zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stochastic affine quadratic regulator with applications to tracking control of quantum systems. (English) Zbl 1152.93501
Summary: This paper deals with the regulator theory of stochastic affine systems. Applying a tensor formal power series method, stochastic bilinear quadratic regulator is solved numerically. An example about tracking control of quantum systems is given to show the usefulness of the developed theory.

93E03General theory of stochastic systems
60H10Stochastic ordinary differential equations
93E20Optimal stochastic control (systems)
Full Text: DOI
[1] Aganovic, Z.; Gajic, Z.: Linear optimal control of bilinear systems with applications to singular perturbations and weak coupling. Lecture notes in control and information sciences 206 (1995) · Zbl 0827.49020
[2] Banks, S. P.: Mathematical theories of nonlinear systems. (1986) · Zbl 0582.93030
[3] Bensoussan, A.: Lecture on stochastic control,-part I, ser. Lecture note in mathematics 972, 1-39 (1983)
[4] Byrnes, C. I.; Isdori, A.; Willems, J. C.: Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE transactions on automatic control 36, 1228-1240 (1991) · Zbl 0758.93007
[5] Chen, B. S., Hsu, F., Chen, W. H., & Zhang, W. (2006). Optimal tracking control design of quantum systems: Formal tensor power series approach. Technical Report. Tsing Hua University
[6] D’alessandro, D.; Dahleh, M.: Optimal control of two-level quantum systems. IEEE transactions on automatic control 46, 866-876 (2001) · Zbl 0993.81070
[7] Has’minskii, R. Z.: Stochastic stability of differential equations. (1980)
[8] Jacobson, D. H.; Martin, D. H.; Pachter, M.; Geveci, T.: Extensions of linear-quadratic control theory. Lecture note in control and information sciences 27 (1980) · Zbl 0435.93001
[9] Kalman, R. E.: Contributions to the theory of optimal control. Boletin de la sociedad matematica mexicana 5, 102-119 (1960)
[10] Kushner, H. J.: Stochastic stability. Lecture note in mathematics 294, 97-124 (1972)
[11] Moylan, P. J.; Anderson, B. D. O.: Nonlinear regulator theory and an inverse optimal control problem. IEEE transactions on automatic control 18, 460-465 (1973) · Zbl 0283.49007
[12] Terdik, Gy.: Stochastic models and related problems of nonlinear time series analysis: A frequency domain approach. Lecture notes in statistics 142 (1999) · Zbl 0928.62068
[13] Wang, F. Y.; Saridis, G. N.: Suboptimal control for nonlinear stochastic systems. Proc. 31st conf. Decision and control, 1856-1861 (1992)
[14] Wonham, W. M.: Random differential equations in control theory. Probabilistic methods in applied mathematics 2, 131-212 (1970) · Zbl 0235.93025
[15] Yamamoto, N.; Tsumura, K.; Hara, S.: Feedback control of quantum entanglement in a two-spin system. Automatica 43, 981-992 (2007) · Zbl 1282.93130
[16] Yaz, E.: Infinite horizon quadratic optimal control of a class of nonlinear stochastic systems. IEEE transactions on automatic control 34, 1176-1180 (1989) · Zbl 0693.93084
[17] Yong, J.; Zhou, X. Y.: Stochastic control: Hamiltonian systems and HJB equations. (1999) · Zbl 0943.93002
[18] Zhang, W.; Chen, B. S.: On stabilizability and exact observability of stochastic systems with their applications. Automatica 40, 87-94 (2004) · Zbl 1043.93009
[19] Zhang, W.; Chen, B. S.: State feedback H$\infty $control for a class of nonlinear stochastic systems. SIAM journal on control optimization 44, 1973-1991 (2006)
[20] Zhang, W.; Zhang, H.; Chen, B. S.: Stochastic H2/H$\infty $control with (x,u,v)-dependent noise: finite horizon case. Automatica 43, 513-521 (2006)