Abstract
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.
Mathematics Subject Classification (2000). 60H10,60F10.
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Kovaleva, A. (2011). Control of Exit Time for Lagrangian Systems with Weak Noise. In: Dalang, R., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications VI. Progress in Probability, vol 63. Springer, Basel. https://doi.org/10.1007/978-3-0348-0021-1_11
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DOI: https://doi.org/10.1007/978-3-0348-0021-1_11
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