Dynamic games approach to controller design: Disturbance rejection in discrete time

Research output: Contribution to journalConference articlepeer-review


It is shown that the discrete-time disturbance-rejection problem, formulated in finite and infinite horizons, can be solved by making direct use of the available results on linear-quadratic zero-sum dynamic geams. Under perfect state measurements the approach leads to a minimax controller which achieves the best performance bound, and also to a characterization of all linear controllers under which disturbance attenuation does not exceed a prescribed bound. For the former, the worst-case disturbance turns out to be a correlated random sequence with a discrete distribution, which means that the problem (viewed as a dynamic game between the controller and the disturbance) does not admit a pure-strategy saddle point. Also formulated is a stochasatic version of the problem, where the disturbance is a partially stochastic process with fixed higher order moments (other than the mean). Here the minimix controller depends on the energy bound of the disturbance, provided that it is below a certain threshold. Several numerical studies are included to illustrate the main results.

Original languageEnglish (US)
Pages (from-to)407-414
Number of pages8
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 1989
EventProceedings of the 28th IEEE Conference on Decision and Control. Part 1 (of 3) - Tampa, FL, USA
Duration: Dec 13 1989Dec 15 1989

ASJC Scopus subject areas

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


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