Functional-Observer Implementation for Road-Profile Prediction in Quarter-Vehicle Model

Abstract

Ensuring safe driving requires continuous monitoring of both vehicle dynamics and external conditions such as road irregularities, which often act as unknown disturbances. Accurately estimating these unmeasured states and inputs is critical for advanced driver assistance systems (ADAS) and vehicle stability control. This study proposes a novel functional observer that simultaneously reconstructs unknown road disturbances and estimates unmeasured vehicle-state variables in real time using only standard onboard sensor measurements. The observer design is grounded in Lyapunov stability theory, with estimation conditions expressed as linear matrix inequalities (LMIs), whose solution guarantees robust convergence and stability. Validation is conducted through numerical simulations of a quarter-car vertical dynamics model under two scenarios. Results demonstrate that the proposed observer achieves accurate and reliable state estimation, outperforming conventional approaches such as the Kalman filter and full-order Luenberger observer, particularly in the presence of unknown inputs.