Structural properties of minimax policies for a class of differential games arising in nonlinear H-control and filtering

Garry Didinsky, Tamer Basar, Pierre Bernhard

Research output: Contribution to journalConference article


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 in [2] and [3], which applies to problems where the `worst-case disturbance' may not be unique (but the worst-case state trajectory is). The generalized certainty equivalence, on the other hand, extends this to accommodate nonunique worst-case state trajectories, and leads to the construction of controllers 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. These results are then applied to the nonlinear minimax filtering problem, which is treated here as a special case of the general control problem.

Original languageEnglish (US)
Pages (from-to)184-189
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - Dec 1 1993
EventProceedings of the 32nd Conference on Decision and Control - San Antonio, TX, USA
Duration: Dec 15 1993Dec 15 1993

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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