A Class of Optimal Control Problems of Forward–Backward Systems with Input Constraint

Jianhui Huang (), Wenqiang Li () and Hanyu Zhao ()
Additional contact information
Jianhui Huang: The Hong Kong Polytechnic University
Wenqiang Li: Yantai University
Hanyu Zhao: The Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 3, No 8, 1050-1084

Abstract: Abstract In this paper, we consider a new class of optimal control problems with admissibility constraint, where the state is driven by a fully coupled forward backward stochastic differential equation (FBSDE) with mixed initial-terminal condition. Different from the classical control problems, both dynamic process control and static initial-terminal perturbations are considered. Moreover, all control/perturbation components are subject to input constraint in terms of closed convex sets and partial information in terms of some sub-filtration for randomness evolution. We first study the nonlinear case of aforementioned FBSDE optimal control by deriving stochastic maximum principle. Next, we consider the linear quadratic case with explicit representation of the optimal admissible controls. More specifically, a new Hamiltonian system involving three projection operators and conditional expectation is derived. Finally, we apply obtained maximum principle to study a general class of large-population system and provide a unified framework to analyze related mean-field game (MFG). Our result includes considerable existing MFG results as its special cases and provides some new features such as recursive functional or input delay average.

Keywords: Mixed forward backward stochastic differential equation; Initial-terminal perturbation; Input constraint; Stochastic maximum principle; Large-population problem; Mean-field game (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-023-02314-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:199:y:2023:i:3:d:10.1007_s10957-023-02314-0

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-023-02314-0

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().