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2013 | 23 | 1 | 5-16
Tytuł artykułu

Attainability analysis in the problem of stochastic equilibria synthesis for nonlinear discrete systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A nonlinear discrete-time control system forced by stochastic disturbances is considered. We study the problem of synthesis of the regulator which stabilizes an equilibrium of the deterministic system and provides required scattering of random states near this equilibrium for the corresponding stochastic system. Our approach is based on the stochastic sensitivity functions technique. The necessary and important part of the examined control problem is an analysis of attainability. For 2D systems, a detailed investigation of attainability domains is given. A parametrical description of the attainability domains for various types of control inputs in a stochastic Henon model is presented. Application of this technique for suppression of noise-induced chaos is demonstrated.
Rocznik
Tom
23
Numer
1
Strony
5-16
Opis fizyczny
Daty
wydano
2013
otrzymano
2012-02-24
poprawiono
2012-06-15
Twórcy
  • Institute of Mathematics and Computer Science, Ural Federal University, 51 Lenin Street, Ekaterinburg, Russia
autor
  • Institute of Mathematics and Computer Science, Ural Federal University, 51 Lenin Street, Ekaterinburg, Russia
Bibliografia
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  • Bashkirtseva, I. and Ryashko, L. (2000). Sensitivity analysis of the stochastically and periodically forced Brusselator, Physica A 278(1-2): 126-139.
  • Bashkirtseva, I. and Ryashko, L. (2005). Sensitivity and chaos control for the forced nonlinear oscillations, Chaos Solitons and Fractals 26(5): 1437-1451.
  • Bashkirtseva, I. and Ryashko, L. (2009). Constructive analysis of noise-induced transitions for coexisting periodic attractors of Lorenz model, Physical Review E 79(4): 041106-041114.
  • Bashkirtseva, I., Ryashko, L. and Stikhin, P. (2010). Noise-induced backward bifurcations of stochastic 3D-cycles, Fluctuation and Noise Letters 9(1): 89-106.
  • Bashkirtseva, I., Ryashko, L. and Tsvetkov, I. (2009). Sensitivity analysis of stochastic equilibria and cycles for the discrete dynamic systems, Dynamics of Continuous, Discrete and Impulsive Systems, Series A: Mathematical Analysis 17(4): 501-515.
  • Chen, G. and Yu, X.E. (2003). Chaos Control: Theory and Applications, Springer-Verlag, New York, NY.
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  • Elaydi, S. (1999). An Introduction to Difference Equations, Springer-Verlag, New York, NY.
  • Fedotov, S., Bashkirtseva, I. and Ryashko, L. (2004). Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo, Physica A 342(3-4): 491-506.
  • Fradkov, A. and Pogromsky, A. (1998). Introduction to Control of Oscillations and Chaos, World Scientific Series of Nonlinear Science, Singapore.
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  • Gassmann, F. (1997). Noise-induced chaos-order transitions, Physical Review E 55(3): 2215-2221.
  • Goswami, B. and Basu, S. (2002). Transforming complex multistability to controlled monostability, Physical Review E 66(2): 026214-026223.
  • Henon, M. (1976). A two-dimensional mapping with a strange attractor, Communications in Mathematical Physics 50(1): 69-77.
  • Karthikeyan, S. and Balachandran, K. (2011). Constrained controllability of nonlinear stochastic impulsive systems, International Journal of Applied Mathematics and Computer Science 21(2): 307-316, DOI: 10.2478/v10006-011-0023-0.
  • Kučera, V. (1973). Algebraic theory of discrete optimal control for single-variable systems, III: Closed-loop control, Kybernetika 9(4): 291-312.
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  • Matsumoto, K. and Tsuda, I. (1983). Noise-induced order, Journal of Statistical Physics 31(1): 87-106.
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  • Mil'shtein, G. and Ryashko, L. (1995). A first approximation of the quasipotential in problems of the stability of systems with random non-degenerate perturbations, Journal of Applied Mathematics and Mechanics 59(1): 47-56.
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  • Ryagin, M. and Ryashko, L. (2004). The analysis of the stochastically forced periodic attractors for Chua's circuit, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 14(11): 3981-3987.
  • Ryashko, L. (1996). The stability of stochastically perturbed orbital motions, Journal of Applied Mathematics and Mechanics 60(4): 579-590.
  • Ryashko, L. and Bashkirtseva, I. (2011a). Analysis of excitability for the FitzHugh-Nagumo model via a stochastic sensitivity function technique, Physical Review E 83(6): 061109-061116.
  • Ryashko, L. and Bashkirtseva, I. (2011b). Control of equilibria for nonlinear stochastic discrete-time systems, IEEE Transactions on Automatic Control 56(9): 2162-2166.
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Bibliografia
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