Optimal fractional-order PID controller based on fractional-order actor-critic algorithm

Abstract In this paper, an online optimization approach of a fractional-order PID controller based on actor-critic algorithm (FOPID-FOAC) is proposed. The proposed FOPID-FOAC scheme exploits the advantages FOPID and FOAC approaches to improve performance nonlinear systems. built by developing FO-based learning for neural network with adaptive rates. Moreover, FO rectified linear unit (RLU) introduced enable AC define optimize its own activation function. By means Lyapunov theorem, convergence stability analysis are investigated. operators obtained using gray wolf (GWO) algorithm. effectiveness proven extensive simulations tracking problem two degrees freedom (2-DOF) helicopter system stabilization issue inverted pendulum (IP) system. compared against optimized control in different conditions, namely when subjected parameter uncertainties external disturbances. comparison conducted terms types indices, error time response indices. first one includes integral absolute (IAE), squared (ISE), whereas second type involves rising time, maximum overshoot (Max. OS), settling time. simulation results explicitly indicate high measurements under scenarios other algorithms.