Optimal control strategy for collisional Brownian engines

Collisional Brownian engines have recently gained attention as alternatives to conventional nanoscale engines. However, a comprehensive optimization of their performance, which could serve as a benchmark for future engine designs, is still lacking. In this work, we build upon this by deriving and analyzing the optimal control strategy for a collisional Brownian engine. By maximizing the average output work, we show that the optimal strategy consists of linear force segments separated by impulsive deltalike kicks that instantaneously reverse the particle's velocity. This structure enforces constant velocity within each stroke, enabling fully analytical expressions for optimal output power, efficiency, and entropy production. We demonstrate that the optimal strategy significantly outperforms standard ones (such as constant, linear, or periodic drivings), achieving higher performance while keeping entropy production under control. Remarkably, when evaluated using realistic experimental parameters, the efficiency approaches near unity at the power optimum, with entropy production remaining well controlled. To analyze a more realistic scenario, we examine the impact of smoothing the deltalike forces by introducing a finite duration and find that, although this reduces efficiency and increases entropy production, the optimal strategy still delivers high power output in a robust manner.