Stochastic Optimal Control Of Vehicle Suspension System

The LQG control based on equivalent linearization and the nonlinear stochastic optimal control based on the stochastic averaging method for suspension systems of vehicles with hysteretic element are studied. First, The method of equivalent linearization is used to derive the equivalent linear equation and the optimal control laws are obtained by using stochastic optimal control theory based on full state information. The responses of controlled and uncontrolled vehicles are evaluated from solving Lyapunov equation. Second, A hysteretic force is replaced equivalently by a non-hysteretic nonlinear restoring force and a nonlinear damping force. An averaged Ito stochastic differential equation is derived from the equivalent nonlinear system by using the stochastic averaging method. A dynamical programming equation is set up for the ergodic control problem of the averaged system. The optimal control force is determined from solving the dynamical programming equation. The responses of controlled and uncontrolled vehicles are evaluated from solving FPK equation associated with averaged Ito equation. Numerical results show better effectiveness of the second control strategy than the first one.