Complex autonomous and Cyber-Physical Systems (CPS) require reliable attack diagnostics with robustness to external disturbances, noise, and parametric uncertainties that ensure minimum time delay to detect cyber or physical attacks. Even using data-driven techniques for this motive poses a challenge because collecting training data that encompasses all possible attack signatures is difficult. Some attacks may have multiple realizations due to varying operating conditions. The proposed solution to this problem is to add physical insights to the data-driven model and use sparse regression to learn the underlying dynamics of the system. To tackle the problem of uncertainty in data due to external disturbances, noise, and parametric uncertainties, the model is learned multiple times using bootstraps of data, and parameter aggregation is performed to get an aggregated model. Then, using this aggregated model, robust residuals are designed to detect and isolate the attacks. Data from the lane keep assist system of an actual car is used to validate the model, and simulations are used to expand the data to varying operating conditions and perform multiple attacks on the system. The proposed approach for attack detection is compared to the baseline model-based diagnostic techniques like structural residuals and Extended Kalman Filter (EKF). In this work, the security implications of the system are analyzed, and robust residuals are designed with minimum knowledge about the underlying system dynamics, thus promoting the need for security by design.