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  1. 15 Fundamenta Informaticae
  2. 7 Archives of Control Sciences
  3. 6 Bulletin of the Polish Academy of Sciences. Technical Sciences
  4. 6 International Journal of Applied Mathematics and Computer Science
  5. 5 Archives of Electrical Engineering
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  1. 25 Kaczorek T.
  2. 5 Köhler-Bußmeier M.
  3. 3 Heitmann F.
  4. 3 Kaczorek Tadeusz
  5. 3 Przyborowski P.
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  1. 1 2023
  2. 2 2021
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1
Content available Standard and fractional discrete-time linear systems with zero transfer matrices
Kaczorek Tadeusz, Ruszewski Andrzej
Acta Mechanica et Automatica
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2023
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Vol. 17, no. 2
188--191
EN
The transfer matrix of the standard and fractional linear discrete-time linear systems is investigated. Necessary and sufficient conditions for zeroing of the transfer matrix of the linear discrete-time systems are established. The considerations are illustrated by examples of the standard and fractional linear discrete-time systems.
2
Content available remote Cost Problems for Parametric Time Petri Nets
Lime Didiera, Roux Olivier H., Seidner Charlotte
Fundamenta Informaticae
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2021
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Vol. 183, nr 1-2
97--123
EN
We investigate the problem of parameter synthesis for time Petri nets with a cost variable that evolves both continuously with time, and discretely when firing transitions. More precisely, parameters are rational symbolic constants used for time constraints on the firing of transitions and we want to synthesise all their values such that some marking is reachable, with a cost that is either minimal or simply less than a given bound. We first prove that the mere existence of values for the parameters such that the latter property holds is undecidable. We nonetheless provide symbolic semi-algorithms for the two synthesis problems and we prove them both sound and complete when they terminate. We also show how to modify them for the case when parameter values are integers. Finally, we prove that these modified versions terminate if parameters are bounded. While this is to be expected since there are now only a finite number of possible parameter values, our algorithms are symbolic and thus avoid an explicit enumeration of all those values. Furthermore, the results are symbolic constraints representing finite unions of convex polyhedra that are easily amenable to further analysis through linear programming. We finally report on the implementation of the approach in Romeo, a software tool for the analysis of time Petri nets.
3
Content available Invariance of reachability and observability for fractional positive linear electrical circuit with delays
Yuan Tong, Yang Hongli
Archives of Electrical Engineering
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2021
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Vol. 70, nr 3
513--530
EN
This paper focuses on the invariance of the reachability and observability for fractional order positive linear electrical circuits with delays and their checking methods. By derivation and comparison, it shows that conditions and checking methods of reachability and observability for integer and fractional order positive linear electrical circuits with delays are invariant. An illustrative example is presented at the end of the paper.
4
Content available Invariant properties of positive linear electrical circuits
Kaczorek Tadeusz
Poznan University of Technology Academic Journals. Electrical Engineering
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2019
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No. 97
109--123
EN
The invariant properties of the stability, reachability, and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
5
Content available Invariant properties of positive linear electrical circuits
Kaczorek Tadeusz
Archives of Electrical Engineering
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2019
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Vol. 68, nr 4
875--890
EN
The invariant properties of the stability, reachability, observability and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
6
Content available Reachability and observability of positive discrete-time linear systems with integer positive and negative powers of the state Frobenius matrices
Kaczorek T.
Archives of Control Sciences
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2018
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Vol. 28, No. 1
119--133
EN
The notions of monomial generalized Frobenius matrices is proposed and the reachability and observability of positive discrete-time linear systems with positive and negative integer powers of the state matrices is addressed. Necessary and sufficient conditions for the reachability of the positive systems are established.
7
Standard and positive electrical circuits with zero transfer matrices
Kaczorek T.
Poznan University of Technology Academic Journals. Electrical Engineering
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2016
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No. 85
11--28
EN
Standard and positive electrical circuits with zero transfer matrices are addressed. It is shown that there exists a large class of electrical circuits composed of resistances, inductances, capacitances and voltage (current) sources with zero transfer matrices. The electrical circuits are unreachable, unobservable and unstable for all values of the resistances, inductances and capacitances. An extension of these considerations to fractional electrical circuits is given.
8
Content available remote Relating Reachability Problems in Timed and Counter Automata
Haase C., Ouaknine J., Worrell J.
Fundamenta Informaticae
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2016
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Vol. 143, nr 3/4
317--338
EN
We establish a relationship between reachability problems in timed automata and spacebounded counter automata. We show that reachability in timed automata with three or more clocks is logarithmic-space inter-reducible with reachability in space-bounded counter automata with two counters. We moreover show the logarithmic-space equivalence of reachability in two-clock timed automata and space-bounded one-counter automata. This last reduction has recently been employed by Fearnley and Jurdziński to settle the computational complexity of reachability in two-clock timed automata.
9
Content available remote Completeness Results for Generalized Communication-free Petri Nets with Arbitrary Arc Multiplicities
Mayr E. W., Weihmann J.
Fundamenta Informaticae
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2016
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Vol. 143, nr 3/4
355--391
EN
We investigate gcf-Petri nets, a generalization of communication-free Petri nets allowing arbitrary arc multiplicities, and characterized by the sole restriction that each transition has at most one incoming arc. We use canonical firing sequences with nice properties for gcf-PNs to show that the RecLFS, (zero-)reachability, covering, and boundedness problems of gcf-PNs are in PSPACE. By simulating PSPACE-Turing machines by gss-PNs, a subclass of gcf-PNs where additionally all transitions have at most one outgoing arc, we ultimately obtain PSPACE-completess for these problems in case of gss-PNs or gcf-PNs. Additionally, we prove PSPACE-completeness for the liveness problem of gcf-PNs. Last, we show PSPACE-hardness as well as a doubly exponential space upper bound for the containment and equivalence problems of gss-PNs or gcf-PNs.
10
Content available remote An Upper Bound for the Reachability Problem of Safe, Elementary Hornets
Köhler-Bußmeier M., Heitmann F.
Fundamenta Informaticae
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2016
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Vol. 143, nr 1/2
89--100
EN
In this paper we study the complexity of the reachability problem HORNETS, an algebraic extension of object nets. Here we consider the restricted class of safe, elementary HORNETS. In previouswork we established the lower bound, i.e. reachability requires at least exponential space. In another work we have shown we can simulate elementary HORNETS with elementary object nets EOS, where reachability is known to be PSpace-complete. Since this simulation leads to a double exponential increase in the size of the simulating EOS, we obtain that for HORNETS the reachability problem is solvable in double exponential space. In this contributionwe show that this kind of simulation is rather bad, since we show that exponential space is sufficient. Together with the known lower bound this shows that the upper is tight.
11
Content available Positive electrical circuits with zero transfer matrices and their discretization
Kaczorek T.
Computer Applications in Electrical Engineering
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2016
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Vol. 14
1--13
EN
Positive continuous–time and discrete–time linear electrical circuits with zero transfer matrices are addressed. It is shown that there exists a large class of positive electrical circuits with zero transfer matrices. The electrical circuits are unreachable, unobservable and unstable for all values of the resistances, inductances and capacitances. The discrete–time linear positive electrical circuits are introduced. It is shown that: 1) the discrete–time electrical circuit is asymptotically stable for all values of the discretization step if and only if the corresponding continuous–time electrical circuit is asymptotically stable; 2) the discretization of the continuous–time electrical circuit does not change their reachability, observability and transfer matrices.
12
Content available Reachability of standard and fractional continuous-time systems with constant inputs
Rogowski K.
Archives of Control Sciences
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2016
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Vol. 26, no. 2
147--159
EN
The reachability of standard and fractional-order continuous-time systems with constant inputs is addressed. Positive and non-positive continuous-time linear systems are considered. Necessary and sufficient conditions for the existence of such constant inputs that steers the system from zero initial conditions to the given final state in desired time are derived and proved. As an example of such systems the electrical circuits with DC voltage sources are presented
13
Content available Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs
Kaczorek T.
Archives of Control Sciences
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2015
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Vol. 25, no. 3
319--331
EN
A new formulation of the minimum energy control problem for the positive 2D continuousdiscrete linear systems with bounded inputs is proposed. Necessary and sufficient conditions for the reachability of the systems are established. Conditions for the existence of the solution to the minimum energy control problem and a procedure for computation of an input minimizing the given performance index are given. Effectiveness of the procedure is demonstrated on numerical example.
14
Content available remote Structural and Dynamic Restrictions of Elementary Object Systems
Heitmann F., Köhler-Bußmeier M.
Fundamenta Informaticae
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2014
|
Vol. 135, nr 4
387--401
EN
Elementary object systems (EOS for short) are Petri nets in which tokens may be Petri nets again. Originally proposed by Valk for a two levelled structure, the formalism was later generalised for arbitrary nesting structures. However, even if restricted to a nesting depth of two, EOS are Turing-complete and thus many problems like reachability and liveness are undecidable for them. Nonetheless, since they are useful to model many practical applications a natural question is how to restrict the formalism in such a way, that the resulting restricted formalism is still helpful in a modelling context, but so that important verification problems like reachability become quickly decidable. In the last years several structural and dynamic restrictions for EOS have therefore been investigated. These investigations have been central to the first author’s recent PhD thesis and have been published in past editions of this journal and on conferences. In this paper we add several new results and present them together with the old in a unified fashion highlighting the central message of these investigations.
15
Content available remote On the Complexity of the Reachability Problem for Safe : Elementary Hornets
Köhler-Bußmeier M.
Fundamenta Informaticae
|
2014
|
Vol. 129, nr 1/2
101--115
EN
In this paper we study the complexity of HORNETS, an algebraic extension of object nets. We define a restricted class: safe, elementary HORNETS, to guarantee finite state spaces. It will turn out, that the reachability problem for this class requires exponential space, which is a major increase when compared to safe, elementary object nets, which require polynomial space.
16
Content available remote A Survey of Decidability Results for Elementary Object Systems
Köhler-Bußmeier M.
Fundamenta Informaticae
|
2014
|
Vol. 130, nr 1
99--123
EN
This contribution presents recent results on Elementary Object Systems (EOS). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. In this work we study the relationship of EOS to existing Petri net formalisms. It turns out that EOS are equivalent to counter programs. But even for the restricted subclass of conservative EOS reachability and liveness are undecidable problems. On the other hand for other properties like boundedness are still decidable for conservative EOS. We also study the sub-class of generalised state machines, which is worth mentioning since it combines decidability of many theoretically interesting properties with a quite rich practical modelling expressiveness.
17
Content available Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state
Busłowicz M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2014
|
Vol. 62, nr 2
233--239
EN
In the paper the problems of controllability, reachability and minimum energy control of a fractional discrete-time linear system with delays in state are addressed. A general form of solution of the state equation of the system is given and necessary and sufficient conditions for controllability, reachability and minimum energy control are established. The problems are considered for systems with unbounded and bounded inputs. The considerations are illustrated by numerical examples. Influence of a value of the fractional order on an optimal value of the performance index of the minimum energy control is examined on an example.
18
Content available Minimum energy control of 2D positive continuous-discrete linear systems
Kaczorek T.
Acta Mechanica et Automatica
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2014
|
Vol. 8, no. 3
165--168
EN
The minimum energy control problem for the 2D positive continuous-discrete linear systems is formulated and solved. Necessary and sufficient conditions for the reachability at the point of the systems are given. Sufficient conditions for the existence of solution to the problem are established. It is shown that if the system is reachable then there exists an optimal input that steers the state from zero boundary conditions to given final state and minimizing the performance index for only one step (q = 1). A procedure for solving of the problem is proposed and illustrated by a numerical example.
19
Content available remote Constructability and observability of standard and positive electrical circuits
Kaczorek T.
Przegląd Elektrotechniczny
|
2013
|
R. 89, nr 7
132--136
EN
The constructability and observability of standard and positive electrical circuits composed of resistors, coils, condensators and voltage (current) sources are addressed. Necessary and sufficient conditions for the constructability and observability of the positive electrical circuits are established. Effectiveness of the conditions is demonstrated on examples of positive electrical circuits.
PL
W pracy rozpatruje się standardowe i dodatnie obwody elektryczne złożone z rezystorów, cewek i kondensatorów oraz źródeł napięcia i prądu. Podano warunki konieczne i wystarczające odtwarzalności i obserwowalności tych obwodów elektrycznych. Warunki te zostały zlustrowane na przykładach dodatnich obwodów elektrycznych.
20
Content available Reachability and controllability of positive fractional-order discrete-time systems
Trzasko W.
Pomiary Automatyka Robotyka
|
2013
|
R. 17, nr 2
365-370
EN
In the paper the positive linear discrete-time noncommensurate fractional-order systems described by the state equations are considered. Definition and necessary and sufficient conditions for the positivity, reachability and controllability to zero are given and proven. The considerations are illustrated by a numerical example.
PL
W pracy rozpatrzono liniowe stacjonarne dodatnie układy dyskretne niecałkowitego niewspółmiernego rzędu. Sformułowano definicje oraz podano warunki konieczne i wystarczające dodatniości, osiągalności i sterowalności układów dyskretnych niewspółmiernego rzeczywistego rzędu oraz współmiernego niecałkowitego rzędu. Rozważania zilustrowano przykładem numerycznym.
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