Stochastic approximations of hybrid systems

A. Abate, A.D. Ames, S.S. Sastry
Proceedings of the 2005, American Control Conference, 2005.  
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 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
more » ... an 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 approximation of a hybrid system is accurate, while being able to handle "pathological cases." Finally, further generalizations of this approach are motivated and discussed.
doi:10.1109/acc.2005.1470189 fatcat:v44jvfgnm5euhe2a4ofpmljq54