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 journalArticlepeer-review

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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