Approximation of escape time for Lagrangian systems with fast noise

IEEE Transactions on Automatic Control

Volumn 52, Issue 12, 2007, Pages 2338-2341

  Kovaleva, Agnessa ^a   Akulenko, Leonid ^b  

^a Russian Academy of Sciences   (Russian Federation)

^b INSTITUTE FOR PROBLEMS IN MECHANICS   (Russian Federation)

Author keywords

Perturbation methods; Stochastic systems

Indexed keywords

ASYMPTOTIC STABILITY; GAUSSIAN NOISE (ELECTRONIC); HAMILTONIANS; JACOBIAN MATRICES; PERTURBATION TECHNIQUES;

HAMILTON-JACOBI EQUATION; LAGRANGIAN SYSTEM;

STOCHASTIC CONTROL SYSTEMS;

EID: 38149046395     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.910696     Document Type: Article

References (19)

1. C. Soize, The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady-State Solutions. Singapore: World Scientific, 1994.
2. M. I. Freidlin, "The averaging principle and theorems on large deviations," Russ. Math. Surveys, vol. 33, pp. 117-176, 1978.
3. M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, 2nd ed. New York: Springer-Verlag, 1998.
4. H. J. Kushner, Approximation and Weak Convergence Methods for Random Processes, With Applications to Stochastic System Theory. Cambridge, MA: The MIT Press, 1984.
5. H. J. Kushner, "Robustness and approximation of escape time and large deviations estimates for systems with small noise effect," SIAM J. Appl. Math., vol. 44, pp. 160-182, 1984.
6. P. Dupuis and H. J. Kushner, "Minimizing escape probability," SIAM J. Control Optim., vol. 27, pp. 432-445, 1989.
7. P. Dupuis and W. M. McEneaney, "Risk-sensitive and robust escape criteria," J. Control Optim., vol. 35, pp. 2021-2049, 1997.
8. M. Boue and P. Dupuis, "Risk-sensitive and robust escape control for degenerate diffusion processes," Math. Control Signal Syst., vol. 14, pp. 62-85, 2001.
9. A. Kovaleva, "Risk-sensitive control for nonlinear oscillatory systems with small noise," in Nonlinear Control 2001, A. L. Fradkov and A. B. Kurzansky, Eds. New York: Elsevier Science, 2002, vol. 2, pp. 1089-1094.
10. A. Kovaleva, "Control against large deviations for oscillatory systems," in Nonlinear Stochastic Dynamics, S. Namachchivaya and Y. Lin, Eds. New York: Springer-Verlag, 2003, pp. 268-275.
11. S. M. Meerkov, "Residence time control," IEEE Trans. Autom. Control vol. 33, pp. 323-332, 1988.
12. L. Wu, "Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems," Stoch. Process. Appl., vol. 91, pp. 205-238, 2001.
13. O. V. Gulinskii and R. S. Liptser, "Example of large deviations for stationary processes," Theory Probab. Appl., vol. 44, pp. 201-217, 2000.
14. R. Liptser, V. Spokoiny, and A. Y. Veretennikov, "Freidlinn-Wentzell type large deviations for smooth processes," Markov Processes and Related Fields, vol. 8, pp. 611-636, 2002.
15. S. V. Fomin and I. M. Gelfand, Calculus of Variations. New York: Dover, 2000.
16. V. I. Arnold, Mathematical Methods of Classic Mechanics. Berlin: Springer-Verlag, 1991.
17. G. Dal Maso and H. Frankowska, "Uniqueness of solutions to Hamilton-Jacobi equations arising in the calculus of variations," in Optimal Control and Partial Differential Equations, J. L. Menaldi, E. Rofman, and A. Sulem, Eds. Amsterdam: IOS, 2001.
18. R. Courant, Partial Differential Equations. New York: Wiley, 1989.
19. L. Akulenko and A. Kovaleva, "Asymptotic estimation of the probability and mean sojourn time for a point in a circle," Doklady Math., vol. 71, pp. 320-325, 2005.