  The identification of black-box nonlinear state-space models requires a
flexible representation of the state and output equation. Artificial neural
networks have proven to provide such a representation. However, as in many
identification problems, a nonlinear optimization problem needs to be solved to
obtain the model parameters (layer weights and biases). A well-thought
initialization of these model parameters can often avoid that the nonlinear
optimization algorithm converges to a poorly performing local minimum of the
considered cost function. This paper introduces an improved initialization
approach for nonlinear state-space models represented as a recurrent artificial
neural network and emphasizes the importance of including an explicit linear
term in the model structure. Some of the neural network weights are initialized
starting from a linear approximation of the nonlinear system, while others are
initialized using random values or zeros. The effectiveness of the proposed
initialization approach over previously proposed methods is illustrated on two
benchmark examples.
