Optimal Control Problem for Fractional Dynamic Systems - Linear Quadratic Discrete-Time Case

Dynamic optimization problems for integer (not fractional) order systems have been widely considered in literature (see e.g. [6, 13, 18, 21]). Mathematical fundamentals of the fractional calculus are given in the monographs [22-24] and the fractional differential equations and their applications have been addressed in [17, 19]. The numerical simulation of the fractional order control systems has been investigated in [7]. One of the fractional discretization method has been presented in [20]. Some optimal control problems for fractional order systems have been investigated in [1-5, 11, 12, 27]. Fractional Kalman filter and its application have been addressed in [25, 26]. Some recent interesting results in fractional systems theory and its applications to standard and positive systems can be found in [14-16].

[1]  Om P. Agrawal,et al.  Fractional variational calculus in terms of Riesz fractional derivatives , 2007 .

[2]  Tadeusz Kaczorek,et al.  New Stability Tests of Positive Standard and Fractional Linear Systems , 2011, Circuits Syst..

[3]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[4]  O. Agrawal.  A General Formulation and Solution Scheme for Fractional Optimal Control Problems , 2004 .

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

[6]  Dominik Sierociuk,et al.  Improved fractional Kalman filter and its application to estimation over lossy networks , 2011, Signal Process..

[7]  Delfim F. M. Torres,et al.  Fractional conservation laws in optimal control theory , 2007, 0711.0609.

[8]  Fawang Liu,et al.  Numerical simulation of the fractional-order control system , 2007 .

[9]  D. Naidu,et al.  Optimal Control Systems , 2018 .

[10]  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.

[11]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[12]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies) , 2006 .

[13]  Zoran D. Jelicic,et al.  Optimality conditions and a solution scheme for fractional optimal control problems , 2009 .

[14]  Om P. Agrawal,et al.  Formulation of Euler–Lagrange equations for fractional variational problems , 2002 .

[15]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[16]  D. Sierociuk,et al.  Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation , 2006 .

[17]  Dominik Sierociuk,et al.  Infinite horizon state-feedback LQR controller for fractional systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[18]  O. Agrawal.  A general finite element formulation for fractional variational problems , 2008 .

[19]  Om P. Agrawal,et al.  Fractional variational calculus and the transversality conditions , 2006 .

[20]  Fawang Liu,et al.  Fractional Differential Equations , 2010 .

[21]  R. Bellman.  Dynamic programming. , 1957, Science.

[22]  M. Meerschaert,et al.  Finite difference approximations for fractional advection-dispersion flow equations , 2004 .

[23]  Przemyslaw M. Czyronis,et al.  Dynamic Programming Problem for Fractional Discrete-Time Dynamic Systems. Quadratic Index of Performance Case , 2014, Circuits Syst. Signal Process..