Structural properties of minimax controllers for a class of differential games arising in nonlinear H control

Garry Didinsky, Tamer Başar, Pierre Bernhard

Research output: Contribution to journalArticle

Abstract

This paper introduces, in precise mathematical terms, two properties (named, certainty equivalence and generalized certainty equivalence) that nonlinear minimax controller problems might possess. The certainty equivalence is a generalization of the one introduced earlier by Başar and Bernhard (1991) and Bernhard (1990), which applies to problems where the 'worst-case disturbance' may not be unique (but the worst-case state trajectory is). The generalized certainty equivalance, on the other hand, extends this to accomodate nonunique worst-case state trajectories, and leads to the constrollers that guarantee a bounded upper value for the underlying game. The paper also shows that for a large class of games (and under certain conditions), certainty-equivalent (as well as generalized certainty-equivalent) controllers admit (infinite-dimensional) estimator (Kalman-filter) structures, where the estimator gain depends on the state of the estimator.

Original languageEnglish (US)
Pages (from-to)433-441
Number of pages9
JournalSystems and Control Letters
Volume21
Issue number6
DOIs
StatePublished - Dec 1993

Keywords

  • H control
  • certainty equivalence
  • differential games
  • minimax controllers
  • nonlinear systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)
  • Mechanical Engineering
  • Electrical and Electronic Engineering

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