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Stochastic Approximations of Hybrid Systems Alessandro Abate, Aaron D. Ames, S. Shankar Sastry
 

Summary: Stochastic Approximations of Hybrid Systems
Alessandro Abate, Aaron D. Ames, S. Shankar Sastry
Department of Electrical Engineering and Computer Sciences
University of California at Berkeley
Berkeley, CA 94720
{aabate,adames,sastry}@eecs.berkeley.edu
Abstract-- This paper introduces a method for approximat-
ing the dynamics of deterministic hybrid systems. Within this
setting, we shall consider jump conditions that are character-
ized by spacial 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 will 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 will show that the stochastic

  

Source: Abate, Alessandro - Faculty of Mechanical, Maritime and Materials Engineering, Technische Universiteit Delft

 

Collections: Engineering