System identification and machine learning are two similar concepts independently used in automatic and computer science community. System identification uses statistical methods to build mathematical models of dynamical systems from measured data. Machine learning algorithms build a mathematical model based on sample data, known as "training data" (clean or not), in order to make predictions or decisions without being explicitly programmed to do so. Except prediction accuracy, converging speed and stability are another two key factors to evaluate the training process, especially in the online learning scenario, and these properties have already been well studied in control theory. Therefore, this thesis will implement the interdisciplinary researches for following topic: 1) System identification and optimal control on macroeconomic data: We first modelize the China macroeconomic data on Vector Auto-Regression (VAR) model, then identify the cointegration relation between variables and use Vector Error Correction Model (VECM) to study the short-time fluctuations around the long-term equilibrium, Granger Causality is also studied with VECM. This work reveals the trend of China's economic growth transition: from export-oriented to consumption-oriented; Due to limitation of China economic data, we turn to use France macroeconomic data in the second study. We represent the model in state-space, put the model into a feedback control framework, the controller is designed by Linear-Quadratic Regulator (LQR). The system can apply the control law to bring the system to a desired state. We can also impose perturbations on outputs and constraints on inputs, which emulates the real-world situation of economic crisis. Economists can observe the recovery trajectory of economy, which gives meaningful implications for policy-making. 2) Using control theory to improve the online learning of deep neural network: We propose a performance-based learning rate algorithm: E (Exponential)/PD (Proportional Derivative) feedback control, which consider the Convolutional Neural Network (CNN) as plant, learning rate as control signal and loss value as error signal. Results show that E/PD outperforms the state-of-the-art in final accuracy, final loss and converging speed, and the result are also more stable. However, one observation from E/PD experiments is that learning rate decreases while loss continuously decreases. But loss decreases mean model approaches optimum, we should not decrease the learning rate. To prevent this, we propose an event-based E/PD. Results show that it improves E/PD in final accuracy, final loss and converging speed; Another observation from E/PD experiment is that online learning fixes a constant training epoch for each batch. Since E/PD converges fast, the significant improvement only comes from the beginning epochs. Therefore, we propose another event-based E/PD, which inspects the historical loss, when the progress of training is lower than a certain threshold, we turn to next batch. Results show that it can save up to 67% epochs on CIFAR-10 dataset without degrading much performance.3) Machine learning out of unreliable data: We propose a generic framework: Robust Anomaly Detector (RAD), The data selection part of RAD is a two-layer framework, where the first layer is used to filter out the suspicious data, and the second layer detects the anomaly patterns from the remaining data. We also derive three variations of RAD namely, voting, active learning and slim, which use additional information, e.g., opinions of conflicting classifiers and queries of oracles. We iteratively update the historical selected data to improve accumulated data quality. Results show that RAD can continuously improve model's performance under the presence of noise on labels. Three variations of RAD show they can all improve the original setting, and the RAD Active Learning performs almost as good as the case where there is no noise on labels.