| Title:
|
Finite-dimensionality of information states in optimal control of stochastic systems: a Lie algebraic approach (English) |
| Author:
|
Charalambous, Charalambos D. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
6 |
| Year:
|
1998 |
| Pages:
|
[725]-738 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce the sufficient statistic algebra which is responsible for propagating the sufficient statistic, or information state, in the optimal control of stochastic systems. Certain Lie algebraic methods widely used in nonlinear control theory, are then employed to derive finite- dimensional controllers. The sufficient statistic algebra enables us to determine a priori whether there exist finite-dimensional controllers; it also enables us to classify all finite-dimensional controllers. (English) |
| Keyword:
|
optimal control of stochastic systems |
| Keyword:
|
sufficient statistic algebra |
| Keyword:
|
finite-dimensional controllers |
| MSC:
|
49K45 |
| MSC:
|
93B25 |
| MSC:
|
93E20 |
| idZBL:
|
Zbl 1274.93281 |
| idMR:
|
MR1695374 |
| . |
| Date available:
|
2009-09-24T19:22:09Z |
| Last updated:
|
2015-03-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135257 |
| . |
| Reference:
|
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| Reference:
|
[2] Brockett R., Clark J.: Geometry of the conditional density equation.In: Proceedings of the International Conference on Analysis and Optimization of Stochastic Systems, Oxford 1978 Zbl 0496.93049 |
| Reference:
|
[3] Charalambous C.: Partially observable nonlinear risk-sensitive control problems: Dynamic programming and verification theorems.IEEE Trans. Automat. Control, to appear Zbl 0886.93070, MR 1469073 |
| Reference:
|
[4] Charalambous C., Elliott R.: Certain nonlinear stochastic optimal control problems with explicit control laws equivalent to LEQG/LQG problems.IEEE Trans. Automat. Control 42 (1997), 4. 482–497 MR 1442583, 10.1109/9.566658 |
| Reference:
|
[5] Charalambous C., Hibey J.: Minimum principle for partially observable nonlinear risk-sensitive control problems using measure-valued decompositions.Stochastics and Stochastics Reports 57 (1996), 2, 247–288 Zbl 0891.93084, MR 1425368, 10.1080/17442509608834063 |
| Reference:
|
[6] Charalambous C., Naidu D., Moore K.: Solvable risk-sensitive control problems with output feedback.In: Proceedings of 33rd IEEE Conference on Decision and Control, Lake Buena Vista 1994, pp. 1433–1434 |
| Reference:
|
[7] Chen J., Yau S.-T., Leung C.-W.: Finite-dimensional filters with nonlinear drift IV: Classification of finite-dimensional estimation algebras of maximal rank with state-space dimension $3$.SIAM J. Control Optim. 34 (1996), 1, 179–198 Zbl 0847.93062, MR 1372910, 10.1137/S0363012993251316 |
| Reference:
|
[8] Hazewinkel M., Willems J.: Stochastic systems: The mathematics of filtering and identification, and applications.In: Proceedings of the NATO Advanced Study Institute, D. Reidel, Dordrecht 1981 Zbl 0486.00016, MR 0674319 |
| Reference:
|
[9] Marcus S.: Algebraic and geometric methods in nonlinear filtering.SIAM J. Control Optim. 26 (1984), 5, 817–844 Zbl 0548.93073, MR 0762622, 10.1137/0322052 |
| . |
