Model structures and fitting criteria for system identification with neural networks

Abstract: This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are fitted to measured data using different criteria including a computationally efficient approach minimizing a regularized multi-step ahead simulation error. In this approach, the neural network parameters are estimated along with the initial conditions used to simulate the output signal in small-size subsequences. A regularization term is included in the fitting cost in order to enforce these initial conditions to be consistent with the estimated system dynamics. Pitfalls and limitations of naive one-step prediction and simulation error minimization are also discussed.