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

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.

[1]  Tadeusz Kaczorek,et al.  Fractional Positive Continuous-Time Linear Systems and Their Reachability , 2008, Int. J. Appl. Math. Comput. Sci..

[2]  Tadeusz Kaczorek Minimum energy control of positive continuous-time linear systems with bounded inputs , 2014 .

[3]  Tadeusz Kaczorek,et al.  Positive Linear Systems Consisting of $n$ Subsystems With Different Fractional Orders , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  Jerzy Klamka,et al.  Controllability and Minimum Energy Control Problem of Fractional Discrete-Time Systems , 2010 .

[5]  P. B. de Moura Oliveira,et al.  FRACTIONAL DYNAMICS IN GENETIC ALGORITHMS , 2006 .

[6]  Tadeusz Kaczorek Controllability and observability of linear electrical circuits , 2011 .

[7]  Tadeusz Kaczorek,et al.  Practical stability and asymptotic stability of positive fractional 2D linear systems , 2009 .

[8]  Tadeusz Kaczorek Minimum energy control of fractional positive continuous-time linear systems , 2013 .

[9]  Tadeusz Kaczorek,et al.  Minimum energy control of descriptor positive discrete-time linear systems , 2014 .

[10]  Jon Rigelsford,et al.  Positive 1D and 2D Systems , 2002 .

[11]  Dominik Sierociuk,et al.  Stability of Discrete Fractional Order State-space Systems , 2008 .

[12]  Tadeusz Kaczorek,et al.  Selected Problems of Fractional Systems Theory , 2011 .

[13]  Tadeusz Kaczorek Minimum energy control of fractional positive continuous-time linear systems , 2013, MMAR.

[14]  Dominik Sierociuk,et al.  Ultracapacitor parameters identification based on fractional order model , 2009, 2009 European Control Conference (ECC).

[15]  Tadeusz Kaczorek Minimum energy control of positive continuous-time linear systems with bounded inputs , 2013, Int. J. Appl. Math. Comput. Sci..

[16]  Tadeusz Kaczorek An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs , 2014 .

[17]  A. Elwakil,et al.  On the stability of linear systems with fractional-order elements , 2009 .

[18]  Tadeusz Kaczorek,et al.  Practical stability of positive fractional discrete-time linear systems , 2008 .

[19]  Dong H. Chyung,et al.  Discrete systems with delays in control , 1969 .

[20]  M. Busłowicz,et al.  Stability of linear continuous-time fractional order systems with delays of the retarded type , 2008 .

[21]  James L. Melsa,et al.  Linear Control Systems , 1992 .

[22]  Tadeusz Kaczorek Reachability and controllability to zero tests for standard and positive fractional discrete-time systems , 2008 .

[23]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[24]  D. Sierociuk,et al.  Stability of Discrete Fractional Order State-space Systems , 2008 .

[25]  S. Rinaldi,et al.  Positive Linear Systems: Theory and Applications , 2000 .

[26]  Jerzy Klamka,et al.  Minimum energy control of 2-D linear systems with variable coefficients , 1986 .

[27]  Tadeusz Kaczorek Minimum energy control of positive discrete-time linear systems with bounded inputs , 2013 .

[28]  Tadeusz Kaczorek,et al.  Positivity and Reachability of Fractional Electrical Circuits , 2011 .

[29]  Jerzy Klamka,et al.  Relative controllability and minimum energy control of linear systems with distributed delays in control , 1976 .

[30]  J. Klamka Controllability of dynamical systems , 1991, Mathematica Applicanda.

[31]  Jerzy Klamka,et al.  Relative and absolute controllability of discrete systems with delays in control , 1977 .

[32]  M. Otter,et al.  Linear Control Systems , 2009 .

[33]  Tadeusz Kaczorek,et al.  Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm , 2011 .