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- John Lygeros, Karl Henrik Johansson, Slobodan N. Simic, Jun Zhang, S. Shankar Sastry
- IEEE Trans. Automat. Contr.
- 2003

Hybrid automata provide a language for modeling and analyzing digital and analogue computations in real-time systems. Hybrid automata are studied here from a dynamical systems perspective. Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the… (More)

We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and the continuous dynamics model the physical processes… (More)

- John Lygeros, Claire J. Tomlin, S. Shankar Sastry
- Automatica
- 1999

The problem of systematically synthesizing hybrid controllers which satisfy multiple control objectives is considered. We present a technique, based on the principles of optimal control, for determining the class of least restrictive controllers that satisses the most important objective (which we refer to as safety). The system performance with respect to… (More)

- Alessandro Abate, Maria Prandini, John Lygeros, S. Shankar Sastry
- Automatica
- 2008

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… (More)

- Jean-Pierre Aubin, John Lygeros, Marc Quincampoix, S. Shankar Sastry, Nicolas Seube
- IEEE Trans. Automat. Contr.
- 2002

Impulse differential inclusions are introduced as a framework for modeling hybrid phenomena. Connections to standard problems in the area of hybrid systems are discussed. Conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion. For sets that violate these… (More)

In this chapter we set up a mathematical structure, called Markov string, to obtaining a very general class of models for stochastic hybrid systems. Markov Strings are, in fact, a class of Markov processes, obtained by a mixing mechanism of stochastic processes, introduced by Meyer. We prove that Markov strings are strong Markov processes with the cadlag… (More)

- Jianghai Hu, John Lygeros, S. Shankar Sastry
- HSCC
- 2000

In this paper, we present a scheme of stochastic hybrid system which introduces randomness to the deterministic framework of the traditional hybrid systems by allowing the flow inside each invariant set of the discrete state variables to be governed by stochastic differential equation (SDE) rather than the deterministic ones. The notion of embedded Markov… (More)

- T. Arampatzis, John Lygeros, S. Manesis
- Proceedings of the 2005 IEEE International…
- 2005

Wireless sensors and wireless sensor networks have come to the forefront of the scientific community recently. This is the consequence of engineering increasingly smaller sized devices, which enable many applications. The use of these sensors and the possibility of organizing them into networks have revealed many research issues and have highlighted new… (More)

We develop a model for General Stochastic Hybrid Systems (GSHS) which is a generalization of PiecewiseDeterministic Markov Processes (PDMP), introduced by Davis and stochastic hybrid systems proposed by Hu, Lygeros and Sastry. This model possesses certain desirable properties, as the strong Markov property and the càdlàg property. Extending results… (More)

- Alessandro Abate, Joost-Pieter Katoen, John Lygeros, Maria Prandini
- Eur. J. Control
- 2010

A method for approximate model checking of stochastic hybrid systems with provable approximation guarantees is proposed. We focus on the probabilistic invariance problem for discrete time stochastic hybrid systems and propose a two-step scheme. The stochastic hybrid system is first approximated by a finite state Markov chain. The approximating chain is… (More)