Abstract
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].
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Dzieliński, A., Czyronis, P.M. (2013). Optimal Control Problem for Fractional Dynamic Systems – Linear Quadratic Discrete-Time Case. In: Mitkowski, W., Kacprzyk, J., Baranowski, J. (eds) Advances in the Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 257. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00933-9_8
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