Equivalence of Multi-Formulated Optimal Slip Control for Vehicular Anti-Lock Braking System

Abstract This paper presents the equivalence of time-optimal and optimal distance slip-control approach for purposes of performing antilock braking. A dynamic braking model is developed encorporating a slip state to facilitate slip tracking. Optimal distance braking is performed with control constraints on the dynamic slip based braking model. A similar treatment is applied for time optimal braking on the braking model. The key contribution is the demonstration of the equivalence of optimal distance and time optimal braking of a vehicle. A generalised none zero-terminal condition is utilised in the optimal formulations. Simulation results demonstrate the validity of the approach along with the development of a key optimality condition for the equivalence approach.