REALIZATION OF PARAMETERS IDENTIFICATION IN ONLY LOCALLY LIPSCHITZIAN DYNAMICAL SYSTEMS WITH MULTIPLE TYPES OF TIME DELAYS?

摘要

Most of the existing results for identifying parameters in dynamical systems through adaptive coupling techniques always require a uniform Lipschitz condition on system vector fields. However, it is not this requirement but the only locally Lipschitz condition that is more suitable for many nonlinear systems in real applications. Also time delays sometimes are essential for modeling real systems, so that in addition to the discrete form, time delays in the distributed form could be considered. This paper thus considers the problem of parameters identification in only locally Lipschitzian dynamical systems with multiple types of time delays through adaptive coupling techniques. In particular, the paper proposes some linear independence conditions for realization of parameters identification in both nonautonomous and autonomous systems and draws a comparison between these conditions and the persistent of excitation condition which is used frequently in the literature. Moreover, the paper proposes an index to determine the nonlinear degree of the considered systems, which enables us to distinguish the systems in which the parameters identification can be globally or only locally achieved. The paper also uses some representative and elaborate examples to illustrate the practical usefulness of the obtained theoretical results. During the discussion, the paper takes into full consideration the property of infinite dimensions for nonautonomous or autonomous dynamical systems with time delays.