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168
Computational Techniques for Hybrid System Verification
 IEEE Trans. on Automatic Control
, 2003
"... Abstract—This paper concerns computational methods for verifying properties of polyhedral invariant hybrid automata (PIHA), which are hybrid automata with discrete transitions governed by polyhedral guards. To verify properties of the state trajectories for PIHA, the planar switching surfaces are p ..."
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Cited by 115 (5 self)
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Abstract—This paper concerns computational methods for verifying properties of polyhedral invariant hybrid automata (PIHA), which are hybrid automata with discrete transitions governed by polyhedral guards. To verify properties of the state trajectories for PIHA, the planar switching surfaces are partitioned to define a finite set of discrete states in an approximate quotient transition system (AQTS). State transitions in the AQTS are determined by the reachable states, or flow pipes, emitting from the switching surfaces according to the continuous dynamics. This paper presents a method for computing polyhedral approximations to flow pipes. It is shown that the flowpipe approximation error can be made arbitrarily small for general nonlinear dynamics and that the computations can be made more efficient for affine systems. The paper also describes CheckMate, a MATLABbased tool for modeling, simulating and verifying properties of hybrid systems based on the computational methods previously described. Index Terms—Hybrid systems, model checking, reachability, verification. I.
Safety Verification of Hybrid Systems Using Barrier Certificates
 In Hybrid Systems: Computation and Control
, 2004
"... This paper presents a novel methodology for safety verification of hybrid systems. For proving that all trajectories of a hybrid system do not enter an unsafe region, the proposed method uses a function of state termed a barrier certificate. The zero level set of a barrier certificate separates ..."
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Cited by 89 (6 self)
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This paper presents a novel methodology for safety verification of hybrid systems. For proving that all trajectories of a hybrid system do not enter an unsafe region, the proposed method uses a function of state termed a barrier certificate. The zero level set of a barrier certificate separates the unsafe region from all possible trajectories starting from a given set of initial conditions, hence providing an exact proof of system safety. No explicit computation of reachable sets is required in the construction of barrier certificates, which makes nonlinearity, uncertainty, and constraints can be handled directly within this framework.
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 ..."
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Cited by 78 (24 self)
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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 ..."
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Cited by 75 (11 self)
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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.
Computational techniques for the verification of hybrid systems
 Proceedings of the IEEE
, 2003
"... Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems that involve the interaction of both discrete state systems, represented by finite automata, and continuous sta ..."
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Cited by 72 (9 self)
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Hybrid system theory lies at the intersection of the fields of engineering control theory and computer science verification. It is defined as the modeling, analysis, and control of systems that involve the interaction of both discrete state systems, represented by finite automata, and continuous state dynamics, represented by differential equations. The embedded autopilot of a modern commercial jet is a prime example of a hybrid system: the autopilot modes correspond to the application of different control laws, and the logic of mode switching is determined by the continuous state dynamics of the aircraft, as well as through interaction with the pilot. To understand the behavior of hybrid systems, to simulate, and to control these systems, theoretical advances, analyses, and numerical tools are needed. In this paper, we first present a general model for a hybrid system along with an overview of methods for verifying continuous and hybrid systems. We describe a particular verification
Stabilization of nonlinear systems with limited information feedback
 IEEE Trans. Automat. Control
, 2005
"... Abstract—This note is concerned with the problem of stabilizing a nonlinear continuoustime system by using sampled encoded measurements of the state. We demonstrate that global asymptotic stabilization is possible if a suitable relationship holds between the number of values taken by the encoder, t ..."
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Cited by 69 (10 self)
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Abstract—This note is concerned with the problem of stabilizing a nonlinear continuoustime system by using sampled encoded measurements of the state. We demonstrate that global asymptotic stabilization is possible if a suitable relationship holds between the number of values taken by the encoder, the sampling period, and a system parameter, provided that a feedback law achieving inputtostate stability with respect to measurement errors can be found. The issue of relaxing the latter condition is also discussed. Index Terms—Asymptotic stability, encoding, inputtostate stability, limited information, measurement errors, nonlinear system.
The d/dt Tool for Verification of Hybrid System
, 2002
"... In this paper we describe the tool d/dt which provides automatic safety verification of hybrid systems with linear continuous dynamics with uncertain input. The verification procedure is based on a method for overapproximating reachable sets by orthogonal polyhedra. The tool also
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Cited by 64 (8 self)
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In this paper we describe the tool d/dt which provides automatic safety verification of hybrid systems with linear continuous dynamics with uncertain input. The verification procedure is based on a method for overapproximating reachable sets by orthogonal polyhedra. The tool also
Reachability Analysis of Hybrid Systems via Predicate Abstraction
 Hybrid Systems: Computation and Control, Fifth International Workshop, LNCS 2289
, 2002
"... 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 appr ..."
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Cited by 62 (8 self)
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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 userdefined 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 by using weakest preconditions to compute abstract transitions corresponding to the discrete switches and conservative polyhedral approximations to compute abstract transitions corresponding to continuous flows. Compared to tools such as Checkmate and d/dt, this approach requires significantly less computational resources as the emphasis is shifted from computing the reachable set to searching in the abstract quotient. We demonstrate the feasibility of the proposed technique by analyzing a parametric timingbased mutual exclusion protocol and safety of a simple controller for vehicle coordination.
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 ..."
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Cited by 58 (6 self)
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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 ..."
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Cited by 55 (7 self)
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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.