Using Fractional Order Adjustment Rules and Fractional Order Reference Models in Model-Reference Adaptive Control

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A fractional adaptation law for sliding mode control (2008, background): “[8], where the integer order integration is replaced with an integration of fractional order 1.”
Sliding mode control approaches to the robust regulation of linear multivariable fractional‐order dynamics (2010, background): “linear control paradigms as well such as the model-reference adaptive control [13, 14, 15].”
Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems (2015, background): “Fractional Order PID controllers [5]; fractional high gain output feedback controllers [6,7] and Fractional Order Model Reference Adaptive Controllers (FOMRAC) [8–14], amongst others.”
On the sliding‐mode control of fractional‐order nonlinear uncertain dynamics (2016, background): “The long-range temporal or spatial hereditary phenomena inherent to the FOSs present unique and intriguing peculiarities, not supported by their integer-order counterpart, which raise numerous challenges and opportunities related to the development of control and estimation methodologies involving f”