ON OPTIMAL STOCHASTIC LINEAR QUADRATIC CONTROL WITH INVERSELY PROPORTIONAL TIME-WEIGHTING IN THE COST*

被引：1

作者：

Palamarchuk, E. S. ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Moscow, Russia

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2022年 / 67卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

  stochastic linear-quadratic regulator; pathwise optimality; inversely proportional time-weighting of costs; absolutely integrable state matrix; DIFFERENTIAL-EQUATION; ASYMPTOTIC-BEHAVIOR; SYSTEM;

D O I：

10.1137/S0040585X97T990733

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider an optimal linear-quadratic control problem for a control system where the matrices corresponding to the state in the controlled process equation and the cost functional are absolutely integrable over an infinite time interval. The integral quadratic performance index includes two mutually inversely proportional time-weighting functions. It is shown that a well-known linear stable feedback law turns out to be optimal with respect to criteria from the class of the extended long-run averages. The results are applied to studying a control system under time-varying dynamic scaling of its parameters.

引用

页码：28 / 43

页数：16

共 23 条

[1]

Adrianova L. Y., 1995, T MATH MONOGR, V146, DOI [10.1090/mmono/146, DOI 10.1090/MMONO/146]

[2] On a stochastic optimality of the feedback control in the lqg-problem [J].

Belkina, TA ;

Kabanov, YM ;

Presman, EL .

THEORY OF PROBABILITY AND ITS APPLICATIONS, 2003, 48 (04) :592-603

[3] ASYMPTOTIC LOWER BOUNDS FOR OPTIMAL TRACKING: A LINEAR PROGRAMMING APPROACH [J].

Cai, Jiatu ;

Rosenbaum, Mathieu ;

Tankov, Peter .

ANNALS OF APPLIED PROBABILITY, 2017, 27 (04) :2455-2514

[4] Persistence of a Brownian particle in a time-dependent potential [J].

Chakraborty, D. .

PHYSICAL REVIEW E, 2012, 85 (05)

[5]

Cramer H., 1967, Stationary and Related Stochastic Processes: Sample Function Properties and Their Applications

[6]

Davis MHA, 1977, Linear Estimation and Stochastic Control

[7] Stochastic dynamic models and Chebyshev splines [J].

Fan, Ruzong ;

Zhu, Bin ;

Wang, Yuedong .

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 2014, 42 (04) :610-634

[8] Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion [J].

Jeon, Jae-Hyung ;

Chechkin, Aleksei V. ;

Metzler, Ralf .

PHYSICAL CHEMISTRY CHEMICAL PHYSICS, 2014, 16 (30) :15811-15817

[9]

Kwakernaak H., 1972, Linear Optimal Control Systems

[10]

LEFEBVRE M, 1988, ANN SCI MATH QUEBEC, V12, P101

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