Improved multiplex control systems: dynamic reliability and stochastic optimality. (English) Zbl 0598.93067
The LQ problem can be complemented by the assumption that the object parameters are functions of a stochastic Markov process r(t) with a finite number of states. Such a jump linear-quadratic (JLQ) problem was formulated by Krasovskiî and Lidskiî twenty-five years ago.
In this paper the JLQ problem is discussed under various hypotheses about the observations of the process r(t) (plant mode) and state vector x(t):
(1) the value of r(t) is known at the moment t as well as x(t);
(2) the value of r(t) is known at t, however only, \(y(t)=c(t)x(t)\) is available;
(3) the value of r(t) is unknown, and it is only possible to use a priori information, but x(t) or y(t) is available.
In case (3) we obtain non-switching feedback. An example which was investigated earlier by Ladde and Šiljak is presented here to compare the effectiveness of various approaches. It is shown that the so called stabilizing constrained feedback introduced by Šiljak gives an effect which is essentially worse than the effect of the type (3) feedback.
In this paper the JLQ problem is discussed under various hypotheses about the observations of the process r(t) (plant mode) and state vector x(t):
(1) the value of r(t) is known at the moment t as well as x(t);
(2) the value of r(t) is known at t, however only, \(y(t)=c(t)x(t)\) is available;
(3) the value of r(t) is unknown, and it is only possible to use a priori information, but x(t) or y(t) is available.
In case (3) we obtain non-switching feedback. An example which was investigated earlier by Ladde and Šiljak is presented here to compare the effectiveness of various approaches. It is shown that the so called stabilizing constrained feedback introduced by Šiljak gives an effect which is essentially worse than the effect of the type (3) feedback.
Reviewer: A.Pervozvanskii
MSC:
| 93E20 | Optimal stochastic control |
| 60J75 | Jump processes (MSC2010) |
| 93C05 | Linear systems in control theory |
| 93E15 | Stochastic stability in control theory |
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