Design and stability analysis of optimal controller and observer for Itô stochastic model of active vehicle suspension system

This paper investigates Itô-type stochastic linear quadratic controller design for uncertain model of vehicle suspension. The Itô stochastic model of quarter-car is constructed considering parametric stochastic perturbations in stiffness and damping characteristics of suspension. To tackle with uncertainties of model, a stochastic optimal control law is obtained applying stochastic Hamilton-Jacobi-Bellman equation. By means of Itô lemma and stochastic extension of Lyapunov method, stochastic stability of the closed-loop system is guaranteed. The stochastic optimal controller is designed for a general form of Itô uncertain model which is comprised multi-dimensional multiplicative perturbations and then it is implemented on perturbed model of vehicle suspension. Furthermore, it is shown that the separation principal does not hold for the system with state multiplicative noise; therefore, the synthesized observer-based controller guarantees the stability of augmented dynamic consists of system and estimation error dynamics. A simulation study is performed to evaluate the effectiveness of stochastic optimal control approach in satisfying objectives of active suspension. To this end, time and frequency responses of ride comfort and road holding characteristics are demonstrated for two specific road cases including sinusoidal bump and ISO random profile.