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 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 2D Positive Continuous-Discrete Linear Systems

2014 ◽  
Vol 8 (3) ◽  
pp. 165-168
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Energy Control ◽  
Final State ◽  
Discrete Linear Systems ◽  
Minimum Energy Control ◽  
One Step ◽  
Necessary And Sufficient

Abstract 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.

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.

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.

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 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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