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Tytuł książki

Forecast horizon in dynamic family of one-dimensional control problems

Seria
Rozprawy Matematyczne tom/nr w serii: 315 wydano: 1991
Zawartość
Warianty tytułu
Abstrakty
EN
The forecast horizon is defined as a property of a class of functions. Some general existence conditions are derived. The results are applied to the process x(·) described by the differential equation
ẋ(t) = e(t,u(t)) - f(t,x(t)), $x(0)=x_{0}$,
where e, f are nonnegative and increasing in the second variable, and u(·) denotes a control variable.
A cost functional is associated with the process and the control. The cost is characterized by three functions: g(t,u), h(t,x), k(x), and a time interval. A class of functions (e, f, g, h, k) for which the forecast horizons can be explicitly obtained is described. Some applications to economic problems are given.
In the second part of the paper a discrete-time, stochastic, linear control problem is considered. The problem is described by means of a sequence of Markov transition functions and two deterministic sequences. For some classes of sequences the forecast horizons are explicitly obtained. Optimal solutions are determined. An economic application of the problem is given.
EN

CONTENTS
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Sufficient conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
3. Definitions and hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
4. Properties of arcs and trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
5. Dynamic family of optimal controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6. The maximum principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
7. Horizon theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
8. Remarks to horizon theorems. An economic application . . . . . . . . . . . . . . . . . . . . 27
9. Discrete-time linear systems with stochastic parameters. Horizon theorems . . . . . 29
10. Proof of horizon theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
11. Final remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
  References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 315
Liczba stron
41
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCXV
Daty
wydano
1991
otrzymano
1990-05-02
poprawiono
1991-04-09
Twórcy
  • Institute of Mathematics, Polish Academy of Sciences, P.O. Box 137, 00-950 Warszawa, Poland
Bibliografia
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Języki publikacji
EN
Uwagi
1991 Mathematics Subject Classification: Primary 90C39; Secondary 93C75, 90B05, 90B30, 90A16, 90A05.
Identyfikator YADDA
bwmeta1.element.zamlynska-8471af74-6613-4ea2-9e91-e201cfd8e5b8
Identyfikatory
ISBN
83-85116-29-X
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

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