Interval methods and contractor-based branch-and-bound procedures for verified parameter identification of quasi-linear cooperative system models

摘要

A large number of dynamic system models in engineering as well as computational physics, chemistry or biology are described after first-principle modeling approaches by sets of either discrete-time difference equations or by sets of ordinary differential equations. In both cases, the structure of those system models results from fundamental physical system properties such as conservation laws of mass, momentum and energy, Newton's or Kirchhoffs laws as well as a structural subdivision into subsystems or individual compartments. Regardless of the area of application, all of these system models involve parameters which are not perfectly known due to uncertainty resulting from tolerances in the construction of the respective real-life systems or which are described by an inherent uncertainty coming from model simplifications or even from a lack of knowledge about detailed microscopic dynamic effects. This is especially true for applications in engineering, where a trade-off between the model accuracy and the resulting computational complexity has to be made in order to obtain mathematical representations which can be evaluated numerically in real time. This real-time applicability is inevitable if tasks such as feedback control or model-based state estimation on the basis of incomplete state measurements are of interest. Hence, all aforementioned tasks depend on the reliable estimation of those parameters of the structurally predefined sets of state equations which are feasible with respect to the knowledge about selected measurable state variables under consideration of the associated measurement tolerances. This paper presents computational techniques for a model-based identification of system parameters under the a-priori knowledge of stability of the underlying open-loop dynamics and the structural constraint of cooperativity. (C) 2019 Elsevier B.V. All rights reserved.