Design of minimax controllers for linear systems with nonzero initial conditions and under specified information structures

Garry Didinsky, M Tamer Basar

Research output: Contribution to journalConference article

Abstract

The solution is obtained to the discrete-time, linear-quadratic, finite-horizon disturbance rejection problem, with hard bounds on the disturbance. It is shown that two regions can be identified in the space of initial conditions: one where a pure-strategy saddle point exists, and the other where no pure-strategy saddle point exists. In the latter region, the structure of the minimax controller is fixed throughout, and a saddle point exists in the class of mixed policies. The construction of such saddle points is discussed. Minimax controllers are obtained for the case in which no information is available to the controller, i.e., the open-loop case. Subsequently, these results are used in solving for minimax controllers with more general information structures.

Original languageEnglish (US)
Pages (from-to)2413-2418
Number of pages6
JournalProceedings of the IEEE Conference on Decision and Control
Volume4
StatePublished - Dec 1 1990
EventProceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) - Honolulu, HI, USA
Duration: Dec 5 1990Dec 7 1990

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Information Structure
Saddlepoint
Minimax
Linear systems
Initial conditions
Linear Systems
Controller
Controllers
Disturbance Rejection
Disturbance rejection
Finite Horizon
Discrete-time
Disturbance
Design
Strategy

ASJC Scopus subject areas

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

Cite this

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N2 - The solution is obtained to the discrete-time, linear-quadratic, finite-horizon disturbance rejection problem, with hard bounds on the disturbance. It is shown that two regions can be identified in the space of initial conditions: one where a pure-strategy saddle point exists, and the other where no pure-strategy saddle point exists. In the latter region, the structure of the minimax controller is fixed throughout, and a saddle point exists in the class of mixed policies. The construction of such saddle points is discussed. Minimax controllers are obtained for the case in which no information is available to the controller, i.e., the open-loop case. Subsequently, these results are used in solving for minimax controllers with more general information structures.

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