  Anti-lock Brake System (ABS) is a mandatory active safety feature on road
vehicles with analogous systems for aircraft and locomotives. This feature aims
to prevent locking of the wheels when braking and to improve the handling
performance, as well as reduce stopping distance of the vehicle. Estimation
uncertainties in the vehicle state and environment (road surface) are often
neglected or handled separately from the ABS controller, leading to sub-optimal
braking. In this paper, a Dual Control for Exploration-Exploitation (DCEE)
approach is taken toward the ABS problem which achieves both accurate state
(and environment) estimation and superior braking performance. Compared with
popular Extremum Seeking methods, improvements of up to $15\%$ and $8.5\%$ are
shown in stopping time and stopping distance, respectively. A Regularized
Particle Filter with Markov Chain Monte Carlo step is used to estimate vehicle
states and parameters of the Magic Formula tyre model that includes the peak
friction coefficient for the environment. The effectiveness of the DCEE
approach is demonstrated across a range of driving scenarios such as low and
high speeds; snow, wet and dry roads and changing road surfaces.
