Identification for systems governed by nonlinear interval differential equations

Abstract

In this paper we consider the identification problem for a class of systems governed by nonlinear time varying interval differential equations having unknown (interval) parameters. Using the fact that system output posses lower and upper bounds, we have developed two sets of ordinary differential equations that represent the behaviour of lower and upper bounds. Based on these differential equations, the interval identification problem is converted into an equivalent identification problem in which the unknown parameters are real valued functions. Using variational arguments, we have developed the necessary conditions of optimality for the equivalent problem on the basis of which the unknown lower and upper parameters (and hence the interval parameters) can be determined. Finally, we present some numerical simulations to illustrate the effectivness of the proposed technique.