On Convergence of Attainability Sets for Controlled Two-Scale Stochastic Linear Systems
| Autor: | Sergei Pergamenshchikov, Yuri Kabanov |
|---|---|
| Rok vydání: | 1997 |
| Předmět: |
Control and Optimization
Differential equation Applied Mathematics Linear system Mathematical analysis Scale (descriptive set theory) Attainability sets Singular perturbations Hausdorff metric Two - scale system Stochastic differential equation symbols.namesake Wiener process Convergence (routing) symbols Limit (mathematics) Controlled stochastic differential equations Mayer problem Mathematics Variable (mathematics) |
| Zdroj: | SIAM Journal on Control and Optimization |
| ISSN: | 1095-7138 0363-0129 |
| DOI: | 10.1137/s0363012994269685 |
| Popis: | A limit of attainability sets is found for a linear two-scale stochastic system for the case when the diffusion coefficient of the fast variable is of order $\varepsilon^{1/2}$. The attainability set is defined as the set of distributions of attainable terminal values of solutions of stochastic differential equations. As a corollary we calculate a limit of the optimal value of the terminal cost in the stochastic Mayer problem. |
| Databáze: | OpenAIRE |
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