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Reachability Analysis of Hybrid Systemsan Experience Report

Manish Goyal
2012 International Journal of Modeling and Optimization  
In all the examples, the approximation of nonlinear systems by linear systems is performed by the rate translation.  ...  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 has proved its worth in linear hybrid systems verification. It helps the user to control the verification process by use of various parameters and abstraction techniques.  ... 
doi:10.7763/ijmo.2012.v2.209 fatcat:etjri2abrvhqnltbmxvjfcnp2e


2006 International Journal of Foundations of Computer Science  
Though model checking itself is a fully automated process, verifying correctness of a hybrid system design using model checking is not.  ...  This paper describes the necessary steps, and choices to be made, to go from an informal description of the problem to the final verification result for a formal model and requirement.  ...  The final result was a fourth-order hybrid system with non-linear dynamics.  ... 
doi:10.1142/s0129054106004169 fatcat:gu4kqbks25hh3gxnyuz7xyvn7a

Computational techniques for hybrid system verification

A. Chutinan, B.H. Krogh
2003 IEEE Transactions on Automatic Control  
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).  ...  In general, finite bisimulations do not exist, which means that verification problems for hybrid systems are usually undecidable (e.g., see [22] ).  ... 
doi:10.1109/tac.2002.806655 fatcat:76bcojfap5ak7cynswg3ll3y4q

Verification of Analog and Mixed-Signal Circuits Using Hybrid System Techniques [chapter]

Thao Dang, Alexandre Donzé, Oded Maler
2004 Lecture Notes in Computer Science  
To model and analyze such circuits under all possible input signals and all values of parameters, we build upon two techniques developed in the context of hybrid (discrete-continuous) control systems.  ...  First, we extend our algorithm for approximating sets of reachable sets for dense-time continuous systems to deal with differential algebraic equations (DAEs) and apply it to a biquad low-pass filter.  ...  All that we know about ∆-Σ modulation is the result of our interactions with Rob Rutenbar, Bruce Krogh and Smriti Gupta at CMU during the summer of 2003.  ... 
doi:10.1007/978-3-540-30494-4_3 fatcat:k7p4dwhrxvaa5f72td7yh6rhgm

Algorithmic Verification of Continuous and Hybrid Systems

Oded Maler
2014 Electronic Proceedings in Theoretical Computer Science  
We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems.  ...  For open under-determined systems, this technique can sometimes replace an infinite number of simulations.  ...  Introduction The goal of this article is to introduce the fundamentals of algorithmic verification of continuous dynamical systems defined by differential equations and of hybrid dynamical systems defined  ... 
doi:10.4204/eptcs.140.4 fatcat:ayqkurojffar3o6a7ud5pwbdse

Effective synthesis of switching controllers for linear systems

E. Asarin, O. Bournez, T. Dang, O. Maler, A. Pnueli
2000 Proceedings of the IEEE  
We have implemented a concrete version of the algorithm, which uses a new approximation scheme for reachability analysis of linear systems.  ...  In this paper, we suggest a novel methodology for synthesizing switching controllers for continuous and hybrid systems whose dynamics are defined by linear differential equations.  ...  Additional useful comments were contributed by J. H. van Schuppen and B. Krogh.  ... 
doi:10.1109/5.871306 fatcat:f76trcckp5actn26dizzqe5zy4

Current Challenges in the Verification of Hybrid Systems [chapter]

Stefan Schupp, Erika Ábrahám, Xin Chen, Ibtissem Ben Makhlouf, Goran Frehse, Sriram Sankaranarayanan, Stefan Kowalewski
2015 Lecture Notes in Computer Science  
for the verification of hybrid systems.  ...  Latest developments brought interesting theoretical results and powerful tools for the reachability analysis of hybrid systems.  ...  Coracan be used for the analysis of systems with linear, linear stochastic and non-linear dynamics with uncertain parameters, where non-linear systems are abstracted by linear or polynomial systems. dReach  ... 
doi:10.1007/978-3-319-25141-7_2 fatcat:zvdce2gma5hwfnpeid64dstaki

Predicate abstraction for reachability analysis of hybrid systems

Rajeev Alur, Thao Dang, Franjo Ivančić
2006 ACM Transactions on Embedded Computing Systems  
of linear systems using polyhedra.  ...  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.  ...  Transition System Semantics and Verification Problem We define the semantics of a linear hybrid system by formalizing its underlying transition system.  ... 
doi:10.1145/1132357.1132363 fatcat:vrnwjfoxvzhlhag6vaka4rbmcm

SPHIN: A model checker for reconfigurable hybrid systems based on SPIN

Hosung Song, Kevin J. Compton, William C. Rounds
2006 Electronical Notes in Theoretical Computer Science  
Open access under CC BY-NC-ND license. components and their configuration can be changed by means of physical or logical mobility of components.  ...  We extend the syntax of PROMELA and the verification algorithms based on the expected semantics. We demonstrate the tool's capabilities by modeling and verifying a reconfigurable hybrid system.  ...  Also, we may choose to store approximations of these unions only (such as convex hull or extrapolation) as visited regions. SPHIN currently supports convex hull approximation for this purpose.  ... 
doi:10.1016/j.entcs.2005.10.011 fatcat:gqihuu6ldbesjjgwjgpr7qyqua

SpaceEx: Scalable Verification of Hybrid Systems [chapter]

Goran Frehse, Colas Le Guernic, Alexandre Donzé, Scott Cotton, Rajarshi Ray, Olivier Lebeltel, Rodolfo Ripado, Antoine Girard, Thao Dang, Oded Maler
2011 Lecture Notes in Computer Science  
The algorithm is implemented as part of SpaceEx, a new verification platform for hybrid systems, available at  ...  Experimental results of full fixed-point computations with hybrid systems with more than 100 variables illustrate the scalability of the approach.  ...  Naturally, the verification of hybrid systems requires ingredients taken from the classical verification of transition systems, augmented with new special techniques for doing verification-like operations  ... 
doi:10.1007/978-3-642-22110-1_30 fatcat:meiynoi5rbbyfhnnpe6iukaonu

Counterexample-guided predicate abstraction of hybrid systems

Rajeev Alur, Thao Dang, Franjo Ivančić
2006 Theoretical Computer Science  
Given a hybrid system with linear dynamics and a set of linear predicates, the verifier performs an on-the-fly search of the finite discrete quotient whose states correspond to the truth assignments to  ...  computation techniques for hybrid systems.  ...  Transition System Semantics and Verification Problem The semantics of a linear hybrid system can be formalized by describing its underlying transition system.  ... 
doi:10.1016/j.tcs.2005.11.026 fatcat:fykkoyrbyza2hhqrsxje2o74xa

Applications of polyhedral computations to the analysis and verification of hardware and software systems

Roberto Bagnara, Patricia M. Hill, Enea Zaffanella
2009 Theoretical Computer Science  
interpretation a b s t r a c t Convex polyhedra are the basis for several abstractions used in static analysis and computer-aided verification of complex and sometimes mission-critical systems.  ...  by automatic analyzers and verifiers; and look at some possible combinations of polyhedra with other numerical abstractions that have the potential to improve the precision of the analysis.  ...  Observe that, although the linear hybrid automata are specified by means of polyhedra, the reachable set R for a linear hybrid automaton and location may not be a convex polyhedron since Eq. (4.1) uses  ... 
doi:10.1016/j.tcs.2009.07.033 fatcat:dnp6uoljs5cahaih6oov4pmwye

Choice of Directions for the Approximation of Reachable Sets for Hybrid Systems [chapter]

Xin Chen, Erika Ábrahám
2012 Lecture Notes in Computer Science  
In this paper we propose an approach to over-approximate the reachable set (with bounded time and number of transitions) of a hybrid system by a finite set of polytopes.  ...  For the hybrid systems whose (1) continuous dynamics are linear, (2) invariants and guards are defined by linear inequalities, and (3) variable resets are expressed by invertible affine maps, we show that  ...  For the verification of safety properties of hybrid systems the main challenge is to compute the set of the reachable states of hybrid automata.  ... 
doi:10.1007/978-3-642-27549-4_69 fatcat:ihoboi27h5bn7bcfqtbxj6zela

Modeling, Verification, and Testing Using Timed and Hybrid Automata [chapter]

Stavros Tripakis, Thao Dang
2009 Model-Based Design for Embedded Systems  
For systems with constant derivatives and where invariants and guards are specified by linear inequalities (such as timed automata and linear hybrid automata) the reachable sets can be expressed by linear  ...  However, unlike for linear systems, this convex hull C clearly does not include all the reachable states at t (as illustrated by the dashed trajectory in the figure) .  ... 
doi:10.1201/9781420067859-c13 fatcat:ipdmb52ph5bjxir65x527fqj2u

Verification of Cyber-Physical Systems (Dagstuhl Seminar 14122)

Rupak Majumdar, Richard M. Murray, Pavithra Prabhakar, Marc Herbstritt
2014 Dagstuhl Reports  
The main focus of the seminar was to discuss issues related to the reliable development of cyber-physical systems by using formal verification.  ...  This report documents the program and the outcomes of Dagstuhl Seminar 14122 "Verification of Cyber-Physical Systems".  ...  give a brief introduction of Flow* which is a reachability analysis tool for non-linear continuous and hybrid systems.  ... 
doi:10.4230/dagrep.4.3.85 dblp:journals/dagstuhl-reports/MajumdarMP14 fatcat:qm5epthwvbgf5mk74me42qcpei
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