A Maximum Principle for Optimal Control of Discrete-Time Stochastic Systems With Multiplicative Noise

被引：48

作者：

Lin, Xiangyun ^{[1
]}

Zhang, Weihai ^{[2
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[2] Shandong Univ Sci & Technol, Coll Elect Engn & Automat, Qingdao 266590, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2015年 / 60卷 / 04期

关键词：

Backward stochastic difference equations; discrete-time stochastic systems; maximum principle; DIFFERENTIAL-EQUATIONS;

D O I：

10.1109/TAC.2014.2345243

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The maximum principle (MP) for the discrete-time stochastic optimal control problems is proved. It is shown that the adjoint equations of the MP are a pair of backward stochastic difference equations.

引用

页码：1121 / 1126

页数：6

共 15 条

[1] INTRODUCTORY APPROACH TO DUALITY IN OPTIMAL STOCHASTIC CONTROL [J].

BISMUT, JM .

SIAM REVIEW, 1978, 20 (01) :62-78

[2] MAXIMUM PRINCIPLE FOR A CLASS OF DISCRETE DYNAMICAL-SYSTEMS WITH LAGS [J].

BURDET, CA ;

SETHI, SP .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1976, 19 (03) :445-454

[3]

Halkin H., 1966, SIAM J. Control, V4, P90, DOI [DOI 10.1137/0304009, 10.1137/0304009]

[4]

Kushner Harold., 1964, J. Math. Anal. Appl, V8, P287, DOI DOI 10.1016/0022-247X(64)90070-8

[5] NECESSARY CONDITIONS FOR CONTINUOUS PARAMETER STOCHASTIC OPTIMIZATION PROBLEMS [J].

KUSHNER, HJ .

SIAM JOURNAL ON CONTROL, 1972, 10 (03) :550-&

[6] Stochastic optimization theory of backward stochastic differential equations with jumps and viscosity solutions of Hamilton-Jacobi-Bellman equations [J].

Li, Juan ;

Peng, Shige .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (04) :1776-1796

[7] A GENERAL STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL-CONTROL PROBLEMS [J].

PENG, SG .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1990, 28 (04) :966-979

[8] Fully coupled forward-backward stochastic differential equations and applications to optimal control [J].

Peng, SG ;

Wu, Z .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1999, 37 (03) :825-843

[9] Discrete-time indefinite LQ control with state and control dependent noises [J].

Rami, MA ;

Chen, X ;

Zhou, XY .

JOURNAL OF GLOBAL OPTIMIZATION, 2002, 23 (3-4) :245-265

[10] A MATHEMATICAL THEORY OF SAVING [J].

Ramsey, F. P. .

ECONOMIC JOURNAL, 1928, 38 (152) :543-559

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