Wyniki wyszukiwania - Biblioteka Nauki

1

Narrowing Petri Net State Spaces Using the State Equation

100%

Schmidt K.

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tom Vol. 47, nr 3,4

325-335

EN

Given a (possibly partially defined) state, all count vectors of transition sequences reaching that state are solutions to a corresponding Petri net state equation. We propose a search strategy where sequences corresponding to a minimal solution of the state equation are explored first. Then step by step the search space is relaxed to arbitrary count vectors. This heuristics relies on the observation that in many (though provably not in all) cases, minimal solutions of the state equation can be realized as a firing sequence. If no target state is reachable, either the state equation does not have solutions, or our search method would yield the full state space. We study the impact of the state equation on reachability, present an algorithm that exploits information from the state equation and discuss its application in stateless search as well as its combination with stubborn set reduction.

2

Analyzing and reducing simultaneous firing in signal-event nets

100%

Roch S.

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2000

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tom Vol. 43, Nr 1-4

321-330

EN

Signal-event nets provide a modular modeling technique based on Petri nets. Actions of a module can be activated or can be prevented by another module through condition arcs. One-sided synchronization of modules is done by signal-events, which cause the execution of actions in steps. But due to condition arcs and signal-events simultaneous firing of steps may lead to markings, which are not reachable by conventional sequential interleaving. We give a criterion, in which situations simultaneous firing of steps can be safely omitted, without missing reachable markings.

3

Finding symmetries of algebraic system nets

100%

Junttila T. A.

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tom Vol. 37, Nr 3

269-289

EN

The problem of finding symmetry information from algebraic system nets prior to the reach-ability graph generation is studied. The approach presented is based on wellformedness of transition descriptions, meaning that some data types in a net may be used in a symmetric way. Permutations on the domains of such data types produce symmetries on the state space level of the net, which in turn can be exploited during the reachability analysis. To ensure that the transitions behave symmetrically with respect to the chosen data domain permutations, a sufficient compatibility condition between data domain permutations and the algebraic terms used as transition guards and arc annotations is proposed. The solution is a general and flexi-ble one as it does not fix the set of applicable operations, enabling the design of customized net classes. To help the process of deciding whether a term is compatible with a data domain permutation, an approximation rule for the compatibility condition is given.

4

Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties

88%

Rauh A. , Minisini J. , Hofer E.

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nr 3

425-439

EN

Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.

5

Stable models for stubborn sets

75%

Varpaaniemi K.

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2000

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tom Vol. 43, Nr 1-4

355-375

EN

The stubborn set method is one of the methods that try to relieve the state space explosion problem that occurs in state space generation. Spending some time in looking for "good'" stubborn sets can pay off in the total time spent in generating a reduced state space. This article shows how the method can exploit tools that solve certain problems of logic programs. The restriction of a definition of stubbornness to a given state can be translated into a variable-free logic program. When a stubborn set satisfying additional constraints is wanted, the additional constraints should be translated, too. It is easy to make the translation in such a way that each acceptable stubborn set of the state is represented by at least one stable model of the program, each stable model of the program represents at least one acceptable stubborn set of the state, and for each pair in the representation relation, the number of certain atoms in the stable model is equal to the number of enabled transitions of the represented stubborn set. So, in order to find a stubborn set which is good w.r.t. the number of enabled transitions, it suffices to find a stable model which is good w.r.t. the number of certain atoms. The article also presents a new NP-completeness result concerning stubborn sets.