Various embodiments of the present disclosure are directed towards free-piston combustion engines. As described herein, a method and system are provided for displacing a free-piston assembly to achieve a desired engine performance by repeatedly determining position-force trajectories over the course of a propagation path and effecting the displacement of the free-piston assembly based, at least in part, on the position-force trajectory. In a dual-piston assembly free-piston engine, synchronization of the two piston assemblies is provided.