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Stochastic approximations of hybrid systems

Abate, Alessandro and Ames, Aaron D. and Sastry, S. Shankar (2005) Stochastic approximations of hybrid systems. In: 2005 American Control Conference. Vol.3. IEEE , Piscataway, NJ, pp. 1557-1562. ISBN 0-7803-9098-9. https://resolver.caltech.edu/CaltechAUTHORS:20190305-074604391

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Abstract

This paper introduces a method for approximating the dynamics of deterministic hybrid systems. Within this setting, we shall consider jump conditions that are characterized by spatial guards. After defining proper penalty functions along these deterministic guards, corresponding probabilistic intensities are introduced and the deterministic dynamics are approximated by the stochastic evolution of a continuous-time Markov process. We would illustrate how the definition of the stochastic barriers can avoid ill-posed events such as "grazing", and show how the probabilistic guards can be helpful in addressing the problem of event detection. Furthermore, this method represents a very general technique for handling Zeno phenomena; it provides a universal way to regularize a hybrid system. Simulations would show that the stochastic approximation of a hybrid system is accurate, while being able to handle ''pathological cases". Finally, further generalizations of this approach are motivated and discussed.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ACC.2005.1470189DOIArticle
ORCID:
AuthorORCID
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2005 AACC. This research is supported by the National Science Foundation (NSF award number CCR-0225610).
Funders:
Funding AgencyGrant Number
NSFCCR-0225610
Record Number:CaltechAUTHORS:20190305-074604391
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190305-074604391
Official Citation:A. Abate, A. D. Ames and S. S. Sastry, "Stochastic approximations of hybrid systems," Proceedings of the 2005, American Control Conference, 2005., Portland, OR, USA, 2005, pp. 1557-1562 vol. 3. doi: 10.1109/ACC.2005.1470189
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:93513
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Mar 2019 16:35
Last Modified:03 Oct 2019 20:55

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