The Norm Optimal Control Problem for Stochastic Linear Control Systems∗
1 School of Mathematics and Statistics,
Southwest University, Chongqing
2 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P.R. China.
Revised: 21 April 2014
In this paper we are concerned with two norm optimal control problems for different stochastic linear control systems. One is for approximately controllable systems with the natural filtration, while another is for exactly controllable systems with a general filtration. For each aforementioned norm optimal control problem, we construct the unique norm optimal control, through building up some suitable quadratic functional and making use of a variational characterization on its minimizer.
Mathematics Subject Classification: 93E20 / 93C05
Key words: Norm optimal control / stochastic linear control systems / controllability / filtration
Part of this work was finished when this author was a Ph.D. student at the “Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences”. This author is supported by the National Basic Research Program of China (973 Program) under grant 2011CB808002, by the NSF of China under Grants 11231007 and 11101452 and by Fundamental Research Funds for the Central Universities under grants SWU113038 and XDJK2014C076.
© EDP Sciences, SMAI 2015