This study develops a novel radial basis function (RBF) neural network (NN) minimal learning backstepping control law for active suspension systems represented by nonlinear dynamics with additive stochastic terms and practical hydraulic actuator saturation. The suggested approach is equipped with an adaptive mechanism to cope with the mismatched uncertainties and a proper adaptation law is designed through the so-called minimal learning and the command filter techniques. By utilizing the concept of the bounded-in-probability Lyapunov stability, the backstepping controller is resilient dealing with stochastic disturbances arisen form un-modeled dynamics of active suspension systems. Moreover, the mean-value theorem is considered for handling the practical issue of the hydraulic actuation saturation issue. The presented robust adaptive control scheme theoretically assures that the output tracks a time-varying desired reference with a pre-determined small error. Eventually, a closed-loop active suspension plant with the hydraulic actuator is simulated numerically to show the advantages and performance of the developed controller over the state-of-the-art methods.

这项研究为主动悬架系统开发了一种新颖的径向基函数（RBF）神经网络（NN）最小学习反推控制律，该律以具有附加随机项和实际液压执行器饱和度的非线性动力学为代表。所建议的方法配备有自适应机制以应对不匹配的不确定性，并且通过所谓的最小学习和命令过滤器技术来设计适当的自适应律。通过利用概率有限Lyapunov稳定性的概念，后推控制器具有弹性，可应对由于主动悬架系统的非建模动力学而产生的随机干扰。此外，考虑平均值定理来处理液压致动饱和问题的实际问题。所提出的鲁棒自适应控制方案在理论上保证了输出跟踪具有预定小误差的时变期望参考。最终，对具有液压执行器的闭环主动悬架设备进行了数值模拟，以显示已开发控制器相对于最新技术的优势和性能。