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Approximate Abstractions of Discrete-Time Controlled Stochastic Hybrid Systems
 

Summary: Approximate Abstractions of
Discrete-Time Controlled Stochastic Hybrid Systems
Alessandro D'Innocenzo, Alessandro Abate, and Maria D. Di Benedetto
Abstract-- This work proposes a procedure to construct
a finite abstraction of a controlled discrete-time stochastic
hybrid system. The state space and the control space of the
original system are partitioned by finite lattices according to
some refinement parameters. The approximation errors can
be explicitly computed, over time, given proper continuity
assumptions on the model. We show that the errors can be
arbitrarily chosen by increasing the partition accuracy. Similar
bounds can be provided if a particular feedback control policy
is selected and quantized. The obtained abstraction can be
interpreted as a Bounded-parameters Markov Decision Process,
or a controlled Markov set-Chain, and can be used both for
verification and control design purposes. We finally test the
approximate abstraction technique on a model from systems
biology.
I. INTRODUCTION
The dynamical analysis of complex, high-dimensional,

  

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

 

Collections: Engineering