Control of Exit Time for Lagrangian Systems with Weak Noise
This paper considers a problem of controlling a stochastic Lagrangian systems so as to prevent it from leaving a prescribed set. In the absence of noise, the system is asymptotically stable; weak noise induces exits from the domain of attraction of the stable equilibrium with a non-zero probability. The paper suggests a control strategy aimed at building a controlled system with exit rate asymptotically independent of noise (in the small noise limit). The analysis employs previously found explicit asymptotics of the mean exit time for stochastic Lagrangian systems. A physically meaningful example illustrates the developed methodology.
KeywordsNonlinear stochastic systems large deviations exit time control.
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- 1.H.S. Black, Stabilized feedback amplifiers, Bell System Technical Journal, 13 (1934), 1–18.Google Scholar
- 2.H.W. Bode, Network Analysis and Feedback Amplifier Design, Van Nostrand, 1945.Google Scholar
- 3.G. Franklin, J.D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 5th Edition, Prentice-Hall, 2006.Google Scholar
- 6.M.I. Freidlin and A.D. Wentzell, Random Perturbations of Dynamical Systems, 2nd Edition, Springer, 1998.Google Scholar
- 7.H.J. Kushner, Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic System Theory, The MIT Press, 1984.Google Scholar
- 10.J. Feng and T. Kurtz, Large Deviations for Stochastic Processes, AMS, 2006.Google Scholar
- 11.E. Olivieri and M.E. Vares, Large Deviations and Metastability, Cambridge University Press, 2005.Google Scholar
- 13.A. Kovaleva, Large deviations estimates of escape time for Lagrangian systems, Proc. 44th Control and Decision Conf., (2005), 8076–8081.Google Scholar
- 17.I.M. Gelfand and S.V. Fomin, Calculus of Variations. Dover Publications, 2000.Google Scholar
- 18.A. Blaquiere, Nonlinear System Analysis, Academic Press, 1966.Google Scholar
- 19.M. Tabor, Chaos and Integrability in Nonlinear Dynamics. An Introduction, Wiley, 1989.Google Scholar