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1
Content available remote Safety and Soundness for Priced Resource : Constrained Workflow Nets
Martos-Salgado M., Rosa-Velardo F.
Fundamenta Informaticae
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2014
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Vol. 131, nr 1
55--80
EN
We extend workflow Petri nets (wf-nets) with discrete prices, by associating a price to the execution of a transition and to the storage of tokens. We first define the safety and the soundness problems for priced wf-nets. A priced wf-net is safe if no execution costs more than a given budget. The soundness problem is that of deciding whether the workflow can always terminate properly, where in the priced setting “properly” also means that the execution does not cost more than a given threshold. Then, we study safety and soundness of resource-constrained workflow nets (rcwf-nets), an extension of wf-nets for the modeling of concurrent executions of a workflow, sharing some global resources. We develop a framework in which to study safety and soundness for priced rcwf-nets, that is parametric on the cost model. Then, that framework is instantiated, obtaining the cases in which the sum, the maximum, the average and the discounted sum of the prices of all instances are considered. We study the decidability and the complexity of these properties, together with their relation.
2
Content available Remarks on five equivalent forms of the fractional – order backward – difference
Ostalczyk P.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2014
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Vol. 62, nr 2
271--278
EN
In this paper a fractional-order backward-difference/sum (FOBD/S) equivalent formulae are considered. From the Gr¨unwald- Letnikov (GL - FOBD) definition formula and its Horner equivalent form one derives the Riemann-Liouville FOBD (RL - FOBD). Also the Caputo and polynomial-like forms are defined. All forms may be useful in real-time calculations (in the evaluation of digital control strategies) due to the reduction of fractional orders. The investigations are illustrated by a numerical example.
3
Content available remote Discrete Duality for Rough Relation Algebras
Düntsch I., Orłowska E.
Fundamenta Informaticae
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2013
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Vol. 127, nr 1-4
35--47
EN
Rough relation algebras are a generalization of relation algebras such that the underlying lattice structure is a regular double Stone algebra. Standard models are algebras of rough relations. A discrete duality is a relationship between classes of algebras and classes of relational systems (frames). In this paper we prove a discrete duality for a class of rough relation algebras and a class of frames.
4
Content available Four positive periodic solutions of a discrete time Lotka-Volterra competitive system with harvesting terms
Liu X., Ren Y., Li Y.
Opuscula Mathematica
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2011
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Vol. 31, no. 2
257-267
EN
In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we establish the existence of at least four positive periodic solutions for a discrete time Lotka-Volterra competitive system with harvesting terms. An example is given to illustrate the effectiveness of our results.
5
Content available remote Kwantowo-podobne własności układów elektrycznych
Trzaska Z.
Przegląd Elektrotechniczny
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2003
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R. 79, nr 2
141--144
PL
Podstawowe zasady i funkcje stosowane w mechanice kwantowej zostały przedstawione z punktu widzenia możliwości ich wykorzystania do interpretacji niektórych procesów w układach elektrycznych o dyskretnej strukturze przestrzennej. Podano odpowiednie relacje wynikające z zasady nieoznaczoności Heisenberga dla kwantów energii i związanych z nimi przedziałów nieokreśloności czasu oraz pulsacji. Wykazano istnienie zależności implikowanych stałą Plancka. Zamieszczono wyniki odpowiednich symulacji komputerowych.
EN
Fundamental principle and functions being in use in quantum mechanics are presented from the point of view of their applications for interpretations of some processes appearing in electrical systems with discrete structure. Corresponding relations resulting from the Heisenberg principle for the energy quants and related time intervals and angular frequency are presented. Existence of relations implicated by the Planck constant are proved. Discrete equation analogical to the Schrödinger wave equation is involved and its solution is given. Results of computer simulations are reported and they attest the existence of relations determined by the methods applied in quantum mechanics. Examples of applications of the presented equations as well as their solutions for effective modeling of processes in real electrical systems are demonstrated.
6
Content available remote LMI Approach to Stability Analysis of Three-dimensional Systems
Galkowski K., Lin Z., Xu S., Lam J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2003
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Vol. 51, nr 4
361-379
EN
An LMI approach to investigating the stability and related problems for linear three-dimensional discrete systems is described. The stability and lower bounds for stability margins are discussed for all principal three-dimensional state-space models. The particular emphasis is put on the robust stability for the uncertain case. A numerical example is presented to illustrate the results developed in the paper.
7
Content available remote A new methody of on-line model identification and update for multichannel active nose control systems
Figwer J.
Archives of Control Sciences
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2003
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Vol. 13, no. 2
141-155
EN
In the paper a new methody of on-line electro-acoustic plant model identification and update for adaptive multichannel feedforward ANC systems is presented. The proposed method uses external multivariate orthogonal multisine excitation added to the control signal. Properties of this excitation allow to decompose the overall multichannel identification problem into independent single-iput single-output identification problems. Additionally, special time-domain averaging of signals efficiently reduces an influence of disturbances on identification results even for low signal-to-noise ratio.
8
Content available remote Controllability of Nonlinear Discrete Systems
Klamka J.
International Journal of Applied Mathematics and Computer Science
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2002
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Vol. 12, no 2
173-180
EN
Local constrained controllability problems for nonlinear finite-dimensional discrete 1-D and 2-D control systems with constant coefficients are formulated and discussed. Using some mapping theorems taken from nonlinear functional analysis and linear approximation methods, sufficient conditions for constrained controllability in bounded domains are derived and proved. The paper extends the controllability conditions with unconstrained controls given in the literature to cover both 1-D and 2-D nonlinear discrete systems with constrained controls.
9
Content available remote On the admissible perturbations for discrete systems
Rachik M., Abdelhak A.
Archives of Control Sciences
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2002
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Vol. 12, no. 3
301-313
EN
We consider a discrete system described by xi+1=Axi, i>0 with the output function yi=Cxi, i>0 which is subject to the constraints (...). Then we investigate the admissible nonlinear perturbations (Ni)i, i.e., the ones such that the corresponding perturbed output function (...) remains in the constraints set omega for all i>0.
10
Content available remote Admissible Disturbance Sets for Discrete Perturbed Systems
Bouyaghroumni J., El Jai A., Rachik M.
International Journal of Applied Mathematics and Computer Science
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2001
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Vol. 11, no 2
349-367
EN
We consider a discrete disturbed system given by the difference bilinear equation x^{w}_{i+1} =Ax^{w}_{i} + De_{i} + sum_{j=1}^{q}f^{j}_{i}B_{j}x^{w}_{i}, i geq 0, where w=((e_{i})_{i geq 0}, (f_{i})_{i geq 0}) are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function y^{w}_{i}=Cx^{w}_{i}, i geq 0. Let varepsilon be a tolerance index on the output. The disturbance w is said to be varepsilon-admissible if ||y^{w}_{i}-y_{i}|| leq varepsilon, forall i geq 0, where (y_{i})_{i geq 0} is the output signal associated with the case of an uninfected system. The set of all varepsilon-admissible disturbances is the admissible set {cal W}(varepsilon). The characterization of {cal W}(varepsilon) is investigated and numerical simulations are given.
11
Content available remote Analiza układów dyskretno-ciągłych za pomocą syntezy podatności dynamicznych
Holka H.
Vibrations in Physical Systems
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2000
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Vol. 19
140--141
12
Content available Limiting ellipsoid for reachability set of 2D continuous-discrete linear system with disturbances
Krasoń E.
Control and Cybernetics
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1999
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Vol. 28, no 2
269--279
EN
A model of 2D continuous-discrete linear system is considered whose input disturbances are unknown but bounded by known ellipsoid. The formula for a support function of reachability set of this system is presented. A method of construction of ellipsoid limiting reachability set is proposed and illustrated with an example.
13
Content available remote Constrained controllability of positive 2D systems
Klamka J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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1998
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Vol. 46, nr 1
95-104
EN
In this paper we examine the issue of controllability for positive linear 2D systems. We look at the connections between reachability, reach ability from zero boundary conditions, and the rank criterion for controllability for systems in which both the state and controls are constrained by practical considerations to lie in a positive orthant. While these concepts are equivalent for unconstrained systems, there are significant changes in the positive case. We analyse these differences and show how they affect control strategy. Example, which illustrates theoretical results is also given.
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