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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1 Approximate Abstractions of Stochastic Hybrid Systems
 

Summary: IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1
Approximate Abstractions of Stochastic Hybrid Systems
Alessandro Abate, Alessandro D'Innocenzo, and
Maria D. Di Benedetto
Abstract--We present a constructive procedure for obtaining a finite ap-
proximate abstraction of a discrete-time stochastic hybrid system. The pro-
cedure consists of a partition of the state space of the system and depends
on a controllable parameter. Given proper continuity assumptions on the
model, the approximation errors introduced by the abstraction procedure
are explicitly computed and it is shown that they can be tuned through
the parameter of the partition. The abstraction is interpreted as a Markov
set-Chain. We show that the enforcement of certain ergodic properties on
the stochastic hybrid model implies the existence of a finite abstraction with
finite error in time over the concrete model, and allows introducing a fi-
nite-time algorithm that computes the abstraction.
Index Terms--Markov Chains, stochastic hybrid systems.
I. INTRODUCTION AND RELATED WORK
The study of complex, heterogeneous, and probabilistic models such
as Stochastic Hybrid Systems poses challenges, both analytically (e.g.,
steady-state analysis, synthesis of optimal controllers [1]) and com-

  

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

 

Collections: Engineering