Time-Comfort Optimal Control of Vehicle Longitudinal Motion Using Pontryagin’s Maximum Principle and Numerical Methods

This paper proposes a simulation-oriented optimal control framework for generating time–comfort optimal longitudinal motion of a vehicle over a prescribed travel distance, under progressively realistic operational constraints. The problem is formulated as a minimum-time optimal control problem with bounded inputs and state constraints and is studied through six model variants that bridge the gap between idealized dynamics and practical driving conditions. The considered scenarios include unconstrained frictionless motion, actuator and acceleration bounds, comfort-driven speed limitations, terminal stopping constraints, road friction effects, and safety-critical constraints accounting for potential brake failure. For each case, the optimal acceleration and braking structure is derived via Pontryagin’s Maximum Principle, leading to a set of switching conditions and boundary-value differential systems. The resulting dynamics are computed numerically using explicit Euler integration and the DASSL solver, enabling robust simulation across both smooth and non-smooth constraint regimes. The numerical results illustrate how increasing model fidelity alters the switching structure and yields motion profiles that satisfy comfort and safety requirements while remaining close to time-optimal performance. The proposed modelling and simulation methodology is applicable to both road vehicles and railway systems and supports predictive control design in intelligent transportation applications where smooth braking, constraint satisfaction, and safety-critical operation are essential.