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Probabilistic Reachability and Safety for Controlled Discrete Time Stochastic Hybrid Systems

Summary: Probabilistic Reachability and Safety for Controlled
Discrete Time Stochastic Hybrid Systems
Alessandro Abate a
, Maria Prandini b
, John Lygeros c
, Shankar Sastry a
Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, USA
Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy
Automatic Control Laboratory, ETH Zurich, Switzerland
In this work, probabilistic reachability over a finite horizon is investigated for a class of discrete time stochastic hybrid systems
with control inputs. A suitable embedding of the reachability problem in a stochastic control framework reveals that it is
amenable to two complementary interpretations, leading to dual algorithms for reachability computations. In particular, the
set of initial conditions providing a certain probabilistic guarantee that the system will keep evolving within a desired `safe'
region of the state space is characterized in terms of a value function, and `maximally safe' Markov policies are determined via
dynamic programming. These results are of interest not only for safety analysis and design, but also for solving those regulation
and stabilization problems that can be reinterpreted as safety problems. The temperature regulation problem presented in the


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


Collections: Engineering