Model quality in nonlinear SM identification

In the paper, the problem of identifying nonlinear regression models with "small" simulation errors is investigated. Models identified by classical methods minimizing the prediction error, do not necessary give "good" simulation error on future inputs and even boundedness of this error is not guaranteed. In the paper, it is shown that using the set membership (SM) identification method of [M. Milanese and C. Novara, 2003], conditions can be derived, assuring boundedness of simulation errors for future inputs. First, conditions are given, assuring that the solutions of the model derived by the optimal SM identification algorithm are uniformly exponentially stable. A quantity r_I, called radius of information, is also derived, giving the worst-case L_∞ norm of the error of the estimated regression function for all regressors in a domain of interest W. Then, under the same conditions giving stability of the identified model solutions, it is shown that, for all initial conditions and input sequences giving solutions of the system to be identified in the domain W, the simulation error can be bounded as a function of r_I that goes to zero as r_I decreases to zero. A numerical example demonstrates the effectiveness of the presented theoretical results.