This paper presents a computational technique for verifying properties of hybrid systems with arbitrary continuous dynamics. The approach is based on the computation of approximating automata, which are nite-state approximations to the (possibly innnite-state) discrete-trace transition system for the hybrid system. The fundamental computation in the generation of approximating automata is the m...

This paper studies the existence of solutions to a class of hybrid automata in which the underlying continuous dynamics are represented by inhomogeneous linear time-invariant systems whose inputs are controls that can be determined by the user. The principal result of the paper is a procedure that searches for global periodic non-terminating solutions of systems having a single cycle.

In the existing abundance of different hybrid automata formalisms concurrent composition is seldom considered or requires additional semantics which is not always defined. This work considers three common reasons of problems with hybrid automata composition: contradicting resets in the discrete transitions, global time reference with contradicting initial conditions and redundant non-determinis...

This paper addresses the analysis of slope-parametric hybrid automata: nding conditions on the slopes of the automaton variables, for some safety property to be veriied. The problem is shown decidable in some practical situations (e.g. nding the running speeds of tasks in a real time application, for all tasks to respect their deadlines). The resolution technique generalizes polyhedral-based sy...

This paper addresses the analysis of slope-parametric hybrid automata: nding conditions on the slopes of the automaton variables, for some safety property to be veriied. The problem is shown decidable in some practical situations (e.g. nding the running speeds of tasks in a real time application, for all tasks to respect their deadlines). The resolution technique generalizes polyhedral-based sy...

We develop definitions to formalize the notion of hybrid systems as dynamical systems that describe the evolution in time of the values of a set of discrete and continuous variables. In this chapter, we restrict our attention to autonomous hybrid automata, that is time invariant hybrid systems without inputs. In subsequent chapters we will extend this class of hybrid models and introduce input ...

In this paper we study the problem of automatically generating switching controllers for the class of Linear Hybrid Automata, with respect to safety objectives. We identify and solve inaccuracies contained in previous characterizations of the problem, providing a sound and complete symbolic fixpoint procedure, based on polyhedral abstractions of the state space. We also prove the termination of...

We define a special class of hybrid automata, called Deterministic and Transversal Linear Hybrid Automata (DTLHA), whose continuous dynamics in each location are linear timeinvariant (LTI) with a constant input, and for which every discrete transition up to a given bounded time is deterministic and, importantly, transversal. For such a DTLHA starting from an initial state, we show that it is po...

Despite researchers’ efforts in the last couple of decades, reachability analysis is still a challenging problem even for linear hybrid systems. Among the existing approaches, the most practical ones are mainly based on bounded-time reachable set over-approximations. For the purpose of unbounded-time analysis, one important strategy is to abstract the original system and find an invariant for t...