The design of a swarm optimization-based fractional control for engineering application is an active research topic in the optimization analysis. This work offers the analysis, design, and simulation of a new neural network- (NN) based nonlinear fractional control structure. With suitable arrangements of the hidden layer neurons using nonlinear and linear activation functions in the hidden and output layers, respectively, and with appropriate connection weights between different hidden layer neurons, a new class of nonlinear neural fractional-order proportional integral derivative (NNFOPID) controller is proposed and designed. It is obtained by approximating the fractional derivative and integral actions of the FOPID controller and applied to the motion control of nonholonomic differential drive mobile robot (DDMR). The proposed NNFOPID controller’s parameters consist of derivative, integral, and proportional gains in addition to fractional integral and fractional derivative orders. The tuning of these parameters makes the design of such a controller much more difficult than the classical PID one. To tackle this problem, a new swarm optimization algorithm, namely, MAPSO-EFFO algorithm, has been proposed by hybridization of the modified adaptive particle swarm optimization (MAPSO) and the enhanced fruit fly optimization (EFFO) to tune the parameters of the NNFOPID controller. Firstly, we developed a modified adaptive particle swarm optimization (MAPSO) algorithm by adding an initial run phase with a massive number of particles. Secondly, the conventional fruit fly optimization (FFO) algorithm has been modified by increasing the randomness in the initialization values of the algorithm to cover wider searching space and then implementing a variable searching radius during the update phase by starting with a large radius which decreases gradually during the searching phase. The tuning of the parameters of the proposed NNFOPID controller is carried out by reducing the MS error of 0.000059, whereas the MSE of the nonlinear neural system (NNPID) is equivalent to 0.00079. The NNFOPID controller also decreased control signals that drive DDMR motors by approximately 45 percent compared to NNPID and thus reduced energy consumption in circular trajectories. The numerical simulations revealed the excellent performance of the designed NNFOPID controller by comparing its performance with that of nonlinear neural (NNPID) controllers on the trajectory tracking of the DDMR with different trajectories as study cases.

This work proposes a new kind of trajectory tracking controller for the differential drive mobile robot (DDMR), namely, the nonlinear neural network fractional-order proportional integral derivative (NNFOPID) controller. The suggested controller’s coefficients comprise integral, proportional, and derivative gains as well as derivative and integral powers. The adjustment of these coefficients turns the design of the proposed NNFOPID control further problematic than the conventional proportional-integral-derivative control. To handle this issue, an Enhanced Fruit Fly Swarm Optimization algorithm has been developed and proposed in this work to tune the NNFOPID’s parameters. The enhancement achieved on the standard fruit fly optimization technique lies in the increased uncertainty in the values of the initialized coefficients to convey a broader search space. subsequently, the search range is varied throughout the updating stage by beginning with a big radius and declines gradually during the course of the searching stage. The proposed NNFOPID controller has been validated its ability to track specific three types of continuous trajectories (circle, line, and lemniscate) while minimizing the mean square error and the control energy. Demonstrations have been run under MATLAB environment and revealed the practicality of the designed NNFOPID motion controller, where its performance has been compared with that of a nonlinear Neural Network Proportional Integral Derivative controller on the tracking of one of the aforementioned trajectories of the DDMR.