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Advances in Mathematical Physics
Volume 2017, Article ID 8730859, 7 pages
https://doi.org/10.1155/2017/8730859
Research Article

Optimal Stochastic Control Problem for General Linear Dynamical Systems in Neuroscience

1Big Data Research Center, Hunan University of Commerce, Changsha 410205, China
2Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China
3School of Business Administration, Hunan University, Changsha 410081, China
4School of Finance, Guangdong University of Foreign Studies, Guangzhou 510006, China

Correspondence should be addressed to Chao Deng; moc.361@nanuhoahcgned

Received 14 May 2017; Revised 25 October 2017; Accepted 22 November 2017; Published 17 December 2017

Academic Editor: Xavier Leoncini

Copyright © 2017 Yan Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper considers a -dimensional stochastic optimization problem in neuroscience. Suppose the arm’s movement trajectory is modeled by high-order linear stochastic differential dynamic system in -dimensional space, the optimal trajectory, velocity, and variance are explicitly obtained by using stochastic control method, which allows us to analytically establish exact relationships between various quantities. Moreover, the optimal trajectory is almost a straight line for a reaching movement; the optimal velocity bell-shaped and the optimal variance are consistent with the experimental Fitts law; that is, the longer the time of a reaching movement, the higher the accuracy of arriving at the target position, and the results can be directly applied to designing a reaching movement performed by a robotic arm in a more general environment.