Initialization approach for decoupling polynomial NARX models using tensor decomposition

The Nonlinear Auto-regressive eXogenous input (NARX) model has been widely used in nonlinear system identification. It's chief disadvantages are that it is a black-box model that suffers from the curse of dimensionality, in that the number of parameters increases rapidly with the nonlinearity degree. One approach to dealing with these problems involves decoupling the nonlinearity, but this requires solving a non-convex optimization problem. Solving non-convex optimization problems has always been challenging due to the possibility of getting trapped in a sub-optimal local optima. As a result, these kinds of optimization problems are sensitive to the initial solution. Providing an appropriate initial solution can increase the likelihood of finding the globally optimal solution. In this paper, an initialization technique that uses the polynomial coefficients in a full, albeit low order, NARX model is proposed. This technique generates a tensor from the coefficients in the from full polynomial NARX model and applies a tensor factorization in order to generate an appropriate starting point for decoupled polynomial NARX model optimization problem. The proposed technique is applied to nonlinear benchmark problem and the results are promising.