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## Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems (2000)

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Citations: | 140 - 31 self |

### Citations

2650 | Timed Automata
- Alur
- 1999
(Show Context)
Citation Context ...over the integers [CC92] where over-approximation is called widening. This is why there is not much hope in nding nite quotients of continuous systems, except for special cases such as timed automata =-=[AD94]-=-. Here we need to nd the right compromise between the desire to converge and the accumulation of errors. We propose a method, specialized for linear systems of the form _x = Ax which achieves this tra... |

711 | The LEDA platform of Combinatorial and Geometric Computing. - Naher - 1999 |

473 | HyTech: A model checker for hybrid systems.
- Henzinger, Ho, et al.
- 1997
(Show Context)
Citation Context ...o state q 1 with F 0 as the set of initial states, calculate ffi 1 (F 0 ) and so on and so forth. This method is similar to the one used in tools such as KRONOS [DOTY96] for timed automata and HyTech =-=[HHW97]-=- for hybrid automata with constant derivatives [ACH + 95]. The main technical difficulty in applying our vertex-based approximation technique to such systems is that not all trajectories departing fro... |

317 | Abstract interpretation and application to logic programs.
- Cousot, Cousot
- 1992
(Show Context)
Citation Context ... result might cover the whole space unless some hardly-formalizable hacking is used [DM98,GM99]. Similar phenomena are exhibited, for example, in abstract interpretation of programs over the integers =-=[CC92]-=- where over-approximation is called widening. This is why there is not much hope in finding finite quotients of continuous systems, except for special cases such as timed automata [AD94]. Here we need... |

270 | The Tool KRONOS
- Daws, Olivero, et al.
- 1996
(Show Context)
Citation Context ... the guard to obtain a set F 0 , move to state q 1 with F 0 as the set of initial states, calculate ffi 1 (F 0 ) and so on and so forth. This method is similar to the one used in tools such as KRONOS =-=[DOTY96]-=- for timed automata and HyTech [HHW97] for hybrid automata with constant derivatives [ACH + 95]. The main technical difficulty in applying our vertex-based approximation technique to such systems is t... |

236 |
A theory of timed automata. Theoretical Computer Science,
- Alur, Dill
- 1994
(Show Context)
Citation Context ... the integers [CC92] where over-approximation is called widening. This is why there is not much hope in finding finite quotients of continuous systems, except for special cases such as timed automata =-=[AD94]-=-. Here we need to find the right compromise between the desire to converge and the accumulation of errors. We propose a method, specialized for linear systems of the formsx = Ax which achieves this tr... |

110 | A.: Effective synthesis of switching controllers for linear systems.
- Asarin, Bournez, et al.
- 2000
(Show Context)
Citation Context ...ity, that is, finding all the points from which a set F is reachable can be performed by computing ffi for the reversed systemsx = \GammaAx. For the purpose of controller synthesis for hybrid systems =-=[ABDPM00] we need a-=-n under-approximation of the "F Until G" operator, which returns the points from which you can stay within the set F either forever or until you reach a set G (which is typically the guard o... |

109 | A new class of decidable hybrid systems. - LAFFERRIERE, PAPPAS, et al. - 1999 |

100 | The Algorithmic Analysis of Hybrid Systems. Theoretical Computer Science, - Alur, Courcoubetis, et al. - 1995 |

91 | Reachability analysis via face lifting.
- Dang, Maler
- 1998
(Show Context)
Citation Context ...states for hybrid systems whose continuous dynamics is defined by linear differential equations. The performance is much better than the more general method of "face-lifting" we have used in=-= the past [DM98]-=-. The rest of the paper is organized as follows. In section 2 we define the problem of calculating reachable states and suggest a general procedure which solves it iteratively. The basic computation s... |

67 | Beyond hytech: Hybrid systems analysis using interval numerical methods,” in Hybrid Systems: Computation and Control, ser. - Henzinger, Horowitz, et al. - 2000 |

57 | Reachability analysis using polygonal projections - Greenstreet, Mitchell - 1999 |

50 | Reach set computation using optimal control.
- Varaiya
- 1998
(Show Context)
Citation Context ...he two parts of F Until G, as calculated by d=dt appear in Figure 6. 4.3 Continuous Disturbances Consider systems of the formsx = Ax+Bu where u ranges inside a convex set U . It has been suggested in =-=[V98]-=- to use the maximum principle from optimal control to find ffi r (F ) of a convex set F = conv(V) under all possible input signals. We have implemented this procedure and incorporated it into our syst... |

23 | Verifying safety properties of differential equations - Greenstreet - 1996 |

19 | Reachability analysis of a class of switched continuous systems by integrating rectangular approximation and rectangular analysis. - Preußig, Stursberg, et al. - 1999 |

14 | Deciding reachability for planar multipolynomial systems - Cerāns, Vīksna - 1996 |

10 |
Valyi I., Ellipsoidal Calculus for Estimation and Control
- Kurzhanski
- 1997
(Show Context)
Citation Context ...ex set F = conv(V) under all possible input signals. We have implemented this procedure and incorporated it into our system. We have tested it on a 4-dimensional example adapted from example 4.5.1 of =-=[KV97]-=-, pp. 279-285, where ellipsoids are used instead of polyhedra. The system is defined by: A = 0 B B @ 0:0 1:0 0:0 0:0 \Gamma8:0 0:0 0:0 0:0 0:0 0:0 0:0 1:0 0:0 0:0 \Gamma4:0 0:0 1 C C A B = 1 (a) (b) F... |

8 |
Reachability Analysis Using
- Greenstreet, Mitchell
- 1999
(Show Context)
Citation Context ...ea here is to separate the accumulation and storage of states reachable in one step (and those must contain an approximation error) from the computation of states reachable in the next step (see also =-=[GM99]-=-). The main attraction of this method compared to traditional ways to treat linear systems is in its adaptability to hybrid systems and to systems with under-specified input. 3 The Approximate Method ... |

4 | Verifying safety properties of dierential equations - Greenstreet - 1996 |

2 | Veri cation of polyhedral invariant hybrid automata using polygonal pipe approximations - Chutinan, Krogh - 1999 |