Minimum Energy Control of Fractional Descriptor Discrete-Time Linear Systems with Bounded Inputs Using The DRAZIN Inverse

2017 ◽  
Vol 19 (6) ◽  
pp. 2211-2218 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Drazin Inverse ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Time Linear

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.

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 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.

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 Descriptor Fractional Discrete–Time Linear Systems with Two Different Fractional Orders

2017 ◽  
Vol 27 (1) ◽  
pp. 33-41 ◽  
Author(s):  
Łukasz Sajewski
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Minimum Energy ◽  
Decomposition Theorem ◽  
State Equation ◽  
Energy Control ◽  
Minimum Energy Control ◽  
Reachability Condition ◽  
Fractional Orders ◽  
Time Linear

Abstract 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.

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.

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