The power density and efficiency of high compression ratio (∼200/1) air compressors/expanders are crucial for the economical viability of a Compressed Air Energy Storage (CAES) system such as the one proposed in . There is a trade-off between power density and efficiency that is strongly dependent on the heat transfer capability within compressor/expander. In previous papers, we have shown that the compression or expansion trajectory can be optimized so that for a given power, the efficiency can be optimized and vice versa. Theoretically, for high compression ratios, the improvement over ad-hoc trajectories can be significant- for example, at the same efficiency of 90%, the power can be increased by 3-5 folds , , , . Yet, the optimal trajectories depend on the heat transfer coefficient profile that is often unknown. In this paper, we focus on the experimental study of an iterative control algorithm to track a compression trajectory that optimizes the efficiency-power trade-off in a liquid piston air compressor. First, an adaptive controller is developed to track any desired compression trajectory characterized by the temperature-volume profile. The controller adaptively estimates the unknown heat transfer coefficient. Second, the estimated heat transfer coefficient from one iteration is then used to estimate the optimal compression trajectory for the next iteration. As the estimate of the heat transfer coefficient improves from one iteration to the next, the quality of the estimated optimal trajectory also improves. This leads to successively improved efficiency. The experimental results of optimal trajectories show up to 2% improvement in compression efficiency compared to linear trajectories in a same power density.