Computation of local radius of information in SM-IBC identification of nonlinear systems

System identification consists in finding a model of an unknown system starting from a finite set of noise-corrupted data. A fundamental problem in this context is to asses the accuracy of the identified model. In this paper, the problem is investigated for the case of nonlinear systems within the Set Membership—Information Based Complexity framework of M. Milanese, C. Novara, Set membership identification of nonlinear systems, Automatica 40(6) (2004) 957–975]. In that paper, a (locally) optimal algorithm has been derived, giving (locally) optimal models in nonlinear regression form. The corresponding (local) radius of information, providing the worst-case identification error, can be consequently used to measure the quality of the identified model. In the present paper, two algorithms are proposed for the computation of the local radius of information: The first provides the exact value but requires a computational complexity exponential in the dimension of the regressor space. The second is approximate but involves a polynomial (quadratic) complexity.