scholarly journals S-synchronization and Excitation Constancy in Structural Identifiability Problem of Nonlinear Systems

2021 ◽  
Vol 248 ◽  
pp. 01004
Author(s):  
Nikolay Karabutov
Keyword(s):  
Nonlinear System ◽  
Nonlinear Dynamical Systems ◽  
Structural Identification ◽  
Structural Identifiability ◽  
Geometric Framework ◽  
Nonlinear Dynamical ◽  
Nonlinear Part ◽  
System A ◽  
Local Identifiability ◽  
Identifiability Problem

An approach to analysis the structural identifiability (SI) of nonlinear dynamical systems under uncertainty was proposed. S-synchronizability condition of an input is the basis for the structural identifiability estimation of the nonlinear system. A method for obtaining a set containing information about the nonlinear part of the system wasproposed. The decision on SI of the system was based on the analysis of geometric frameworks reflected the state of the system nonlinear part. Geometric frameworks were defined on the specified set. Conditions for structural indistinguishability of geometric frameworks and local identifiability of the nonlinear part were obtained. It shown that a non-S-synchronizing input gives an insignificant geometric framework. This input is a sign of structural non-identifiability of the nonlinear system. The method for estimating the structural identifiability of the nonlinear system was proposed. We show that the structural identifiability is the basis for structural identification of the system. The structural identifiability degree was introduced, and the method of its estimation was proposed.

S-synchronization Structural Identifiability and Identification of Nonlinear Dynamic Systems

2020 ◽  
Vol 21 (6) ◽  
pp. 323-336
Author(s):  
N. N. Karabutov
Keyword(s):  
Nonlinear System ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Structural Parameters ◽  
Linear Part ◽  
Structural Identification ◽  
Nonlinear Dynamic Systems ◽  
Necessary Condition ◽  
Structural Identifiability ◽  
Nonlinear Part

An approach to the structural identifiability analysis of nonlinear dynamic systems under uncertainty is proposed. We have shown that S-synchronization is the necessary condition for the structural identifiability of a nonlinear system. Conditions are obtained for the design of a model which identifies the nonlinear part of the system. The method is proposed for the obtaining of a set which contains the information on the nonlinear part. A class of geometric frameworks which reflect the state of the system nonlinear part is introduced. Geometrical frameworks are defined on the synthesized set. The conditions are given for the structural indistinguishability of geometric frameworks on the set of S-synchronizing inputs. Local identifiability conditions are obtained for the nonlinear part. We are shown that a non-synchronizing input gives an insignificant geometric framework. This leads to a structural non-identifiability of the system nonlinear part. The method is proposed for the estimation of the structural identifiability the nonlinear part of the system. Conditions for parametric identifiability of the system linear part are obtained. We show that the structural identifiability is the basis for the structural identification of the system. The hierarchical immersion method is proposed for the estimation of nonlinear system structural parameters. The method is used for the structural identification of a system with Bouc-Wen hysteresis.

On Role of S-Synchronizability and Excitation Constancy in Structural Identifiability Problem of Nonlinear Systems

2021 ◽  
Vol 22 (2) ◽  
pp. 59-70
Author(s):  
N. N. Karabutov
Keyword(s):  
Nonlinear System ◽  
Geometric Structure ◽  
Nonlinear Dynamic System ◽  
System Structure ◽  
Structural Identifiability ◽  
Geometric Framework ◽  
System Requirements ◽  
Identifiability Problem ◽  
The Given

A class of dynamical systems with a single nonlinearity considered. The S-synchronizability concept of input introduced. It is shown that S-synchronizability is a condition for the structural identifiability of a nonlinear system. The decisionmaking on structural identifiability based on the properties analysis for a special class of geometric frameworks. Geometric frameworks reflect properties of the nonlinear dynamic system. Requirements for the model allowed us to obtain a geometric structure based on the input and output data considered. The constant excitation effect of input on the structural identifiability of the system is studied. The constant excitation effect of input studied on the structural identifiability of the system. Nonfulfillment the constant excitation condition gives a nonsignificant geometric framework. Various types of structural identifiability based on structure analysis considered. The concept of d-optimality described properties of the geometric structure introduced. Conditions for non-identifiability of nonlinear system structure obtained if the d-optimality of the geometric framework does not hold for the given properties of the input. Methods for estimating identifiability of the system and determining the identifiability area under uncertainty proposed. The proposed approach is generalized to the system having two nonlinearities. Conditions for partial structural identifiability obtained. Structural identifiability features of this class systems noted. The method for estimating the structure of the system proposed when the condition of structural identifiability satisfied. It has shown how the phase portrait used to estimate the system non-identifiability. A method proposed for constructing the structural identifiability domain of the system. Proposed methods and procedures are applied to study systems with Bouc-Wen hysteresis and two nonlinearity.

scholarly journals Symbolic Encoding of Periodic Orbits and Chaos in the Rucklidge System

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Chengwei Dong ◽  
Lian Jia ◽  
Qi Jie ◽  
Hantao Li
Keyword(s):  
Periodic Orbits ◽  
Nonlinear Dynamical Systems ◽  
Unstable Periodic Orbits ◽  
Nonlinear Dynamical ◽  
System A ◽  
Return Maps ◽  
Phase Portrait Analysis ◽  
Encoding Method ◽  
First Return Maps ◽  
Parameter Values

To describe and analyze the unstable periodic orbits of the Rucklidge system, a so-called symbolic encoding method is introduced, which has been proven to be an efficient tool to explore the topological properties concealed in these periodic orbits. In this work, the unstable periodic orbits up to a certain topological length in the Rucklidge system are systematically investigated via a proposed variational method. The dynamics in the Rucklidge system are explored by using phase portrait analysis, Lyapunov exponents, and Poincaré first return maps. Symbolic encodings of the periodic orbits with two and four letters based on the trajectory topology in the phase space are implemented under two sets of parameter values. Meanwhile, the bifurcations of the periodic orbits are explored, significantly improving the understanding of the dynamics of the Rucklidge system. The multiple-letter symbolic encoding method could also be applicable to other nonlinear dynamical systems.

scholarly journals STABILITY AND STABILIZATION OF NONLINEAR DYNAMICAL SYSTEMS

2017 ◽  
Vol 20 (1) ◽  
pp. 61-70
Author(s):  
P. Sattayatham ◽  
R. Saelim ◽  
S. Sujitjorn
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Feedback Controllers ◽  
Nonlinear Dynamical ◽  
System A ◽  
Continuous Feedback ◽  
Stability And Stabilization ◽  
The Stability

Exponential and asymptotic stability for a class of nonlinear dynamical systems with uncertainties is investigated.  Based on the stability of the nominal system, a class of bounded continuous feedback controllers is constructed.  By such a class of controllers, the results guarantee exponential and asymptotic stability of uncertain nonlinear dynamical system.  A numerical example is also given to demonstrate the use of the main result.

Structural Identifiability of Nonlinear Dynamic Systems

2019 ◽  
Vol 20 (4) ◽  
pp. 195-205
Author(s):  
N. N. Karabutov
Keyword(s):  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Adaptive Systems ◽  
Input Parameter ◽  
Estimation Method ◽  
Structural Identification ◽  
Nonlinear Dynamic Systems ◽  
Problem Solution ◽  
Structural Identifiability ◽  
Nonlinear Part

Approach to the analysis of nonlinear dynamic systems structural identifiability (SI) under uncertainty is proposed. This approach has difference from methods applied to SI estimation of dynamic systems in the parametrical space. Structural identifiability is interpreted as of the structural identification possibility a system nonlinear part. We show that the input should synchronize the system for the SI problem solution. The S-synchronizability concept of a system is introduced. An unsynchronized input gives an insignificant framework which does not guarantee the structural identification problem solution. It results in structural not identifiability of a system. The subset of the synchronizing inputs on which systems are indiscernible is selected. The structural identifiability estimation method is based on the analysis of framework special class. The structural identifiability estimation method is proposed for systems with symmetric nonlinearities. The input parameter effect is studied on the possibility of the system SI estimation. It is showed that requirements of an excitation constancy to an input in adaptive systems and SI systems differ.

scholarly journals The Study of Identification Method for Dynamic Behavior of High-Dimensional Nonlinear System

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Pan Fang ◽  
Liming Dai ◽  
Yongjun Hou ◽  
Mingjun Du ◽  
Wang Luyou
Keyword(s):  
Numerical Methods ◽  
Nonlinear System ◽  
Dynamic Behavior ◽  
Evaluation Method ◽  
Nonlinear Dynamical Systems ◽  
Autonomous Systems ◽  
High Dimensional ◽  
Nonlinear Dynamical ◽  
System Parameters ◽  
Research Findings

The dynamic behavior of nonlinear systems can be concluded as chaos, periodicity, and the motion between chaos and periodicity; therefore, the key to study the nonlinear system is identifying dynamic behavior considering the different values of the system parameters. For the uncertainty of high-dimensional nonlinear dynamical systems, the methods for identifying the dynamics of nonlinear nonautonomous and autonomous systems are treated. In addition, the numerical methods are employed to determine the dynamic behavior and periodicity ratio of a typical hull system and Rössler dynamic system, respectively. The research findings will develop the evaluation method of dynamic characteristics for the high-dimensional nonlinear system.

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