Results 1  10
of
62
Approximation metrics for discrete and continuous systems
 IEEE Transactions on Automatic Control
, 2005
"... Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In thi ..."
Abstract

Cited by 105 (16 self)
 Add to MetaCart
(Show Context)
Established system relationships for discrete systems, such as language inclusion, simulation, and bisimulation, require system observations to be identical. When interacting with the physical world, modeled by continuous or hybrid systems, exact relationships are restrictive and not robust. In this paper, we develop the first framework of system approximation that applies to both discrete and continuous systems by developing notions of approximate language inclusion, approximate simulation, and approximate bisimulation relations. We define a hierarchy of approximation pseudometrics between two systems that quantify the quality of the approximation, and capture the established exact relationships as zero sections. Our approximation framework is compositional for a synchronous composition operator. Algorithms are developed for computing the proposed pseudometrics, both exactly and approximately. The exact algorithms require the generalization of the fixed point algorithms for computing simulation and bisimulation relations, or dually, the solution of a static game whose cost is the socalled branching distance between the systems. Approximations for the pseudometrics can be obtained by considering Lyapunovlike functions called simulation and bisimulation functions. We illustrate our approximation framework in reducing the complexity of safety verification problems for both deterministic and nondeterministic continuous systems.
Reachability of uncertain linear systems using zonotopes
 IN HYBRID SYSTEMS : COMPUTATION AND CONTROL, LNCS 3414
, 2005
"... We present a method for the computation of reachable sets of uncertain linear systems. The main innovation of the method consists in the use of zonotopes for reachable set representation. Zonotopes are special polytopes with several interesting properties: they can be encoded efficiently, they are ..."
Abstract

Cited by 97 (14 self)
 Add to MetaCart
(Show Context)
We present a method for the computation of reachable sets of uncertain linear systems. The main innovation of the method consists in the use of zonotopes for reachable set representation. Zonotopes are special polytopes with several interesting properties: they can be encoded efficiently, they are closed under linear transformations and Minkowski sum. The resulting method has been used to treat several examples and has shown great performances for high dimensional systems. An extension of the method for the verification of piecewise linear hybrid systems is proposed.
Hierarchical Modeling and Analysis of Embedded Systems
, 2003
"... This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is ..."
Abstract

Cited by 78 (24 self)
 Add to MetaCart
This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of CHARON in the design of embedded control software using examples from automated highways concerning vehicle coordination
Safety verification of hybrid systems by constraint propagation based abstraction refinement
, 2005
"... This paper deals with the problem of safety verification of nonlinear hybrid systems. We start from a classical method that uses interval arithmetic to check whether trajectories can move over the boundaries in a rectangular grid. We put this method into an abstraction refinement framework and impr ..."
Abstract

Cited by 75 (11 self)
 Add to MetaCart
(Show Context)
This paper deals with the problem of safety verification of nonlinear hybrid systems. We start from a classical method that uses interval arithmetic to check whether trajectories can move over the boundaries in a rectangular grid. We put this method into an abstraction refinement framework and improve it by developing an additional refinement step that employs interval constraint propagation to add information to the abstraction without introducing new grid elements. Moreover, the resulting method allows switching conditions, initial states and unsafe states to be described by complex constraints instead of sets that correspond to grid elements. Nevertheless, the method can be easily implemented since it is based on a welldefined set of constraints, on which one can run any constraint propagation based solver. Tests of such an implementation are promising.
Incremental search methods for reachability analysis of continuous and hybrid systems
 In Hybrid Systems: Computation and Control
, 2004
"... Abstract. In this paper we present algorithms and tools for fast and efficient reachability analysis, applicable to continuous and hybrid systems. Most of the work on reachability analysis and safety verification concentrates on conservative representations of the set of reachable states, and conseq ..."
Abstract

Cited by 58 (6 self)
 Add to MetaCart
Abstract. In this paper we present algorithms and tools for fast and efficient reachability analysis, applicable to continuous and hybrid systems. Most of the work on reachability analysis and safety verification concentrates on conservative representations of the set of reachable states, and consequently on the generation of safety certificates; however, inability to prove safety with these tools does not necessarily result in a proof of unsafety. In this paper, we propose an alternative approach, which aims at the fast falsification of safety properties; this approach provides the designer with a complementary set of tools to the ones based on conservative analysis, providing additional insight into the characteristics of the system under analysis. Our algorithms are based on algorithms originally proposed for robotic motion planning; the key idea is to incrementally grow a set of feasible trajectories by exploring the state space in an efficient way. The ability of the proposed algorithms to analyze the reachability and safety properties of general continuous and hybrid systems is demonstrated on examples from the literature. 1
Abstraction and CounterexampleGuided Refinement in Model Checking of Hybrid Systems
, 2003
"... Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finitestate abstraction. Model checking can be inconclusive, however, in which case t ..."
Abstract

Cited by 55 (7 self)
 Add to MetaCart
(Show Context)
Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finitestate abstraction. Model checking can be inconclusive, however, in which case the abstraction must be refined. This paper presents a new procedure to perform this refinement operation for abstractions of hybrid systems. Following an approach originally developed for finitestate systems [11, 25], the refinement procedure constructs a new abstraction that eliminates a counterexample generated by the model checker. For hybrid systems, analysis of the counterexample requires the computation of sets of reachable states in the continuous state space. We show how such reachability computations with varying degrees of complexity can be used to refine hybrid system abstractions efficiently.
Benchmarks for Hybrid Systems Verification
 In Hybrid Systems: Computation and Control (HSCC 2004) (2004
, 2004
"... There are numerous application examples for hybrid systems verification in recent literature. Most of them were introduced to illustrate a new approach to hybrid systems verification, and are therefore of a limited size. Others are case studies that serve to prove that an approach can be applied to ..."
Abstract

Cited by 55 (1 self)
 Add to MetaCart
(Show Context)
There are numerous application examples for hybrid systems verification in recent literature. Most of them were introduced to illustrate a new approach to hybrid systems verification, and are therefore of a limited size. Others are case studies that serve to prove that an approach can be applied to real world problems. Verification of these typically requires a lot of domain experience to obtain a tractable, verifiable model. Verification of a case study yields a singular result that is hard to compare and timeconsuming to reproduce.
CounterExample Guided Predicate Abstraction of Hybrid Systems
, 2003
"... Predicate abstraction has emerged to be a powerful technique for extracting finitestate models from infinitestate systems, and has been recently shown to enhance the effectiveness of the reachability computation techniques for hybrid systems. Given a hybrid system with linear dynamics and a set of ..."
Abstract

Cited by 44 (8 self)
 Add to MetaCart
(Show Context)
Predicate abstraction has emerged to be a powerful technique for extracting finitestate models from infinitestate systems, and has been recently shown to enhance the effectiveness of the reachability computation techniques for hybrid systems. Given a hybrid system with linear dynamics and a set of linear predicates, the verifier performs an onthefly search of the finite discrete quotient whose states correspond to the truth assignments to the input predicates. The success of this approach crucially depends on the choice of the predicates used for abstraction. In this paper, we focus on identifying these predicates automatically by analyzing spurious counterexamples generated by the search in the abstract statespace. We present the basic techniques for discovering new predicates that will rule out closely related spurious counterexamples, optimizations of these techniques, implementation of these in the verification tool, and case studies demonstrating the promise of the approach.
Robust Test Generation and Coverage for Hybrid Systems
, 2007
"... Testing is an important tool for validation of the system design and its implementation. Modelbased test generation allows to systematically ascertain whether the system meets its design requirements, particularly the safety and correctness requirements of the system. In this paper, we develop a fr ..."
Abstract

Cited by 42 (13 self)
 Add to MetaCart
(Show Context)
Testing is an important tool for validation of the system design and its implementation. Modelbased test generation allows to systematically ascertain whether the system meets its design requirements, particularly the safety and correctness requirements of the system. In this paper, we develop a framework for generating tests from hybrid systems’ models. The core idea of the framework is to develop a notion of robust test, where one nominal test can be guaranteed to yield the same qualitative behavior with any other test that is close to it. Our approach offers three distinct advantages. 1) It allows for computing and formally quantifying the robustness of some properties, 2) it establishes a method to quantify the test coverage for every test case, and 3) the procedure is parallelizable and therefore, very scalable. We demonstrate our framework by generating tests for a navigation benchmark application.
Predicate abstraction for reachability analysis of hybrid systems
 ACM Trans. Embedded Comput. Syst
, 2006
"... Embedded systems are increasingly finding their way into a growing range of physical devices. These embedded systems often consist of a collection of software threads interacting concurrently with each other and with a physical, continuous environment. While continuous dynamics have been well studie ..."
Abstract

Cited by 41 (3 self)
 Add to MetaCart
Embedded systems are increasingly finding their way into a growing range of physical devices. These embedded systems often consist of a collection of software threads interacting concurrently with each other and with a physical, continuous environment. While continuous dynamics have been well studied in control theory, and discrete and distributed systems have been investigated in computer science, the combination of the two complexities leads us to the recent research on hybrid systems. This paper addresses the formal analysis of such hybrid systems. Predicate abstraction has emerged to be a powerful technique for extracting finitestate models from infinitestate discrete programs. This paper presents algorithms and tools for reachability analysis of hybrid systems by combining the notion of predicate abstraction with recent techniques for approximating the set of reachable states of linear systems using polyhedra. Given a hybrid system and a set of predicates, we consider the finite discrete quotient whose states correspond to all possible truth assignments to the input predicates. The tool performs an onthefly exploration of the abstract system. We present the basic techniques for guided search in the abstract statespace, optimizations of these techniques, implementation of these in our verifier, and case studies demonstrating the promise of the approach. We also address the completeness of our abstractionbased verification strategy by showing that predicate abstraction of hybrid systems can be used to prove bounded safety.