A revisit to stochastic near-optimal controls: The critical case |
| |
| Affiliation: | 1. Department of Mathematical Sciences, Huzhou University, Zhejiang 313000, China;2. School of Risk and Actuarial Studies and CEPAR, UNSW Business School, The University of New South Wales, Sydney, NSW 2052, Australia;1. Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA;2. Department of Electrical and Computer Engineering, University of Cyprus, Nicosia, Cyprus;1. Banco de la República (Central Bank of Colombia), Colombia;2. CEMLA, Mexico;1. School of Automotive and Transport Engineering, Hefei University of Technology, Hefei 230009, China;2. School of Computer Science and Technology, Beihang University, Beijing 230009, China;1. Laboratoire des Signaux et Systèmes, CNRS-Supélec-Université Paris Sud, 3 rue Joliot-Curie, 91192 Gif-sur-Yvette cedex, France;2. Institut Polytechnique des Sciences Avancées, 7 rue Maurice Grandcoing, 94200 Ivry-sur-Seine, France;3. Université de Lorraine, CRAN, UMR 7039, 2 avenue de la forêt de Haye, 54516 Vandoeuvre-lès-Nancy Cedex, France;4. CNRS, CRAN, UMR 7039, 2 avenue de la forêt de Haye, 54516 Vandoeuvre-lès-Nancy Cedex, France |
| |
| Abstract: | This paper revisits the stochastic near-optimal control problem considered in Zhou (1998), where the stochastic system is given by a controlled stochastic differential equation with the control variable taking values in a general control space and entering both the drift and diffusion coefficients. A necessary condition of near-optimality is derived using Ekeland’s variational principle, spike variation techniques, and some delicate estimates for the state and the adjoint processes. We improve the error bound of order from “almost” in Zhou (1998) to “exactly” . |
| |
| Keywords: | Stochastic near-optimal control Necessary condition Maximum principle Ekeland’s variational principle Error bound |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
