In this talk, an open problem is solved, for the stochastic optimal control problem with delay where the control domain is nonconvex and the diffusion term contains both control and its delayed term. Inspired by previous results about delayed stochastic control systems, Peng's general stochastic maximum principle is generalized to the time delayed case, which is called the global maximum principle. A special backward stochastic differential equation is introduced to deal with the cross terms, when applying the duality technique. Comparing with the classical result, the maximum condition contains an indicator function, which in fact is the characteristic of the stochastic optimal control problem with delay. Furthermore, to illustrate the applications of our theoretical results, two dynamic optimization problems are addressed.
史敬涛，山东大学数学学院教授、博士生导师。主要从事随机控制、微分对策、正倒向随机系统、时滞随机系统与金融数学等方面的研究。曾赴美国、澳大利亚、香港、澳门等国家和地区访问交流。目前在 IEEE Transactions on Automatic Control、Automatica、SIAM Journal on Control and Optimization 等国际 学术期刊发表论文30余篇，曾获中国科协期刊优秀学术论文奖、张嗣瀛优秀青年论文奖、山东省高等学校科学技术奖等奖项，主持和参与多项国家和山东省自然科学基金项目，参与国家重点研发计划和国家自然科学基金重点项目。现为中国自动化学会控制论专业委员会随机系统控制学组委员。