Nonlinear and Robust SDRE–H∞ Control for Brake-by-Wire under Variable Friction and μ-split

Abstract

This paper proposes a nonlinear and robust State-Dependent Riccati Equation (SDRE) combined with H∞ control architecture for brake- by-wire systems, specifically designed to handle severe tire-road friction variations and μ-split scenarios. The primary objective is to maximize deceleration capabilities while rigorously maintaining yaw stability, trajectory tracking, and passenger comfort through jerk limitation. Situated within the domain of active safety, this research addresses robustness against real-world uncertainties by utilizing a high-fidelity 14-degree-of-freedom vehicle model that accounts for longitudinal, lateral, and yaw dynamics, suspension-induced pitch and roll effects, and nonlinear tire behavior with explicit load transfer. To ensure near-optimal slip tracking under variable surface conditions, the system employs online friction estimation via Extended and Unscented Kalman Filters (EKF/UKF) fusing wheel and IMU data to adaptively adjust slip targets. The control strategy is bifurcated: the SDRE component manages dominant nonlinearities through state-dependent gains to prevent wheel lock-up, while the H∞ component provides robust disturbance rejection against parametric uncertainties such as mass variations and sensor noise. Control efforts are distributed via a Quadratic Programming (QP) torque allocator featuring anti-windup mechanisms and explicit saturation handling to compensate for lateral drift during μ-split braking. Validation is conducted through a Model- in-the-Loop (MIL) to Software-in-the-Loop (SIL) pipeline using scenarios including wet surfaces and panic braking. Simulation results demonstrate enhanced yaw stability and controlled deceleration profiles compared to conventional baselines, ensuring computational feasibility for automotive Electronic Control Units (ECUs).