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].