Optimal Controllers with Complex Order Derivatives

This paper studies the optimization of complex‐order algorithms for the discrete‐time control of linear and nonlinear systems. The fundamentals of fractional systems and genetic algorithms are introduced. Based on these concepts, complex‐order control schemes and their implementation are evaluated in the perspective of evolutionary optimization. The results demonstrate not only that complex‐order derivatives constitute a valuable alternative for deriving control algorithms, but also the feasibility of the adopted optimization strategy.