Incorporating Recurrent Networks for Online System Identification Alongside Traditional Sine-Sweep Experiments

The experimental identification of an unknown system, and the blind system identification (BSI) methods, allows engineers to establish mathematical models that represent the real system behavior. However, when the system operates in a non-stationary environments influenced by external disturbances, models with adaptive properties are required for predicting the real-time domain response. This study defines and analyzes in detail two system identification methods. The first method, which operates offline and requires post-processing, is mathematically defined to achieve the highest level of automation. It is based on sine sweep theory and involves conducting long-term experiments on a real system to determine its frequency domain properties. The second method, which operates online, employs computational learning theory and information theory to predict the system response through online learning. This modern approach uses convex optimization to obtain the optimal parameters of a time-lagged recurrent network (TLRN) in each iteration, which incorporates, among other features, a gamma filter as a mapper. This iterative online method was mathematically described addressing stability, convergence, and disturbances issues.