A second-order maximum principle for singular optimal controls with recursive utilities of stochastic delay systems. (November 2019)

• Record Type: Journal Article
• Authors: Hao, Tao; Meng, Qingxin
• Is Part Of: European journal of control. Volume 50(2019)
• Page Start: 96
• Page End: 106
• Publication Date: 2019-11
• Subjects: Second-order maximum principle -- Adjoint equation -- Delay -- Recursive utility -- Taylor expansion; 93E20 -- 60H10; Control theory -- Periodicals; Automatic control -- Periodicals; Automatic control -- Mathematics -- Periodicals; Electronic journals; 629.805
• DOI: 10.1016/j.ejcon.2019.04.001
• Languages: English
• ISSNs: 0947-3580

Abstract

Abstract: This paper is devoted to the investigation of the second-order necessary conditions of singular control problems for controlled forward-backward delay systems in the case where the control domain is non-convex and the diffusion coefficients are independent of control. A second-order matrix-valued adjoint system is constructed to solve the obstacle caused by the product of the solution and its delay counterpart of the first-order variational equations. With the help of this observation, the second-order expansion of cost functional Y ε and the stochastic maximum principle are proved. Our work generalizes the classical case to the delay case