Last issue
2017 (vol. 27) - Number 2


W. Bozejko, M. Wodecki:

Discrete Systems: Theory and Applications. Special issue.



G. Bocewicz, Z. Banaszak, I. Nielsen:

Delivery-flow routing and scheduling subject to constraints imposed by vehicle flows in fractal-like networks



W. Bozejko, A. Gnatowski, R. Idzikowski, M. Wodecki:

Cyclic flow shop scheduling problem with two-machine cells



W. Bozejko, M. Uchronski,, Z. Chaczko, M. Wodecki:

Parallel patterns determination in solving cyclic flow shop problem with setups



J. Brodny, S. Alszer, J. Krystek, M. Tutak:

Availability analysis of selected mining machinery



K. Chmielewska, D. Formanowicz, P. Formanowicz:

The effect of cigarette smoking on endothelial damage and atherosclerosis development - modeled and analyzed using Petri nets



A. Galuszka, J. Krystek, A. Swierniak, T. Grzejszczak, C. Lungoci:

Information management in passenger traffic supporting system design as a multi-criteria discrete optimization task



M. Kardynska, J. Smieja:

Sensitivity analysis of signaling pathway models based on discrete-time measurements



J. Kasprzyk, P. Krauze, S. Budzan, J. Rzepecki:

Vibration control in semi-active suspension of the experimental off-road vehicle using information about suspension deflection



M. Koryl, D. Mazur:

Towards emergence phenomenon in business process management



M. Koryl:

Active resources concept of computation for enterprise software



H. Krawczyk, M. Nykiel:

Mobile devices and computing cloud resources allocation for interactive applications



W. Mitkowski, W. Bauer, M. Zagórowska:

Discrete-time feedback stabilization



J. Pempera:

An exact block algorithm for no-idle RPQ problem



K. Rzosinska, D. Formanowicz, P. Formanowicz:

The study of the influence of micro-environmental signals on macrophage differentiation using a quantitative Petri net based model



K. Skrzypczyk , M. Mellado:

Vehicle navigation in populated areas using predictive control with environmental uncertainty handling



W. Bozejko, J. Pempera, M. Wodecki:

A fine-grained parallel algorithm for the cyclic flexible job shop problem




ACS Abstract:

2004 (Volume 14)
Number 2
1. Using control theory to make cancer chemotherapy beneficial from phase dependence and resistant to drug resistance
2. (1kB)- norm computation for stable linear continuous-time periodic systems
3. A controllability problem for a class of uncertain - parameters discrete-time linear dynamic systems
4. A note on zeros, output-nulling subspaces and zero-dynamics in MIMO LTI systems
5. A time-varying switching plane design for variable structure control of the third order system with input constraint


Using control theory to make cancer chemotherapy beneficial from phase dependence and resistant to drug resistanceDownload full PDF article
Marek Kimmel
(Rice University, USA)
Andrzej ¦wierniak
(Silesian University of Technology, Poland)

Two major obstacles against successful chemotherapy of cancer are the cell-cycle-phase dependence of treatment, and the emergence of resistance of cancer cells to cytotoxic agents. One way to understand and overcome these two problems is to apply optimal control theory to mathematical models of cell cycle dynamics. These models should include division of the cell cycle into subphases and/or the mechanisms of drug resistance. We review our relevant results in mathematical modelling and control of the cell cycle and of the mechanisms of gene amplification (related to drug resistance), and estimation of parameters of the constructed models.

keywords: optimal control, biomathematical models, cancer chemotherapy, bilinear systems, cell cycle dynamics.

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(1kB)- norm computation for stable linear continuous-time periodic systemsDownload full PDF article
B.P. Lampe
(University of Rostock, Germany)
M. Obraszov and E. Rosenwasser
(St. Petersburg State University of Ocean Technology, Russia)

The paper deals with the (1kB)-norm of finite dimensional linear continuous-time periodic (FDLCP) systems, represented in state space. On basis of general formulae for the (1kB)-norm significantly simpler formulae are derived under the assumption of stability of the system. The proposed method needs to compute the transition matrix on the interval (1kB), where T is the period of the system, and it operates only with matrices of finite dimension. An example is given, where the (1kB)-norm is determined exactly, and the proposed method turns out to be superior to other known methods.

keywords: time-varying systems, periodic motion, Laplace transforms, Green functions, transfer functions, norms.

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A controllability problem for a class of uncertain - parameters discrete-time linear dynamic systemsDownload full PDF article
Krzysztof Oprzedkiewicz
(University of Mining and Metallurgy, Poland)

In the paper a controllability problem for a class of time invariant, discrete linear SISO systems with uncertain parameters is discussed. The system under consideration is described by a finite dimensional state - space equation with an interval diagonal state matrix, an interval control matrix, the known output matrix and the two - dimensional uncertain parameters space. From the considerations shown in the paper it turns out, that the general controllability conditions for the discussed discrete system are the same as for the analogical continuous system with uncertain parameters. As an example the controllability problem for an interval parabolic system is discussed, numerical examples are also presented.

keywords: linear discrete-time systems with uncertain parameters, controllability.

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A note on zeros, output-nulling subspaces and zero-dynamics in MIMO LTI systemsDownload full PDF article
Jerzy Tokarzewski
(Military University of Technology, Poland)

In a standard multi-input, multi-output linear time invariant (MIMO LTI) continuous-time system S(A,B,C) the classical notion of the Smith zeros does not characterize fully the output-zeroing problem nor the zero dynamics. The question how this notion can be extended and related to the state-space methods is discussed. Nothing is assumed about the relationship of the number of inputs to the number of outputs nor about the normal rank of the underlying system matrix. The proposed extension treats multivariable zeros (called further the invariant zeros) as the triples (complex number, nonzero state-zero direction, input-zero direction). Such a treatment is strictly connected with the output zeroing problem and in that spirit the zeros can be easily interpreted even in the degenerate case (i.e., when any complex number is such a zero).
A simple sufficient and necessary condition of nondegeneracy is presented. The condition decomposes the class of all systems S(A,B,C) such that B(1kB)0 and C(1kB)0 into two disjoint subclasses: of nondegenerate and degenerate systems. In nondegenerate systems the Smith zeros and the invariant zeros are exactly the same objects which are determined as the roots of the so-called zero polynomial. The degree of this polynomial equals the dimension of the maximal (A,B)-invariant subspace contained in ker C, while the zero dynamics are independent upon control vector. In degenerate systems the zero polynomial determines merely the Smith zeros, while the set of the invariant zeros equals the whole complex plane. The dimension of the maximal (A,B)-invariant subspace contained in ker C is strictly larger than the degree of the zero polynomial, whereas the zero dynamics essentially depend upon control vector.

keywords: linear systems, zeros, degeneracy, zero dynamics, Markov parameters, singular value decomposition.

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A time-varying switching plane design for variable structure control of the third order system with input constraintDownload full PDF article
Andrzej Bartoszewicz and Aleksandra Nowacka
(Technical University of £ód¼, Poland)

In this paper a new sliding mode control algorithm for the third order uncertain, nonlinear and time-varying dynamic system subject to unknown disturbance and input constraint is proposed. The algorithm employs a time-varying switching plane. At the initial time (1kB), the plane passes through the point determined by the system initial conditions in the error state space. Afterwards, the plane moves with a constant velocity to the origin of the space. The plane is selected in such a way that the integral of the absolute value of the system error over the whole period of the control action is minimized and the input constraint is satisfied. By this means, the reaching phase is eliminated, insensitivity of the system to the external disturbance is guaranteed from the very beginning of the proposed control action and fast, monotonic error convergence to zero is achieved.

keywords: sliding mode control, variable structure systems, time-varying switching planes, switching surface design.

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