Abstract: To guarantee the asymptotic stability and improve the ride comfort of vehicles, this paper develops the fuzzy neural network (NN) evolved bat algorithm (EBA) adaptive backstepping controller with grey signal predictors. To keep track of these ideal signals, Lyapunov's theory is proposed to acquire the control final laws. The gray DGM (2.1) models are also used to design suspension movements so that commands can be executed before the movement to achieve timely control. The convergence and stability of the whole system is also proven by the Lyapunov-like theory. The control expands the practices of mechanical elastic wheels (MEW) and provides a good methodical basis for a new wheel adaptation.