| Title:
|
Optimal control of linear stochastic evolution equations in Hilbert spaces and uniform observability (English) |
| Author:
|
Ungureanu, Viorica Mariela |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
317-342 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study the existence of the optimal (minimizing) control for a tracking problem, as well as a quadratic cost problem subject to linear stochastic evolution equations with unbounded coefficients in the drift. The backward differential Riccati equation (BDRE) associated with these problems (see \cite {chen}, for finite dimensional stochastic equations or \cite {UC}, for infinite dimensional equations with bounded coefficients) is in general different from the conventional BDRE (see \cite {1990}, \cite {ukl}). Under stabilizability and uniform observability conditions and assuming that the control weight-costs are uniformly positive, we establish that BDRE has a unique, uniformly positive, bounded on ${\mathbf R}_{+}$ and stabilizing solution. Using this result we find the optimal control and the optimal cost. It is known \cite {ukl} that uniform observability does not imply detectability and consequently our results are different from those obtained under detectability conditions (see \cite {1990}). (English) |
| Keyword:
|
Riccati equation |
| Keyword:
|
stochastic uniform observability |
| Keyword:
|
stabilizability |
| Keyword:
|
quadratic control |
| Keyword:
|
tracking problem |
| MSC:
|
49K45 |
| MSC:
|
93E20 |
| idZBL:
|
Zbl 1224.93135 |
| idMR:
|
MR2532378 |
| . |
| Date available:
|
2010-07-20T15:11:09Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140483 |
| . |
| Reference:
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