Handling of Time Delays in MISO Processes with Regularized Finite Impulse Response Models

Data driven system identification is the technique for learning models from input/output data. To increase the robustness of the model estimation, prior knowledge can be incorporated, the so-called gray-box identification. In finite impulse response (FIR) models, prior knowledge of the process under investigation can be introduced by regularization. In the regularization term basic impulse response characteristics such as smoothness and exponentially decaying behavior can be incorporated. For estimation of time-delay systems, the novel impulse response and time-delay preserving (IRDP) regularization matrix is proposed. In this contribution this method is extended to the estimation of multiple input single output (MISO) processes and is compared to other state-of-the-art approaches. A linear process with four inputs and different input dynamics and time-delays is investigated. The focus of the evaluation is placed on model quality, time-delay estimation, and computation time. The simulation results point out the superiority of the novel regularization approach in comparison to state-of-the-art methods.