### 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 language | English (US) |
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Pages (from-to) | 2413-2418 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 4 |

State | Published - Dec 1 1990 |

Event | Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) - Honolulu, HI, USA Duration: Dec 5 1990 → Dec 7 1990 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

### Cite this

**Design of minimax controllers for linear systems with nonzero initial conditions and under specified information structures.** / Didinsky, Garry; Basar, M Tamer.

Research output: Contribution to journal › Conference article

}

TY - JOUR

T1 - Design of minimax controllers for linear systems with nonzero initial conditions and under specified information structures

AU - Didinsky, Garry

AU - Basar, M Tamer

PY - 1990/12/1

Y1 - 1990/12/1

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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0025561598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025561598&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0025561598

VL - 4

SP - 2413

EP - 2418

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -