First-order and second-order necessary optimality conditions for discrete-time stochastic systems with delay. (29th April 2022)

• Record Type: Journal Article
• Authors: Song, Teng; Liu, Bin
• Is Part Of: IMA journal of mathematical control and information. Volume 39:Number 2(2022)
• Page Start: 731
• Page End: 750
• Publication Date: 2022-04-29
• Subjects: Discrete-time stochastic systems -- necessary optimality conditions -- discrete-time backward stochastic equations -- quasi-singular control; Control theory -- Periodicals; 629.831205
• DOI: 10.1093/imamci/dnac010
• Languages: English
• ISSNs: 0265-0754

Abstract

Abstract: This paper is concerned with the first-order and second-order necessary optimality conditions for discrete-time stochastic systems with delay under weak assumptions. Based on a characteristic method and a discrete-time backward stochastic equation, we establish the linearized discrete-time stochastic maximum principle and Euler-type necessary optimality condition. Moreover, by a new discrete-time backward stochastic matrix equation, we also obtain the necessary optimality condition of quasi-singular control and the pointwise second-order optimality condition.