Several example vehicle deceleration maneuvers arising in automated transportation systems are specified, and their correctness verified, using the hybrid I/O automaton model of Lynch, Segala, Vaandrager and Weinberg [16]. All system components are formalized using hybrid I/O automata, and their combination described using automaton composition. The proofs use invariant assertions, simulation m...

Action Systems is a predicate transformer based formalism for the devel opment of reactive and distributed systems by re nement Lately Action Systems was extended with a di erential action that models continuous be haviour Such action systems capture hybrid systems where a discrete con troller interacts with some continuously evolving environment Recently we investigated a class of Action Syste...

This paper presents a hierarchical hybrid system modeling and simulation framework using the Ptolemy I1 environment. Ptolemy I1 is a system-level design tool that supports the integration of multiple models of computation. The modeling of hierarchical hybrid systems is achieved by combining continuous-time models with finite state automata. Breakpoint handling, event detection and invariant mon...

Given an asymptotically stabilizing linear MPC controller, this paper proposes an algorithm to construct invariant polyhedral sets for the closed-loop system. The approach exploits a recently developed DC (Difference of Convex functions) programming technique developed by the authors to construct a polyhedral set in between two convex sets. Here, the inner convex set is any given level set V (x...

Hybrid systems are digital real-time systems that are embedded in analog environments. Model-checking tools are available for the automatic analysis of linear hybrid automata, whose environment variables are subject to piecewise-constant poly-hedral diierential inclusions. In most embedded systems, however, the environment variables have diierential inclusions that vary with the values of the v...

We consider the problem of safety verification for hybrid systems, whose continuous dynamics in each mode is affine, Ẋ = AX + b, and invariants and guards are specified using rectangular constraints. We present a counter-example guided abstraction refinement framework (CEGAR), which abstract these hybrid automata into simpler ones with rectangular inclusion dynamics, ẋ ∈ I, where x is a variabl...

Hybrid systems are digital real-time systems that are embedded in analog environments. Model-checking tools are available for the automatic analysis of linear hybrid automata, whose environment variables are subject to piecewise-constant polyhedral di erential inclusions. In most embedded systems, however, the environment variables have di erential inclusions that vary with the values of the va...

We explore the combination of bounded model checking and induction for proving safety properties of infinite-state systems. In particular, we define a general k-induction scheme and prove completeness thereof. A main characteristic of our methodology is that strengthened invariants are generated from failed k-induction proofs. This strengthening step requires quantifier-elimination, and we prop...

We show that regarding finite automata (FA) as discrete, time-invariant linear systems over semimodules, allows to: (1) express FA minimization and FA determinization as particular observability and reachability transformations of FA, respectively; (2) express FA pumping as a property of the FA’s reachability matrix; (3) derive canonical forms for FAs. These results are to our knowledge new, an...