TY - JOUR

T1 - Minimax control of switching systems under sampling

AU - Basar, Tamer

N1 - Funding Information:
Research supported in part by the U.S. Department of Energy under Grant DE-FG-02-88-ER-13935, and in part by the National Science Foundation under Grant NSF ECS 92-16487 and the Joint Services Electronics Program through the University of Illinois. The paper has also been presented at the 33rd CDC, held in Orlando, Florida, December 14-16, 1994. * Tel: 217/333-3607; Fax: 217/244-1653; E-mail: [email protected].

PY - 1994

Y1 - 1994

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.

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M3 - Conference article

AN - SCOPUS:0028753210

SN - 0191-2216

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

T2 - Proceedings of the 33rd IEEE Conference on Decision and Control. Part 1 (of 4)

Y2 - 14 December 1994 through 16 December 1994

ER -