First-order and second-order necessary optimality conditions concerning components for discrete-time stochastic systems. Issue 10 (3rd October 2022)

• Record Type: Journal Article
• Authors: Song, Teng; Liu, Bin; Zhou, Qinglong
• Is Part Of: International journal of control. Volume 95:Issue 10(2022)
• Page Start: 2695
• Page End: 2709
• Publication Date: 2022-10-03
• Subjects: Discrete-time backward stochastic equations -- necessary optimality conditions -- discrete-time stochastic systems -- singular and quasi-singular controls; 93E20 -- 93C55 -- 49K45 -- 49M05; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2021.1929498
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : This paper deals with the first-order and second-order necessary optimality conditions concerning the components for discrete-time stochastic systems under weakened convexity assumptions. By means of a new discrete-time backward stochastic equation, we establish a first-order necessary optimality condition concerning every component in the form of a global stochastic maximum principle. Besides, we also obtain an optimality condition concerning one component of vector control in the form of a global stochastic maximum principle and concerning the other in the form of linearised stochastic maximum principle. Moreover, by introducing a new discrete-time backward stochastic matrix equation, we derive diverse second-order necessary optimality conditions of singular and quasi-singular controls concerning the components.