Fuzzy fractional-order adaptive robust feedback linearization control optimized by the multi-objective artificial hummingbird algorithm for a nonlinear ball–wheel system

For stabilizing a nonlinear ball–wheel system, this research suggests a fuzzy fractional-order adaptive robust feedback linearization control approach. The feedback linearization-based controller uses the decoupled sliding mode to locate the sliding surfaces and determine the adaptive coefficients. Then, the fractional-order calculus and fuzzy logic-based systems are implemented to improve the efficiency of the controller. Additionally, the multi-objective artificial hummingbird algorithm (MAHA) is employed to optimize the control coefficients by including two objective functions, namely the integral of the absolute values of the control efforts and the system errors. The success of the suggested strategy is then evaluated by applying it on the ball–wheel system and comparing the outcomes to those documented in the literature.