Mobile Deep Learning (MDL) has emerged as a privacy-preserving learning paradigm for mobile devices. This paradigm offers unique features such as privacy preservation, continual learning and low-latency inference to the building of personal mobile sensing applications. However, squeezing Deep Learning to mobile devices is extremely challenging due to resource constraint. Traditional Deep Neural Networks (DNNs) are usually over-parametered, hence incurring huge resource overhead for on-device learning. In this paper, we present a novel on-device deep learning framework named MDLdroidLite that transforms traditional DNNs into resource-efficient model structures for on-device learning. To minimize resource overhead, we propose a novel Release-and-Inhibit Control (RIC) approach based on Model Predictive Control theory to efficiently grow DNNs from tiny to backbone. We also design a gate-based fast adaptation mechanism for channel-level knowledge transformation to quickly adapt new-born neurons with existing neurons, enabling safe parameter adaptation and fast convergence for on-device training. Our evaluations show that MDLdroidLite boosts on-device training on various PMS datasets with 28x to 50x less model parameters, 4x to 10x less floating number operations than the state-of-the-art model structures while keeping the same accuracy level.