### Abstract

We consider a general class of systems subject to two types of uncertainty: A continuous deterministic uncertainty that affects the system dynamics, and a discrete stochastic uncertainty that leads to jumps in the system structure at random times, with the latter described by a continuous-time finite state Markov chain. When only sampled values of the system state is available to the controller, along with perfect measurements on the state of the Markov chain, we obtain a characterization of minimax controllers, which involves the solutions of two finite sets of coupled PDE's, and a finite dimensional compensator. For the linear-quadratic case, a complete characterization is given in terms of coupled generalized Riccati equations, which also provides the solution to a particular H^{∞} optimal control problem with randomly switching system structure and sampled state measurements.

Original language | English (US) |
---|---|

Pages (from-to) | 716-721 |

Number of pages | 6 |

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

Volume | 1 |

State | Published - Dec 1 1994 |

Event | Proceedings of the 33rd IEEE Conference on Decision and Control. Part 1 (of 4) - Lake Buena Vista, FL, USA Duration: Dec 14 1994 → Dec 16 1994 |

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### ASJC Scopus subject areas

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

### Cite this

**Minimax control of switching systems under sampling.** / Basar, Tamer.

Research output: Contribution to journal › Conference article

*Proceedings of the IEEE Conference on Decision and Control*, vol. 1, pp. 716-721.

}

TY - JOUR

T1 - Minimax control of switching systems under sampling

AU - Basar, Tamer

PY - 1994/12/1

Y1 - 1994/12/1

N2 - We consider a general class of systems subject to two types of uncertainty: A continuous deterministic uncertainty that affects the system dynamics, and a discrete stochastic uncertainty that leads to jumps in the system structure at random times, with the latter described by a continuous-time finite state Markov chain. When only sampled values of the system state is available to the controller, along with perfect measurements on the state of the Markov chain, we obtain a characterization of minimax controllers, which involves the solutions of two finite sets of coupled PDE's, and a finite dimensional compensator. For the linear-quadratic case, a complete characterization is given in terms of coupled generalized Riccati equations, which also provides the solution to a particular H∞ optimal control problem with randomly switching system structure and sampled state measurements.

AB - We consider a general class of systems subject to two types of uncertainty: A continuous deterministic uncertainty that affects the system dynamics, and a discrete stochastic uncertainty that leads to jumps in the system structure at random times, with the latter described by a continuous-time finite state Markov chain. When only sampled values of the system state is available to the controller, along with perfect measurements on the state of the Markov chain, we obtain a characterization of minimax controllers, which involves the solutions of two finite sets of coupled PDE's, and a finite dimensional compensator. For the linear-quadratic case, a complete characterization is given in terms of coupled generalized Riccati equations, which also provides the solution to a particular H∞ optimal control problem with randomly switching system structure and sampled state measurements.

UR - http://www.scopus.com/inward/record.url?scp=0028753210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028753210&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0028753210

VL - 1

SP - 716

EP - 721

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -