Optimal synergetic control for fractional-order systems

Nowadays, the control of fractional-order system is one of the most popular topics in control theory. Recent studies have demonstrated the interest of fractional calculus both for systems modeling in many areas of science and engineering and for robust controller design. Thus, several research contributions have been devoted to the extension of control theory to fractional-order systems. Synergetic control was introduced in power electronics and other industrial processes. The benefit of this control scheme has been recognized for both integer-order linear and nonlinear systems. In this paper, a fractional-order synergetic control for fractional-order systems is proposed. Both linear and nonlinear cases are considered. The macro-variable is defined by the fractional-order integral of state variables. Optimality and stability properties are analyzed. A numerical example is investigated to confirm the effectiveness of the proposed method.