS WITH QUADRATIC ERROR MEASURE.

Abstract

The problem of finding a sequence of N amplitudelimited controls which minimizes a quadratic error measure over N sampling intervals is studied. The error measure is the integral of a quadratic form in the state of the plant and the control variable. Conditions governing the uniqueness of the solution to the optimization problem are investigated. A new algorithm for solution of the problem is presented, and other methods of solution are discussed in the light of their possible use as part of a real-time controller. The algorithm is similar to the simplex algorithm of linear programming, but it solves the problem using fewer variables and equations. The logic involved in the algorithm is more complicated. Three controllers based on the N-stage optimization problem -- constant-N, periodic-N, and dual-mode -are studied. Necessary conditions for asymptotic stability in the large are stated for both the constant-N and the periodic-N controllers. These conditions are also sufficient for asymptotic stability in a restricted region of state space.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1965
Accession Number
AD0622513

Entities

People

  • Philip Auten Reynolds

Organizations

  • Cornell University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Amplitude
  • Computer Programming
  • Dual Mode
  • Equations
  • Evolutionary Algorithms
  • Heuristic Methods
  • Integrals
  • Intervals
  • Linear Programming
  • Mathematics
  • Optimization
  • Sampling
  • Simplex Method

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Control Systems Engineering.
  • Operations Research

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers