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1
Minimum energy control of degenerate Cauchy problem with skew-Hermitian pencil
Benaoued Meriem, Bouagada Djillali
Journal of Applied Analysis
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2022
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Vol. 28, nr 2
251--261
EN
The present research paper deals with the effectiveness of the control of an infinite-dimensional degenerate Cauchy problem with variable operator coefficients, skew-Hermitian pencil and bounded input condition. This study explores the minimum energy control problem. The investigation follows a set of methods to examine the procedure for developing a new result to solve the problem. Indeed, by the use of decomposition transformation of the considered system and the application of the Gramian operator, the formula of the process for controlling the system with minimum energy is obtained. Afterwards, a procedure to compute the optimal input for minimizing the performance index is then proposed. In a nutshell, the obtained results indicate that optimal control for minimizing the performance index ensures the solution of the minimum energy control of an infinite-dimensional degenerate Cauchy problem.
2
Content available An extension of Klamka’s method to positive descriptor discrete-time linear systems with bounded inputs
Kaczorek T.
Archives of Control Sciences
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2018
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Vol. 28, No. 2
255--268
EN
The minimum energy control problem for the positive descriptor discrete-time linear systems with bounded inputs by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the positivity and reachability of descriptor discrete-time linear systems are given. Conditions for the existence of solution and procedure for computation of optimal input and the minimal value of the performance index is proposed and illustrated by a numerical example.
3
Content available Minimum energy control of descriptor fractional discrete-time linear systems with two different fractional orders
Sajewski Ł.
International Journal of Applied Mathematics and Computer Science
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2017
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Vol. 27, no. 1
33--41
EN
Reachability and minimum energy control of descriptor fractional discrete-time linear systems with different fractional orders are addressed. Using the Weierstrass–Kronecker decomposition theorem of the regular pencil, a solution to the state equation of descriptor fractional discrete-time linear systems with different fractional orders is given. The reachability condition of this class of systems is presented and used for solving the minimum energy control problem. The discussion is illustrated with numerical examples.
4
Content available Minimum energy control of fractional positive continuous-time linear systems using Caputo-Fabrizio definition
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2017
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Vol. 65, nr 1
45--51
EN
The Caputo-Fabrizio definition of the fractional derivative is applied to minimum energy control of fractional positive continuous- time linear systems with bounded inputs. Conditions for the reachability of standard and positive fractional linear continuous-time systems are established. The minimum energy control problem for the fractional positive linear systems with bounded inputs is formulated and solved.
5
Content available Minimum energy control of fractional positive electrical circuits
Kaczorek T.
Archives of Electrical Engineering
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2016
|
Vol. 65, nr 2
191--201
EN
Minimum energy control problem for the fractional positive electrical circuits is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by an example of fractional positive electrical circuit.
6
Content available Minimum energy control of descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition
Kaczorek T., Borawski K.
Archives of Control Sciences
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2016
|
Vol. 26, no. 2
177--187
EN
The minimum energy control problem for the descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the reachability of descriptor discrete-time linear systems are given. A procedure for computation of optimal input and a minimal value of the performance index is proposed and illustrated by a numerical example.
7
Content available Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs
Kaczorek T.
Archives of Control Sciences
|
2015
|
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.
8
Content available Minimum energy control of positive time-varying linear systems
Kaczorek T.
Acta Mechanica et Automatica
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2015
|
Vol. 9, no. 4
225--228
EN
The minimum energy control problem for the positive time-varying linear systems is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.
9
Content available Minimum energy control of fractional positive continuous-time linear systems with bounded inputs
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2014
|
Vol. 24, no. 2
335--340
EN
A minimum energy control problem for fractional positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
10
Content available Minimum energy control of fractional descriptor positive discrete-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2014
|
Vol. 24, no. 4
735--743
EN
Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems are established. The minimum energy control problem for descriptor positive systems is formulated and solved. Sufficient conditions for the existence of a solution to the minimum energy control problem are given. A procedure for computation of optimal input sequences and a minimal value of the performance index is proposed and illustrated by a numerical example.
11
Content available Necessary and sufficient conditions for the minimum energy control of positive discrete-time linear systems with bounded inputs
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2014
|
Vol. 62, nr 1
85--89
EN
The minimum energy control problem for the positive discrete-time linear systems with bounded inputs is formulated and solved. Necessary and sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.
12
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.
13
Content available An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2014
|
Vol. 62, nr 2
227--231
EN
The Klamka’s method of minimum energy control problem is extended to fractional positive discrete-time linear systems with bounded inputs. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by numerical example.
14
Content available Minimum energy control of positive continuous-time linear systems with bounded inputs
Kaczorek T.
Archives of Electrical Engineering
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2014
|
Vol. 63, nr 1
19-27
EN
The minimum energy control problem for the positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.
15
Content available Minimum energy control of 2D positive continuous-discrete linear systems
Kaczorek T.
Acta Mechanica et Automatica
|
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.
16
Content available Minimum energy control of positive continuous-time linear systems with bounded inputs
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2013
|
Vol. 23, no. 4
725--730
EN
The minimum energy control problem for positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
17
Content available Minimum energy control of fractional positive continuous-time linear systems
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2013
|
Vol. 61, nr 4
803--807
EN
The minimum energy control problem for the fractional positive continuous-time linear systems is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.
18
Content available Minimum energy control of positive discrete-time linear systems with bounded inputs
Kaczorek T.
Archives of Control Sciences
|
2013
|
Vol. 23, no. 2
205--211
EN
The minimum energy control problem for the positive discrete-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.
19
Content available remote Sterowanie minimalnoenergetyczne silnikiem prądu stałego
Długosz M.
Prace Naukowe Politechniki Śląskiej. Elektryka
|
2011
|
z. 1
89-98
PL
W pracy jest rozważane sterowanie minimalno energetyczne silnika prądu stałego. Zadnie poszukiwania takiego sterowania zostało sformułowane w odpowiednio dobranej przestrzeni Hilberta z definicją iloczynu skalarnego. Dzięki takiemu sformułowaniu zdania sterowania, rozwiązanie można wyznaczyć korzystając z twierdzenia o rzucie ortogonalnym. Tak wyznaczone sterowanie minimalizuje zadany wskaźnik jakości, ale jest to sterowanie w pętli otwartej. W pracy zawarto wyniki symulacji komputerowych wyznaczonych sterowań minimalno energetycznych.
EN
In this paper the minimum energy control of DC motor is considered. In order to solve the presented problem the Hilbert space and the orthogonal projection theorem are used. Most computation for finding the optimal control can be done with a computer. Numerical experiments confirming accuracy are also included in the paper.
20
Content available remote Remarks about DC motor control
Baranowski J., Długosz M., Mitkowski W.
Archives of Control Sciences
|
2008
|
Vol. 18, no. 3
289-322
EN
This paper was motivated by known results in the electric motor control where classical control algorithms were verified in the experimental framework. We want to show, that the control theory offers more sophisticated control methods that await their practical implementation. Presented algorithms for both continuous and discrete control and state estimation give many possibilities of improvement in the field of electric drive control. Our results are illustrated with simulations, but with available technology (such as MATLAB/Simulink/RTWT) can be easily verified in practice.
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