Forward–backward linear–quadratic optimal control and stabilization problems for discrete-time stochastic delayed system. (September 2020)

• Record Type: Journal Article
• Authors: Song, Teng; Liu, Bin
• Is Part Of: IFAC journal of systems and control. Volume 13(2020)
• Publication Date: 2020-09
• Subjects: 93E20 -- 93C55 -- 49N10 -- 49J21 -- 93E15; Forward–backward stochastic difference equations -- LQ stochastic optimal control -- Stabilization -- Time-delay -- Riccati–ZXL difference equations; Automatic control -- Periodicals; Relay control systems -- Periodicals; Embedded computer systems -- Periodicals; Feedback control systems -- Periodicals; Artificial intelligence -- Periodicals; Artificial intelligence; Automatic control; Embedded computer systems; Feedback control systems; Relay control systems; Electronic journals; Periodicals; 629.89
• DOI: 10.1016/j.ifacsc.2020.100093
• Languages: English
• ISSNs: 2468-6018

Abstract

Abstract: This paper is concerned with a type of forward–backward linear–quadratic (FBLQ) stochastic optimal control and stabilization problems for the discrete-time forward–backward stochastic delayed system (FBSDS). We first present the necessary and sufficient unique solvability condition of a kind of general forward–backward stochastic difference delayed equations (FBSDDEs) in terms of the Riccati-ZXL difference equations. Then, by virtue of the solution to the FBSDDEs and the stochastic maximum principle, we explicitly design the optimal controller, which is a linear function of the conditional expectation of the state. In addition, an equivalent condition of the mean-square exponential stabilizability for the FBSDS is obtained by investigating the asymptotic behavior of the Riccati-ZXL difference equations. Finally, some numerical examples are exploited to illustrate the validity of the obtained results.