Time-inconsistent stochastic linear quadratic control for discrete-time systems  

作　　者：Qingyuan QI Huanshui ZHANG 

机构地区：[1]School of Control Science and Engineering, Shandong University, Jinan 250061, China

出　　处：《Science China(Information Sciences)》2017年第12期40-52,共13页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61120106011,61573221,61633014);Qingyuan QI was supported by the Program for Outstanding Ph.D.Candidate of Shandong University

摘　　要：This paper is mainly concerned with the time-inconsistent stochastic linear quadratic（LQ） control problem in a more general formulation for discrete-time systems. The time-inconsistency arises from three aspects： the coefficient matrices depending on the initial pair, the terminal of the cost function involving the initial pair together with the nonlinear terms of the conditional expectation. The main contributions are： firstly,the maximum principle is derived by using variational methods, which forms a flow of forward and backward stochastic difference equations（FBSDE）; secondly, in the case of the system state being one-dimensional, the equilibrium control is obtained by solving the FBSDE with feedback gain based on several nonsymmetric Riccati equations; finally, the necessary and sufficient solvability condition for the time-inconsistent LQ control problem is presented explicitly. The key techniques adopted are the maximum principle and the solution to the FBSDE developed in this paper.This paper is mainly concerned with the time-inconsistent stochastic linear quadratic（LQ） control problem in a more general formulation for discrete-time systems. The time-inconsistency arises from three aspects： the coefficient matrices depending on the initial pair, the terminal of the cost function involving the initial pair together with the nonlinear terms of the conditional expectation. The main contributions are： firstly,the maximum principle is derived by using variational methods, which forms a flow of forward and backward stochastic difference equations（FBSDE）; secondly, in the case of the system state being one-dimensional, the equilibrium control is obtained by solving the FBSDE with feedback gain based on several nonsymmetric Riccati equations; finally, the necessary and sufficient solvability condition for the time-inconsistent LQ control problem is presented explicitly. The key techniques adopted are the maximum principle and the solution to the FBSDE developed in this paper.

关 键 词：time-inconsistency open-loop equilibrium control maximum principle FBSDE nonsymmetric Riccati equations 

分 类 号：O231[理学—运筹学与控制论]