Almost global stochastic stability

被引：27
作者：
van Handel, Ramon [1 ]
机构：
[1] CALTECH, Dept Phys, Pasadena, CA 91125 USA
[2] CALTECH, Dept Control & Dynam Syst, Pasadena, CA 91125 USA
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2006年 / 45卷 / 04期
关键词：
stochastic stability; stochastic flows; nonlinear stochastic control;
D O I：
10.1137/040618850
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We develop a method to prove almost global stability of stochastic differential equations in the sense that almost every initial point (with respect to the Lebesgue measure) is asymptotically attracted to the origin with unit probability. The method can be viewed as a dual to Lyapunov's second method for stochastic differential equations and extends the deterministic result of [A. Rantzer, Syst. Control Lett., 42 (2001), pp. 161-168]. The result can also be used in certain cases to find stabilizing controllers for stochastic nonlinear systems using convex optimization. The main technical tool is the theory of stochastic flows of diffeomorphisms.
引用
收藏
页码：1297 / 1313
页数：17
相关论文
共 24 条
[1]  
[Anonymous], 2013, Nonlinear control systems
[2]  
Arnold L, 1997, COMPUT APPL MATH, V16, P3
[3]  
Arnold L., 1998, Springer Monographs in Mathematics
[4]  
Baxendale P. H., 1992, PROGR PROBAB, V27, P3
[5]  
Bensoussan A., 1992, STOCHASTIC CONTROL P
[6]   Stabilization of stochastic nonlinear systems driven by noise of unknown covariance [J].
Deng, H. ;
Krstić, M. ;
Williams, R.J. .
1600, Institute of Electrical and Electronics Engineers Inc. (46)
[7]   Stochastic nonlinear stabilization .1. A backstepping design [J].
Deng, H ;
Krstic, M .
SYSTEMS & CONTROL LETTERS, 1997, 32 (03) :143-150
[8]   A UNIVERSAL FORMULA FOR THE STABILIZATION OF CONTROL STOCHASTIC DIFFERENTIAL-EQUATIONS [J].
FLORCHINGER, P .
STOCHASTIC ANALYSIS AND APPLICATIONS, 1993, 11 (02) :155-162
[9]   LYAPUNOV-LIKE TECHNIQUES FOR STOCHASTIC STABILITY [J].
FLORCHINGER, P .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1995, 33 (04) :1151-1169
[10]   A stochastic Jurdjevic-Quinn theorem [J].
Florchinger, P .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2002, 41 (01) :83-88
123