Open-loop and closed-loop solvabilities for stochastic linear quadratic optimal control problems of Markovian regime switching system

Xin Zhang, Xun Li, Jie Xiong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markovian regime switching system. The representation of the cost functional for the stochastic LQ optimal control problem of Markovian regime switching system is derived by the technique of Itô's formula with jumps. For the stochastic LQ optimal control problem of Markovian regime switching system, we establish the equivalence between the open-loop (closed-loop, resp.) solvability and the existence of an adapted solution to the corresponding forward-backward stochastic differential equation with constraint. (i.e., the existence of a regular solution to Riccati equations). Also, we analyze the interrelationship between the strongly regular solvability of Riccati equations and the uniform convexity of the cost functional. Finally, we present an example which is open-loop solvable but not closed-loop solvable.

Original languageEnglish
Article number69
Pages (from-to)1-35
Number of pages35
JournalESAIM - Control, Optimisation and Calculus of Variations
Volume27
DOIs
Publication statusE-pub ahead of print - Jul 2021

Keywords

  • Closed-loop solvability
  • Linear quadratic optimal control
  • Markovian regime switching
  • Open-loop solvability
  • Riccati equations

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Control and Optimization
  • Computational Mathematics

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