Novel Fractional-Order Model Predictive Control: State-Space Approach

Abstract

This paper deals with a novel approach to the fractional-order model predictive control in state space. Except well known fractional-order models of processes (plants) with arbitrary (real) order of the derivatives in fractional differential equations a new fractional performance index (cost function) and fractional control action are considered. Such combined approach to the model predictive control provides more degrees of freedom and incorporates fractional-order dynamics into the control in the form of memory due to the property of the fractional-order operator. An illustrative example of this approach is presented.INDEX TERMS model predictive control (MPC), fractional calculus, fractional-order model, fractional derivative, fractional-order cost function, fractional integral, constrains, linear quadratic regulator (LQR)

Stability Analysis of Fractional-Order Periodic Piecewise Nonlinear Systems

“…The most frequently used fractional-order operators are expressed in terms of Caputo, Riemann-Liouville, and Grünwald-Letnikov [19]. Since the introduction of fractional derivative, fractional-order systems have become a prominent research topic [20]- [24], with applications in fields such as physics, biology, electrical engineering, and control theory. To pave the way for the engineering application of fractional-order systems, the Mittag-Leffler stability and the fractional Lyapunov direct method were proposed in [25], [26].…”