Adaptive control for the nonlinear suspension systems with stochastic disturbances and unknown time delay

In this work, an adaptive control problem is investigated for the nonlinear active suspension systems (ASSs) with stochastic disturbances and time delay. Also, in the suspension system, the nonlinearity of the springs and the dampers are considered. In order to be closer to the actual system, the external random disturbances are not neglected in this paper. It is worth mentioning that unknown time-varying delay is considered in this study to facilitate the treatment of transmission time delay. Based on Lyapunov theory and backstepping technique, the presented adaptive controller is able to ensure that all the signals in close-loop system are uniformly ultimately bounded in probability. Finally, the simulation results further illustrate the effectiveness of the proposed approach.