Robust expansion of uncertain Volterra kernels into orthonormal series

This paper is concerned with the computation of uncertainty bounds for the expansion of uncertain Volterra models into an orthonormal basis of functions, such as the Laguerre or Kautz bases. This problem has already been addressed in the context of linear systems by means of an approach in which the uncertainty bounds of the expansion coefficients have been estimated from a structured set of impulse responses describing a linear uncertain process. This approach is extended here towards nonlinear Volterra models through the computation of the uncertainty bounds of the expansion coefficients from a structured set of uncertain Volterra kernels. The proposed formulation assures that the resulting model is able to represent all the original uncertainties with minimum intervals for the expansion coefficients. An example is presented to illustrate the effectiveness of the proposed formulation.