Stochastic stability of four-wheel-steering system

A four-wheel-steering system subjected to white noise excitations was reduced to a two-degree-of-freedom quasi-non-integrable-Hamiltonian system. Subsequently we obtained an one-dimensional Itô stochastic differential equation for the averaged Hamiltonian of the system by using the stochastic averaging method for quasi-non-integrable-Hamiltonian systems. Thus, the stochastic stability of four-wheel-steering system was analyzed by analyzing the sample behaviors of the averaged Hamiltonian at the boundary H = 0 and calculating its Lyapunov exponent. An example given at the end demonstrated that the conclusion obtained is of considerable significance.