Deterministic Identification Of Dynamical Systems

Deterministic Identification of Dynamical Systems

Deterministic Identification of Dynamical Systems

In deterministic identification the identified system is determined on the basis of a complexity measure of models and a misfit measure of models with respect to data. The choice of these measures and corresponding notions of optimality depend on the objectives of modelling. In this monograph, the cases of exact modelling, model reduction and approximate modelling are investigated. For the case of exact modelling a procedure is presented which is inspired by objectives of simplicity and corroboration. This procedure also gives a new solution for the partial realization problem. Further, appealing measures of complexity and distance for linear systems are defined and explicit numerical expressions are derived. A simple and new procedure for approximating a given system by one of less complexity is described. Finally, procedures and algorithms for deterministic time series analysis are presented. The procedures and algorithms are illustrated by simple examples and by numerical simulations.

Perspectives in Dynamical Systems II — Numerical and Analytical Approaches

This proceedings volume gathers selected, peer-reviewed papers presented at the Dynamical Systems Theory and Applications International Conference - DSTA 2021, held virtually on December 6-9, 2021, organized by the Department of Automation, Biomechanics, and Mechatronics at Lodz University of Technology, Poland. This volume focuses on numerical and analytical approaches, while Volume I concentrates on studies on applications. Being a truly international conference, this 16th iteration of DSTA received submissions from authors representing 52 countries. The program covered both theoretical and experimental approaches to widely understood dynamical systems, including topics devoted to bifurcations and chaos, control in dynamical systems, asymptotic methods in nonlinear dynamics, stability of dynamical systems, lumped mass and continuous systems vibrations, original numerical methods of vibration analysis, non-smooth systems, dynamics in life sciences and bioengineering, as well as engineering systems and differential equations. DSTA conferences aim to provide a common platform for exchanging new ideas and results of recent research in scientific and technological advances in modern dynamical systems. Works contained in this volume can appeal to researchers in the field, whether in mathematics or applied sciences, and practitioners in myriad industries.