By Ruth F. Curtain (auth.)

ISBN-10: 3540060502

ISBN-13: 9783540060505

ISBN-10: 3540380000

ISBN-13: 9783540380009

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Additional resources for Stability of Stochastic Dynamical Systems: Proceedings of the International Symposium Organized by “The Control Theory Centre”, University of Warwick, July 10–14, 1972 Sponsored by the “International Union of Theoretical and Applied Mechanics”

Sample text

Is applied A description then sometimes perimental mentation alone tice the models perimentation processes dynamics accuracy is often can not be d e t e r m i n e d becomes a necessity. to the process through a p p r o p r i a t e and m o d e l l i n g processing teristics setting, of d y n a m i c a l with the classical is not r e a s o n a b l e systems. to assume A significant problems independent can by experi- approach. In pracof ex- laws. problem although because we are trying to estimate statistical are ob- of the ex- are derived The p r o b l e m we are faced with is thus a statistic a fairly complex outputs an in- and the disturbances through a c o m b i n a t i o n based on physical Many from ~ priori knowledge called the black-box obtained reasonably missing.

E. Let ~(t) o for all te N be the solution of the system y(t+l)=(A+ ~bc')y(t) with y(o)=~. From condition (3) it follows that lim ~( t ):o Let ~(t)= ~c'~(t). ~o7] it follows that there exist a positive ~efinite matrix E, a vector q and a real nnmber ~ such that y,(t+l)Hy(t+l)-y,(o)~j(o)= for all t >. i~ C :-:o~ Let toe N , ~ e ~ e , ~e ~ tem (4) with X(to,~ )-~(~ ). "

Control a control can a suitable in order to arrive be much more reasonable desired in the introduction is to design from the criterion it is reasonable fication outputs may arise. 4) by modeling is clear that difficulties 5. 1) 51 where le(t)} is a sequence of independent uncorrelated disturbances and where the parameters known. 2) Ey2(t) is minimal at each step and let the admissible control strategies be such that the control signal at time t is a function of the inputs observed up to time t and of the past control signals.

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Stability of Stochastic Dynamical Systems: Proceedings of the International Symposium Organized by “The Control Theory Centre”, University of Warwick, July 10–14, 1972 Sponsored by the “International Union of Theoretical and Applied Mechanics” by Ruth F. Curtain (auth.)


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