Finite-dimensionality of information states in optimal control of stochastic systems: a Lie algebraic approach. (English) Zbl 1274.93281
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.
Keywords:
optimal control of stochastic systems; sufficient statistic algebra; finite-dimensional controllersReferences:
| [1] | Beneš V.: Exact finite-dimensional filters for certain diffusions with nonlinear drift. Stochastics 5 (1981), 65-92 · Zbl 0458.60030 · doi:10.1080/17442508108833174 |
| [2] | Brockett R., Clark J.: Geometry of the conditional density equation. Proceedings of the International Conference on Analysis and Optimization of Stochastic Systems, Oxford 1978 · Zbl 0496.93049 |
| [3] | Charalambous C.: Partially observable nonlinear risk-sensitive control problems: Dynamic programming and verification theorems. IEEE Trans. Automat. Control, to appear · Zbl 0886.93070 · doi:10.1109/9.618242 |
| [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 · Zbl 0874.93093 · doi:10.1109/9.566658 |
| [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 · doi:10.1080/17442509608834063 |
| [6] | Charalambous C., Naidu D., Moore K.: Solvable risk-sensitive control problems with output feedback. Proceedings of 33rd IEEE Conference on Decision and Control, Lake Buena Vista 1994, pp. 1433-1434 |
| [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 · doi:10.1137/S0363012993251316 |
| [8] | Hazewinkel M., Willems J.: Stochastic systems: The mathematics of filtering and identification, and applications. Proceedings of the NATO Advanced Study Institute, D. Reidel, Dordrecht 1981 · Zbl 0486.00016 |
| [9] | Marcus S.: Algebraic and geometric methods in nonlinear filtering. SIAM J. Control Optim. 26 (1984), 5, 817-844 · Zbl 0548.93073 · doi:10.1137/0322052 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
