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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.
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 ..."
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Cited by 42 (13 self)
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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.
Orthogonal polyhedra: Representation and computation
 Schuppen (Eds.), Hybrid Systems: Computation and Control, LNCS 1569
, 1999
"... Abstract. In this paper we investigate orthogonal polyhedra, i.e. polyhedra which are finite unions of fulldimensional hyperrectangles. We define representation schemes for these polyhedra based on their vertices, and show that these compact representation schemes are canonical for all (convex and ..."
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Cited by 42 (4 self)
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Abstract. In this paper we investigate orthogonal polyhedra, i.e. polyhedra which are finite unions of fulldimensional hyperrectangles. We define representation schemes for these polyhedra based on their vertices, and show that these compact representation schemes are canonical for all (convex and nonconvex) polyhedra in any dimension. We then develop efficient algorithms for membership, facedetection and Boolean operations for these representations. 1
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 ..."
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Cited by 41 (3 self)
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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.
Nonlinear Systems: Approximating Reach Sets
, 2004
"... We describe techniques to generate useful reachability information for nonlinear dynamical systems. These techniques can be automated for polynomial systems using algorithms from computational algebraic geometry. The generated information can be incorporated into other approaches for doing reachab ..."
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Cited by 39 (6 self)
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We describe techniques to generate useful reachability information for nonlinear dynamical systems. These techniques can be automated for polynomial systems using algorithms from computational algebraic geometry. The generated information can be incorporated into other approaches for doing reachability computation. It can also be used when abstracting hybrid systems that contain modes with nonlinear dynamics. These techniques are most naturally embedded in the hybrid qualitative abstraction approach proposed by the authors previously. They also show that the formal qualitative abstraction approach is well suited for dealing with nonlinear systems.
On the decidability of the reachability problem for planar differential inclusions
 In HSCC’2001, number 2034 in LNCS
, 2001
"... Abstract. In this paper we develop an algorithm for solving the reachability problem of twodimensional piecewise rectangular differential inclusions. Our procedure is not based on the computation of the reachset but rather on the computation of the limit of individual trajectories. A key idea is ..."
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Cited by 38 (16 self)
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Abstract. In this paper we develop an algorithm for solving the reachability problem of twodimensional piecewise rectangular differential inclusions. Our procedure is not based on the computation of the reachset but rather on the computation of the limit of individual trajectories. A key idea is the use of onedimensional affine Poincaré maps for which we can easily compute the fixpoints. As a first step, we show that between any two points linked by an arbitrary trajectory there always exists a trajectory without selfcrossings. Thus, solving the reachability problem requires considering only those. We prove that, indeed, there are only finitely many “qualitative types ” of those trajectories. The last step consists in giving a decision procedure for each of them. These procedures are essentially based on the analysis of the limits of extreme trajectories. We illustrate our algorithm on a simple model of a swimmer spinning around a whirlpool. 1
M.: Verification of hybrid systems based on counterexampleguided abstraction refinement. In: Technical Report. (2002) Downloadable from http://www.cs.cmu.edu
 In: HSCC. LNCS 1569
, 1999
"... Abstract. 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 ..."
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Cited by 38 (6 self)
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Abstract. 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 infinitestate systems, in particular of hybrid systems. Following an approach originally developed for finitestate systems [1, 2], 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. A detailed example illustrates our counterexampleguided refinement procedure. Experimental results for a prototype implementation of the procedure indicate its advantages over existing methods. 1
Recent progress in continuous and hybrid reachability analysis
 In Proc. IEEE International Symposium on ComputerAided Control Systems Design. IEEE Computer
, 2006
"... Abstract — Setbased reachability analysis computes all possible states a system may attain, and in this sense provides knowledge about the system with a completeness, or coverage, that a finite number of simulation runs can not deliver. Due to its inherent complexity, the application of reachabilit ..."
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Cited by 30 (1 self)
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Abstract — Setbased reachability analysis computes all possible states a system may attain, and in this sense provides knowledge about the system with a completeness, or coverage, that a finite number of simulation runs can not deliver. Due to its inherent complexity, the application of reachability analysis has been limited so far to simple systems, both in the continuous and the hybrid domain. In this paper we present recent advances that, in combination, significantly improve this applicability, and allow us to find better balance between computational cost and accuracy. The presentation covers, in a unified manner, a variety of methods handling increasingly complex types of continuous dynamics (constant derivative, linear, nonlinear). The improvements include new geometrical objects for representing sets, new approximation schemes, and more flexible combinations of graphsearch algorithm and partition refinement. We report briefly some preliminary experiments that have enabled the analysis of systems previously beyond reach. I.
Scalable Nonlinear Dynamical Systems for Agent Steering and Crowd Simulation
, 2001
"... We present a new methodology for agent modeling that is scalable and efficient. It is based on the integration of nonlinear dynamical systems and kinetic data structures. The method consists of threelayers, which together model 3D agent steering, crowds and flocks among moving and static obstacles. ..."
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Cited by 27 (2 self)
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We present a new methodology for agent modeling that is scalable and efficient. It is based on the integration of nonlinear dynamical systems and kinetic data structures. The method consists of threelayers, which together model 3D agent steering, crowds and flocks among moving and static obstacles. The first layer, the local layer employs nonlinear dynamical systems theory to models lowlevel behaviors. It is fast and efficient, and it does not depend on the total number of agents in the environment. This dynamical systemsbased approach also allows us to establish continuous numerical parameters for modifying each agent's behavior. The second layer, a global environment layer consists of a specifically designed kinetic data structure to track efficiently the immediate environment of each agent and know which obstacles/agents are near or visible to the given agent. This layer reduces the complexity in the local layer. In the third layer, a global planning layer, the problem of target tracking is generalized in a way that allows navigation in mazelike terrains, avoidance of local minima and cooperation between agents. We implement this layer based on two approaches that are suitable for different applications: One approach is to track the closest single moving or static target; the second is to use a prespecified vector field, which may be generated automatically (with harmonic functions, for example) or based on user input to achieve tht desired output. We also discuss how hybrid s7stems concepts for global planning can capitalize on both our layered approach and the continuous, reactive nature of our agent steering.