scholarly journals Minimum energy control of descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition

2016 ◽  
Vol 26 (2) ◽  
pp. 177-187 ◽  
Author(s):  
Tadeusz Kaczorek ◽  
Kamil Borawski
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Discrete Time ◽  
Performance Index ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract 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.

scholarly journals Minimum energy control of fractional descriptor positive discrete-time linear systems

2014 ◽  
Vol 24 (4) ◽  
pp. 735-743 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Existence Of A Solution ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract 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.

Minimum energy control of descriptor positive discrete-time linear systems

2014 ◽  
Vol 33 (3) ◽  
pp. 976-988 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Content Type ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Purpose – The purpose of this paper is to formulate and solve the minimum energy control problem of descriptor positive discrete-time linear systems. Design/methodology/approach – A procedure for computation of the optimal input sequences and the minimal value of the performance index is proposed. Findings – Necessary and sufficient conditions for the positivity and reachability of descriptor positive discrete-time linear systems and sufficient conditions for the existence of solution to the minimum energy control problem are given. Originality/value – A method for solving of the minimum energy control problem of descriptor positive discrete-time linear systems is proposed.

Necessary and sufficient conditions for the minimum energy control of positive discrete-time linear systems with bounded inputs

2014 ◽  
Vol 62 (1) ◽  
pp. 85-89 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Necessary And Sufficient Conditions ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract 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.

scholarly journals Minimum energy control of positive discrete-time linear systems with bounded inputs

2013 ◽  
Vol 23 (2) ◽  
pp. 205-211 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Energy Control ◽  
Numerical Example ◽  
Minimum Energy Control ◽  
Time Linear

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.

scholarly journals An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs

2014 ◽  
Vol 62 (2) ◽  
pp. 227-231 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Energy Control ◽  
Numerical Example ◽  
Minimum Energy Control ◽  
Time Linear

Abstract 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.

scholarly journals Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs

2015 ◽  
Vol 25 (3) ◽  
pp. 319-331
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Discrete Linear Systems ◽  
Minimum Energy Control ◽  
New Formulation ◽  
Necessary And Sufficient ◽  
The Given

AbstractA new formulation of the minimum energy control problem for the positive 2D continuous-discrete 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.

scholarly journals Minimum energy control of fractional positive continuous-time linear systems with bounded inputs

2014 ◽  
Vol 24 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Continuous Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Existence Of A Solution ◽  
Numerical Example ◽  
Minimum Energy Control ◽  
Time Linear

Abstract 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.

scholarly journals Minimum energy control of positive continuous-time linear systems with bounded inputs

2013 ◽  
Vol 23 (4) ◽  
pp. 725-730 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Continuous Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Energy Control ◽  
Existence Of A Solution ◽  
Numerical Example ◽  
Minimum Energy Control ◽  
Time Linear

Abstract 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.

scholarly journals Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state

2014 ◽  
Vol 62 (2) ◽  
pp. 233-239 ◽  
Author(s):  
M. Busłowicz
Keyword(s):  
Discrete Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
State Equation ◽  
Multiple Delays ◽  
Energy Control ◽  
Optimal Value ◽  
Minimum Energy Control ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract 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.

scholarly journals Minimum energy control of positive continuous-time linear systems with bounded inputs

2014 ◽  
Vol 63 (1) ◽  
pp. 19-27 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Continuous Time ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Energy Control ◽  
Numerical Example ◽  
Minimum Energy Control ◽  
Time Linear

Abstract 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

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