Development of stochastic optimal controller for Itô uncertain model of active suspension system

Abstract

In this paper, Itô-type stochastic optimal control approach for uncertain model of vehicle suspension is developed. The model of quarter-car is constructed using linear characteristics of damping and springs. In order to elicit Itô stochastic dynamic of vehicle, parametric perturbations of sprung damping and spring characteristics are taken into account. Furthermore, the road disturbance is considered as a Gaussian white noise process. By using stochastic Hamilton-Jacobi-Bellman method, the stochastic optimal linear quadratic regulator controller for active suspension system is designed. Based on the concept of stochastic stability and using extension of Lyapunov method for Itô uncertain models, it is proven that the optimal control law, stochastically stabilizes the active perturbed suspension system. Moreover, it is shown that the well-known linear quadratic Gaussian controller cannot stabilize the perturbed system in certain conditions given by a linear matrix inequality. A simulation study is performed to evaluate the effectiveness of proposed stochastic control approach.