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  1. 21 Bulletin of the Polish Academy of Sciences. Technical Sciences
  2. 19 International Journal of Applied Mathematics and Computer Science
  3. 15 Control and Cybernetics
  4. 7 Archives of Control Sciences
  5. 6 Acta Mechanica et Automatica
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  1. 23 Klamka J.
  2. 8 Kaczorek T.
  3. 7 Kaczorek Tadeusz
  4. 4 Czornik A.
  5. 3 Balachandran K.
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  1. 2 2025
  2. 2 2024
  3. 5 2023
  4. 4 2022
  5. 6 2021
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1
Content available Representation of solutions of linear discrete systems with constant coefficients and with delays
Diblík Josef
Opuscula Mathematica
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2025
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Vol. 45, no. 2
145--177
EN
The paper surveys the results achieved in representing solutions of linear non-homogeneous discrete systems with constant coefficients and with delays and their fractional variants by using special matrices called discrete delayed-type matrices. These are used to express solutions of initial problems in a closed and often simple form. Then, results are briefly discussed achieved by such representations of solutions in stability, controllability and other fields. In addition, a similar topic is dealt with concerning linear non-homogeneous differential equations with delays and their variants. Moreover, some comments are given to this parallel direction pointing some important moments in the developing this theory. An outline of future perspectives in this direction is discussed as well.
2
Content available Descriptor continuous- and discrete-time linear systems with zero transfer matrices
Kaczorek Tadeusz, Klamka Jerzy, Dzieliński Andrzej
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2025
|
Vol. 73, nr 2
art. no. e152710
EN
In this paper, necessary and sufficient conditions for zeroing of the transfer matrices of descriptor continuous-time and discrete-time linear systems are established. The conditions are illustrated by simple numerical examples of the descriptor continuous-time and discrete-time linear systems. Also some remarks on the systems with delays in control are given.
3
Content available Nonlocal controllability of mild solutions for neutral evolution equations with state-dependent delay in Fréchet spaces
Boudefla Chahrazed, Baghli-Bendimerad Selma
Archives of Control Sciences
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2024
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Vol. 34, No. 1
117--148
EN
In this paper, we prove the controllability of mild solutions of neutral functional evolution equations with state-dependent delay and nonlocal conditions. We establish the non local controllability of mild solutions under certain conditions by combining Avramescu’s nonlinear alternative for the sum of compact and contraction operators in Fréchet spaces with semigroup theory.
4
Content available Positive state controllability of discrete linear time-invariant systems
Ouyadri Mourad, Laabissi Mohamed, Achhab Mohammed Elarbi
Acta Mechanica et Automatica
|
2024
|
Vol. 18, no. 1
110--118
EN
Positive state controllability is the controllability of systems where the state is positive and the input remains in ℝn. Under some conditions, we established a relation between the reachability map of systems with only the positive state and the reachability map of a related positive system where the state and input are both positive. Using this connection, necessary and sufficient conditions are obtained for the positive state reachability of discrete linear time-invariant (LTI) systems, and then we deduced the positive state controllability. These conditions are evaluated over some numerical examples that support the theoretical results.
5
Content available Automated Linearization of a System of Nonlinear Ordinary Differential Equations
Mazakova Aigerim, Jomartova Sholpan, Wójcik Waldemar, Mazakov Talgat, Ziyatbekova Gulzat
International Journal of Electronics and Telecommunications
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2023
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Vol. 69, No. 4
655--600
EN
This paper investigates the possibility of automatically linearizing nonlinear models. Constructing a linearised model for a nonlinear system is quite labor-intensive and practically unrealistic when the dimension is greater than 3. Therefore, it is important to automate the process of linearisation of the original nonlinear model. Based on the application of computer algebra, a constructive algorithm for the linearisation of a system of non-linear ordinary differential equations was developed. A software was developed on MatLab. The effectiveness of the proposed algorithm has been demonstrated on applied problems: an unmanned aerial vehicle dynamics model and a twolink robot model. The obtained linearized models were then used to test the stability of the original models. In order to account for possible inaccuracies in the measurements of the technical parameters of the model, an interval linearized model is adopted. For such a model, the procedure for constructing the corresponding interval characteristic polynomial and the corresponding Hurwitz matrix is automated. On the basis of the analysis of the properties of the main minors of the Hurwitz matrix, the stability of the studied system was analyzed.
6
Content available Zeroing the transfer matrix of the Roesser model of 2-D linear systems
Kaczorek Tadeusz
International Journal of Applied Mathematics and Computer Science
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2023
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Vol. 33, no. 4
513--519
EN
Controllability, observability and the transfer matrix of the discrete 2-D Roesser model are analyzed. It is shown that the controllability of the Roesser model is invariant under state feedbacks and the observability under output feedbacks. Sufficient conditions are established for the zeroing of the transfer matrix of the Roesser model.
7
Content available Controllability of consensus heterogeneous multi-agent networks over continuous time scale
Athira V. S., Muni Vijayakumar S., Rafeek Kallu Vetty Muhammed, Reddy Gudala Janardhana
Control and Cybernetics
|
2023
|
Vol. 52, No. 2
199--245
EN
The research, presented in this paper, concernes the controllability of a multi-agent network with a directed, unweighted, cooperative, and time-invariant communication topology. The network’s agents follow linear and heterogeneous dynamics, encompassing first-order, second-order, and third-order differential equations over continuous time. Two classes of neighbour-based linear distributed control protocols are considered: the first one utilises average feedback from relative velocities/relative accelerations, and the second one utilises feedback from absolute velocities/absolute accelerations. Under both protocols, the network’s agents achieve consensus in their states asymptotically. We observe that both of the considered dynamical rules exploit the random-walk normalised Laplacian matrix of the network’s graph. By categorising the agents of the network into leaders and followers, with leaders serving as exogenous control inputs, we analyse the controllability of followers within their state space through the influence of leaders. Specifically, matrix-rank conditions are established to evaluate the leader-follower controllability of the network under both control protocols. These matrix-rank conditions are further refined in terms of the system matrices’ eigenvalues and eigenvectors. The inference diagrams presented in this work provide deeper insights into how leader-follower interactions impact the network controllability. The efficacy of the theoretical findings is validated through numerical examples.
8
Content available Results on the controllability of Caputo’s fractional descriptor systems with constant delays
Beata Sikora
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2023
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Vol. 71, nr 4
art. no. e146287
EN
The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example.
9
Content available On the control of the final speed for a class of finite-dimensional linear systems: controllability and regulation
Rachik Mostafa, Khaloufi Issam, Benfatah Youssef, Boutayeb Hamza, Laarabi Hassan
Archives of Control Sciences
|
2023
|
Vol. 33, No. 3
497--525
EN
In this article, we extended the concept of controllability, traditionally used to control the final state of a system, to the exact control of its final speed. Inspired by Kalman’s theory, we have established some conditions to characterize the control that allows the system to reach a desired final speed exactly. When the assumptions ensuring speed-controllability are not met, we adopt a regulation strategy that involves determining the control law to make the system’s final speed approach as closely as possible to the predefined final speed, and this at a lower cost. The theoretical results obtained are illustrated through three examples.
10
Content available remote On the computation of hierarchical control results for one-dimensional transmission line
Pinheiro de Carvalho Pitagoras, Pereira de Jesus Isaías, Pereira de Sá Neto Olimpio
Mathematica Applicanda
|
2022
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Vol. 50, no. 1
107--128
EN
In this paper, motivated by a physics problem, we investigate some numerical and computational aspects for the problem of hierarchical controllability in one-dimensional wave equation in domains with a moving boundary. Some controls act in part of the boundary and define a strategy of equilibrium between them, considering a leader control and a follower. Thus, we introduced the concept of hierarchical control to solve the problem and mapped the Stackelberg Strategy between these controls. The numerical methods described here consist of a combination of the following: finite element method (FEM) for space approximation; finite difference method (FDM) for time discretization and fixed-point algorithm for the solution of the total discrete control problem. Data programming and computer simulations are performed in FreeFem++ and for a better presentation of the experiments we use Matlab.
PL
W tym artykule, motywowanym problemem fizycznym, badamy pewne aspekty numeryczne i obliczeniowe problemu sterowalności hierarchicznej w jednowymiarowym równaniu falowym w domenach z ruchomą granicą. Niektóre sterowania są na brzegu i definiują strategię równowagi między nimi, biorąc pod uwagę sterowania lidera i naśladowcę. W związku z tym wprowadziliśmy koncepcję sterowań hierarchicznych w celu rozwiązania tego problemu i przyporządkowaliśmy strategię Stackelberga między tymi strategiami. Opisane tutaj metody numeryczne składają się z kombinacji następujących elementów: metoda elementów skończonych (MES) dla aproksymacji przestrzennej; metoda różnic skończonych (FDM) do dyskretyzacji czasu i algorytm stałoprzecinkowy do rozwiązania problemu całkowitego sterowania dyskretnego. Programowanie danych i symulacje komputerowe wykonujemy w FreeFem++, a dla lepszej prezentacji eksperymentów używamy Matlaba.
11
Content available Some analysis problems of the linear systems
Kaczorek Tadeusz
Journal of Automation, Electronics and Electrical Engineering
|
2022
|
Vol. 4, No. 2
7--12
EN
New approaches to the transformations of the uncontrollable and unobservable matrices of linear systems to their canonical forms are proposed. It is shown that the uncontrollable pair (A,B) and unobservable pair (A,C) of linear systems can be transform to their controllable (𝐴̅ , 𝐵̅ ) and observable (𝐴̅ , 𝐶̅ ) canonical forms by suitable choice of nonsingular matrix M satisfying the condition 𝑀[𝐴 𝐵] = [𝐴̅ 𝐵̅ ] and [𝐴 𝐵]𝑀 = [𝐴̂ 𝐵̂ ], respectively. It is also shown that by suitable choice of the gain matrix K of the feedbacks of the derivative of the state vector it is possible to reduce the descriptor system to the standard one.
PL
Zaproponowano nowe podejścia do transformacji niesterowalnych i nieobserwowalnych macierzy układów liniowych do ich postaci kanonicznych. Wykazano, że niesterowalna para (A,B) i nieobserwowalna para (A,C) układów liniowych może być przekształcona do ich postaci kanonicznych sterowalnych i obserwowalnych prze odpowiedni dobór nieosobliwej macierzy M spełniającej warunki 𝑀[𝐴 𝐵] = [𝐴̅ 𝐵̅ ] i [𝐴 𝐵]𝑀 = [𝐴̂ 𝐵̂ ]. Pokazano,żeprzezodpowiednidobórmacierzyKsprzężeniazwrotnego od pochodnej wektora stanu jest możliwa redukcja układu deskryptorowegodoukładustandardowego.
12
Content available Eigenvalues assignment in uncontrollable linear systems
Kaczorek Tadeusz
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2022
|
Vol. 70, nr 6
art. no. e141987
EN
It is shown that in uncontrollable linear system x = Ax + Bu it is possible to assign arbitrarily the eigenvalues of the closed-loop system with state feedbacks u = Kx, K ∈ ℜn⨉m if rank [A B] = n. The design procedure consists in two steps. In the step 1 a nonsingular matrix M ∈ ℜn⨉m is chosen so that the pair (MA,MB) is controllable. In step 2 the feedback matrix K is chosen so that the closed-loop matrix Ac = A − BK has the desired eigenvalues. The procedure is illustrated by simple example.
13
Content available Controllability of linear convex combination of linear discrete-time fractional systems
Kaczorek Tadeusz, Klamka Jerzy, Dzieliński Andrzej
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2022
|
Vol. 70, nr 5
art. no. e143102
EN
In this paper the controllability properties of the convex linear combination of fractional, linear, discrete-time systems are characterized and investigated. The notions of linear convex combination and controllability in the context of fractional-order systems are recalled. Then, the controllability property of such a linear combination of discrete-time, linear fractional systems is proven. Further, the reduction of an infinite problem of transition matrix derivation is reduced to a finite one, which greatly simplifies the numerical burden of the controllability issue. Examples of controllable and uncontrollable, single-input, linear systems are presented. The possibility of extension of the considerations to multi-input systems is shown.
14
Content available Improving the controllability of the electro-hydraulic complex in emergency operating modes
Korenkova Tetyana, Kovalchuk Viktoriya
Przegląd Elektrotechniczny
|
2021
|
R. 97, nr 12
121--124
EN
The possibility of using reversible operating modes of hydraulic and electric machines in the problems of improving the controllability of an electrohydraulic complex is shown. The schemes of energy balance in pumping and turbine operating modes of hydraulic machines are given. A mathematical description of the four-quadrant characteristics of the pumping unit is proposed. The complete characteristics of the pump operating on the pipeline network with back pressure, when the direction of rotation of the pump electric motor was changed and there was reverse of the liquid in the hydraulic system, are obtained. A structural diagram of a system for active regulation of pumping unit parameters based on the use of hydro turbine units or reversible hydraulic machines is proposed.
PL
Pokazano możliwość użycia odwracalnego trybu pracy maszyn hydraulicznych i elektrycznych w polepszaniu sterowności zespołu elektrohydraulicznego. Podane zostały schematy równowagi energii w trybie pompowania i pracy turbinowej maszyny hydraulicznej. Dla jednostki pompowanie z czterokwadrantowym trybem pracy opracowano modele matematyczne. Otrzymano finalne charakterystyki działania pompy i sieci rurociągowej z ciśnieniem wstecznym w warunkach zmiany kierunku obrotów napędu elektrycznego pompy i cofania płynu w systemie hydraulicznym. Zaproponowany został diagram parametrów aktywnej regulacji jednostki pompowania, wykorzystujący jednostki turbin wodnych lub odwracalnych maszyn hydraulicznych.
15
Content available Positive output controllability of linear discrete–time invariant systems
Ouyadri Mourad, Laabissi Mohamed, Achhab Mohammed Elarbi
Control and Cybernetics
|
2021
|
Vol. 50, No. 4
521--539
EN
This paper studies the output controllability of discrete linear time invariant systems (LTI) with non-negative input constraints. Some geometrical arguments and positive invariance concepts are used to derive the necessary and/or sufficient conditions for the positive output controllability of discrete LTI systems. The paper also provides several academic examples, which support the theoretical results.
16
Content available Convex linear combination of the controllability pairs for linear systems
Kaczorek Tadeusz, Klamka Jerzy
Control and Cybernetics
|
2021
|
Vol. 50, No. 4
541--551
EN
The convex linear combination of the controllability pairs of linear continuous-time linear systems is defined and its properties are discussed. The main result is obtained using pure algebraic methods. In the illustrative examples different cases of linear convex combinations are analyzed.
17
Content available On controllability of fractional positive continuous-time linear systems with delay
Sikora Beata, Matlok Natalia
Archives of Control Sciences
|
2021
|
Vol. 31, No. 1
29--51
EN
In the paper positive fractional continuous-time linear systems are considered. Positive fractional systems without delays and positive fractional systems with a single delay in control are studied. New criteria for approximate and exact controllability of systems without delays as well as a relative controllability criterion of systems with delay are established and proved. Numerical examples are presented for different controllability criteria. A practical application is proposed.
18
Content available Application of maximum principle to optimization of production and storage costs
Popescu Liviu, Dimitrov Ramona
Archives of Control Sciences
|
2021
|
Vol. 31, No. 4
865--881
EN
A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.
19
Content available The practical feedback stabilization for evolution equations in Banach spaces
Hanen Damak
Acta Mechanica et Automatica
|
2021
|
Vol. 15, no. 2
58--65
EN
This paper investigates the notion of practical feedback stabilization of evolution equations satisfying some relaxed conditions in infinite-dimensional Banach spaces. Moreover, sufficient conditions are presented that guarantee practical stabilizability of uncertain systems based on Lyapunov functions. These results are applied to partial differential equations.
20
Controllability of multi-term time-fractional differential systems with state-dependent delay
Chaudhary Renu, Singh Vikram, Pandey D. N.
Journal of Applied Analysis
|
2020
|
Vol. 26, nr 2
241--255
EN
In this paper, controllability results for a class of multi-term time-fractional differential systems with state-dependent delay have been studied. The concept of fractional calculus, measure of noncompactness and Mönch fixed-point theorem has been implemented to obtain a new set of controllability results. Finally, an application is given to illustrate the obtained results.
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