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44
Systematic simulation using sensitivity analysis
 IN HSCC
, 2007
"... In this paper we propose a new technique for verification by simulation of continuous and hybrid dynamical systems with uncertain initial conditions. We provide an algorithmic methodology that can, in most cases, verify that the system avoids a set of bad states by conducting a finite number of sim ..."
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Cited by 37 (4 self)
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In this paper we propose a new technique for verification by simulation of continuous and hybrid dynamical systems with uncertain initial conditions. We provide an algorithmic methodology that can, in most cases, verify that the system avoids a set of bad states by conducting a finite number of simulation runs starting from a finite subset of the set of possible initial conditions. The novelty of our approach consists in the use of sensitivity analysis, developed and implemented in the context of numerical integration, to efficiently characterize the coverage of sampling trajectories.
Symbolic analysis for improving simulation coverage of simulink/stateflow models
 in EMSOFT ’08: Proceedings of the 8th ACM international conference on Embedded software, 2008
"... Aimed at verifying safety properties and improving simulation coverage for hybrid systems models of embedded control software, we propose a technique that combines numerical simulation and symbolic methods for computing statesets. We consider systems with linear dynamics described in the commercial ..."
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Cited by 37 (4 self)
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Aimed at verifying safety properties and improving simulation coverage for hybrid systems models of embedded control software, we propose a technique that combines numerical simulation and symbolic methods for computing statesets. We consider systems with linear dynamics described in the commercial modeling tool Simulink/Stateflow. Given an initial state x, and a discretetime simulation trajectory, our method computes a set of initial states that are guaranteed to be equivalent to x, where two initial states are considered to be equivalent if the resulting simulation trajectories contain the same discrete components at each step of the simulation. We illustrate the benefits of our method on two case studies. One case study is a benchmark proposed in the literature for hybrid systems verification and another is a Simulink demo model from Mathworks.
Reachability Analysis of Nonlinear Systems with Uncertain Parameters using Conservative Linearization
"... Given an initial set of a nonlinear system with uncertain parameters and inputs, the set of states that can possibly be reached is computed. The approach is based on local linearizations of the nonlinear system, while linearization errors are considered by Lagrange remainders. These errors are adde ..."
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Cited by 33 (15 self)
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Given an initial set of a nonlinear system with uncertain parameters and inputs, the set of states that can possibly be reached is computed. The approach is based on local linearizations of the nonlinear system, while linearization errors are considered by Lagrange remainders. These errors are added as uncertain inputs, such that the reachable set of the locally linearized system encloses the one of the original system. The linearization error is controlled by splitting of reachable sets. Reachable sets are represented by zonotopes, allowing an efficient computation in relatively highdimensional space.
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.
Analog/MixedSignal Circuit Verification Using Models Generated from Simulation Traces ⋆
"... Abstract. Formal and semiformal verification of analog/mixedsignal circuits is complicated by the difficulty of obtaining circuit models suitable for analysis. We propose a method to generate a formal model from simulation traces. The resulting model is conservative in that it includes all of the ..."
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Cited by 22 (6 self)
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Abstract. Formal and semiformal verification of analog/mixedsignal circuits is complicated by the difficulty of obtaining circuit models suitable for analysis. We propose a method to generate a formal model from simulation traces. The resulting model is conservative in that it includes all of the original simulation traces used to generate it plus additional behavior. Information obtained during the model generation process can also be used to refine the simulation and verification process. 1
Approximately bisimilar finite abstractions of stable linear systems
 in Hybrid Systems: Computation and Control, ser. Lecture
, 2007
"... The use of bisimilar finite abstractions of continuous and hybrid systems, greatly simplifies complex computational tasks such as verification or control synthesis. Unfortunately, because of the strong requirements of bisimulation relations, such abstractions exist only for quite restrictive class ..."
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Cited by 20 (4 self)
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The use of bisimilar finite abstractions of continuous and hybrid systems, greatly simplifies complex computational tasks such as verification or control synthesis. Unfortunately, because of the strong requirements of bisimulation relations, such abstractions exist only for quite restrictive classes of systems. Recently, the notion of approximate bisimulation relations has been introduced, allowing the definition of less rigid relationships between systems. This relaxed notion should certainly allow us to build approximately bisimilar finite abstractions for more general classes of continuous and hybrid systems. In this paper, we show that for the class of stable discretetime linear systems with constrained inputs, there exists an approximately bisimilar finite state system of any desired precision. We describe an effective procedure for the construction of this abstraction, based on compositional reasoning and samples of the set of initial states and inputs. Finally, we briefly show how our finite abstractions can be used for verification or control synthesis.
Generating and Analyzing Symbolic Traces of Simulink/Stateflow Models
"... Abstract. We present a methodology and a toolkit for improving simulation coverage of Simulink/Stateflow models of hybrid systems using symbolic analysis of simulation traces. We propose a novel instrumentation scheme that allows the simulation engine of Simulink/Stateflow to output, along with the ..."
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Cited by 18 (3 self)
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Abstract. We present a methodology and a toolkit for improving simulation coverage of Simulink/Stateflow models of hybrid systems using symbolic analysis of simulation traces. We propose a novel instrumentation scheme that allows the simulation engine of Simulink/Stateflow to output, along with the concrete simulation trace, the symbolic transformers needed for our analysis. Given a simulation trace, along with the symbolic transformers, our analysis computes a set of initial states that would lead to traces with the same sequence of discrete components at each step of the simulation. Such an analysis relies critically on the use of convex polyhedra to represent sets of states. However, the exponential complexity of the polyhedral operations implies that the performance of the analysis would degrade rapidly with the increasing size of the model and the simulation traces. We propose a new representation, called the bounded vertex representation, which allows us to perform underapproximate computations while fixing the complexity of the representation a priori. Using this representation we achieve a tradeoff between the complexity of the symbolic computation and the quality of the underapproximation. We demonstrate the benefits of our approach over existing simulation and verification methods with case studies. 1
Temporal Logic Verification Using Simulation
 In Proc. FORMATS’06
, 2006
"... Abstract. In this paper, we consider a novel approach to the temporal logic verification problem of continuous dynamical systems. Our methodology has the distinctive feature that enables the verification of the temporal properties of a continuous system by verifying only a finite number of its (simu ..."
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Cited by 16 (7 self)
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Abstract. In this paper, we consider a novel approach to the temporal logic verification problem of continuous dynamical systems. Our methodology has the distinctive feature that enables the verification of the temporal properties of a continuous system by verifying only a finite number of its (simulated) trajectories. The proposed framework comprises two main ideas. First, we take advantage of the fact that in metric spaces we can quantify how close are two different states. Based on that, we define robust, multivalued semantics for MTL (and LTL) formulas. These capture not only the usual Boolean satisfiability of the formula, but also topological information regarding the distance from unsatisfiability. Second, we use the recently developed notion of bisimulation functions to infer the behavior of a set of trajectories that lie in the neighborhood of the simulated one. If the latter set of trajectories is bounded by the tube of robustness, then we can infer that all the trajectories in the neighborhood of the simulated one satisfy the same temporal specification as the simulated trajectory. The interesting and promising feature of our approach is that the more robust the system is with respect to the temporal logic specification, the less is the number of simulations that are required in order to verify the system. 1
The Complete Proof Theory of Hybrid Systems
, 2011
"... as representing the official policies, either expressed or implied, of any sponsoring institution or government. Keywords: proof theory; hybrid dynamical systems; differential dynamic logic; axiomatization; Hybrid systems are a fusion of continuous dynamical systems and discrete dynamical systems. T ..."
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Cited by 16 (12 self)
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as representing the official policies, either expressed or implied, of any sponsoring institution or government. Keywords: proof theory; hybrid dynamical systems; differential dynamic logic; axiomatization; Hybrid systems are a fusion of continuous dynamical systems and discrete dynamical systems. They freely combine dynamical features from both worlds. For that reason, it has often been claimed that hybrid systems are more challenging than continuous dynamical systems and than discrete systems. We now show that, prooftheoretically, this is not the case. We present a complete prooftheoretical alignment that interreduces the discrete dynamics and continuous dynamics of hybrid systems. We give a sound and complete axiomatization of hybrid systems relative to continuous dynamical systems and a sound and complete axiomatization of hybrid systems relative to discrete dynamical systems. Thanks to our axiomatization, proving properties of hybrid systems is exactly the same as proving properties of continuous dynamical systems and again, exactly the same as proving properties of discrete dynamical systems. This fundamental cornerstone sheds light on the nature of hybridness and enables flexible and provably perfect combinations of discrete reasoning with continuous reasoning that lift to all aspects of hybrid systems and their fragments. 1
Probabilistic Temporal Logic Falsification of CyberPhysical Systems
"... We present a MonteCarlo optimization technique for finding system behaviors that falsify a Metric Temporal Logic (MTL) property. Our approach performs a random walk over the space of system inputs guided by a robustness metric defined by the MTL property. Robustness is guiding the search for a fals ..."
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Cited by 14 (12 self)
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We present a MonteCarlo optimization technique for finding system behaviors that falsify a Metric Temporal Logic (MTL) property. Our approach performs a random walk over the space of system inputs guided by a robustness metric defined by the MTL property. Robustness is guiding the search for a falsifying behavior by exploring trajectories with smaller robustness values. The resulting testing framework can be applied to a wide class of CyberPhysical Systems (CPS). We show through experiments on complex system models that using our framework can help automatically falsify properties with more consistency as compared to other means such as uniform sampling.