Reachability Analysis of Hybrid Systems via Predicate Abstraction

We present a general framework for the formal speci cation and algorithmic analysis of hybrid systems. A hybrid system consists of a discrete program with an analog environment. We model hybrid systems as nite automata equipped with variables that evolve continuously with time according to dynamical laws. For veri cation purposes, we restrict ourselves to linear hybrid systems, where all variables follow piecewise-linear trajectories. We provide decidability and undecidability results for classes of linear hybrid systems, and we show that standard programanalysis techniques can be adapted to linear hybrid systems. In particular, we consider symbolic model-checking and minimization procedures that are based on the reachability analysis of an in nite state space. The procedures iteratively compute state sets that are de nable as unions of convex polyhedra in multidimensional real space. We also present approximation techniques for dealing with systems for which the iterative procedures do not converge.

2017

Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of reachability - namely, the reflexive and transitive closure of a transition relation - can be unsafe, ie, it may compute a proper subset of the set of states reachable in finite time from a set of initial states. Therefore, we propose safe reachability, which always computes a superset of the set of reachable states. Second, in safety analysis of hybrid and continuous systems, it is important to ensure that a reachability analysis is also robust wrt small perturbations to the set of initial states and to the system itself, since discrepancies between a system and its mathematical models are unavoidable. We show that, under certain conditions, the best Scott continuous approximation of an analysis A is also its best robust approximation. Finally, we exe...

A new algorithm is presented for computing approximations of the reached sets of linear hybrid automata. First, we present some new theoretical results on termination of a class of reachability algorithms, which includes Botchkarev's, based on ellipsoidal calculus. The main con- tribution of the paper is a revised reachability computation that avoids the approximations caused by the union operation in the discretized flow tube estimation. Therefore, the new algorithm may correctly classify as unreachable states that are reachable according to the previous algorithm because of the looser over-approximations introduced by the union op- eration. We implemented the new reachability algorithm and tested it successfully on a real-life case modeling a hybrid model of a controlled car engine.

Electronic proceedings in theoretical computer science, 2017

In this paper we propose an improvement for flowpipe-construction-based reachability analysis techniques for hybrid systems. Such methods apply iterative successor computations to pave the reachable region of the state space by state sets in an over-approximative manner. As the computational costs steeply increase with the dimension, in this work we analyse the possibilities for improving scalability by dividing the search space in sub-spaces and execute reachability computations in the sub-spaces instead of the global space. We formalise such an algorithm and provide experimental evaluations to compare the efficiency as well as the precision of our sub-space search to the original search in the global space.

Annual Reviews in Control, 2009

Safety verification and reachability analysis for hybrid systems is a very active research domain. Many approaches that seem quite different, have been proposed to solve this complex problem. This paper presents an overview of various approaches for autonomous, continuous-time hybrid systems and presents them with respect to basic problems related to verification.

1999

Linear hybrid systems are nite state machines with linear vector elds of the form _ x = Ax in each discrete location. Very recently, the reachability problem for classes of linear hybrid systems was shown to be decidable. In this paper, the decidability result is extended to capture classes of linear hybrid systems where in each location the dynamics are of the form _ x = Ax + Bu, f o r v arious types of inputs.

International Journal of Modeling and Optimization, 2012

Hybrid systems are mathematical models of control systems whose safety verification is critical for many applications. In practice, a rigorous tool is still not available for verifying every class of hybrid systems. HyTech was the first attempt in this direction followed by PHaver, both restricted to Linear Hybrid Automata (LHA). HSolver is another successful contribution for verification of nonlinear systems. PHaver can efficiently verify safety properties with the help of piecewise constant bounds on derivatives. Its use is greatly motivated by on-the-fly over approximations of piecewise affine dynamics with various user-specified parameters. HSolver verifies safety of nonlinear systems using constraint propagation based abstraction refinement. We have evaluated a few examples and shown that both tools have their strengths and weaknesses. In all the examples, the approximation of nonlinear systems by linear systems is performed by the rate translation.