scholarly journals On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-17
Author(s):  
M. De la Sen
Keyword(s):  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Stability Theory ◽  
Nonlinear Dynamic ◽  
General Class ◽  
The Other ◽  
Nonlinear Dynamic Systems ◽  
Time Varying ◽  
Controlled Systems ◽  
Input And Output

This paper investigates some parallel relations between the operators I-G and G in Hilbert spaces in such a way that the pseudocontractivity, asymptotic pseudocontractivity, and asymptotic pseudocontractivity in the intermediate sense of one of them are equivalent to the accretivity, asymptotic accretivity, and asymptotic accretivity in the intermediate sense of the other operator. If the operators are self-adjoint then the obtained accretivity-type properties are also passivity-type properties. Such properties are very relevant in stability theory since they refer to global stability properties of passive feed-forward, in general, nonlinear, and time-varying controlled systems controlled via feedback by elements in a very general class of passive, in general, nonlinear, and time-varying controllers. These results allow the direct generalization of passivity results in controlled dynamic systems to wide classes of tandems of controlled systems and their controllers, described by G-operators, and their parallel interpretations as pseudocontractive properties of their counterpart I-G-operators. Some of the obtained results are also directly related to input-passivity, output-passivity, and hyperstability properties in controlled dynamic systems. Some illustrative examples are also given in the framework of dynamic systems described by extended square-integrable input and output signals.

Diagnosing Irregularities of Nonlinear Dynamic Systems With Implementation of Periodicity-Ratio

2008 ◽  
Author(s):  
Liming Dai ◽  
Guoqing Wang
Keyword(s):  
Nonlinear Systems ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
The Other ◽  
Nonlinear Dynamic Systems ◽  
Deterministic System ◽  
Final States ◽  
Regular Motion ◽  
Chaotic Vibrations ◽  
Irregular Behavior

Among the irregular responses of nonlinear dynamic systems, chaotic responses of nonlinear systems are probably the most attractive phenomena along with the new observations in the last decades. A nonlinear deterministic system may behavior chaotically under regular such as periodic excitations. Regular motion of a system subjected to periodic exertions is usually periodic. In contrast with regular motions, final states of chaotic vibrations are extremely nonperiodic. This research is to analyzing the irregular behavior of dynamic systems with implementation of a newly developed criterion named Periodicity-Ratio. The development of a methodology for diagnosing the irregular motions from the regular motions of a dynamic system is presented. The Periodicity-Ratio describes the degree of periodicity of motion and can be conveniently used to distinguish a nonperiodic motion from a regular vibration or oscillation and to diagnose whether or not a motion is chaotic and the other irregular responses of the nonlinear dynamic systems, without plotting any figures. The analyses on the irregular behavior of nonlinear dynamic systems with the implementation of the Periodicity-Ratio will be demonstrated.

An Improved Symbolic Manipulation Technique for the Simulation of Nonlinear Dynamic Systems With Mixed Time-Varying and Constant Terms

1977 ◽  
Vol 99 (3) ◽  
pp. 157-166 ◽  
Author(s):  
C. R. Witham ◽  
S. Dubowsky
Keyword(s):  
Numerical Integration ◽  
Dynamic Systems ◽  
Nonlinear Dynamic ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Systems ◽  
Time Varying ◽  
Symbolic Manipulation ◽  
The Time Domain ◽  
Improved Technique ◽  
Time Invariant

The time domain behavior of nonlinear dynamic systems often is obtained by numerical integration on the digital computer. These solutions are usually expensive and limit the scope of the dynamic study. The proposed improved technique results in a substantial increase in the computational efficiency by using automatic symbolic manipulation to generate explicit equations of motion algebraically prior to numerical integration. A model is presented which considers the effects of the presence of time-invariant and time-varying symbolic terms and of the sparsity of system elements to provide analytical guidelines for the use of this technique. A number of case studies including typical computational costs are presented.

Data-Driven ILC for Trajectory Tracking in Nonlinear Dynamic Systems

2019 ◽  
Author(s):  
Yu-Hsiu Lee ◽  
Tsu-Chin Tsao
Keyword(s):  
Adaptive Filtering ◽  
Dynamic Systems ◽  
Trajectory Tracking ◽  
Nonlinear Dynamic ◽  
Fast Convergence ◽  
Data Driven ◽  
Nonlinear Dynamic Systems ◽  
Time Varying ◽  
Error Signal ◽  
Inverse Filter

Abstract The aim of this work is to propose a data-driven ILC algorithm that features fast convergence for nonlinear dynamic systems. This idea utilizes adaptive filtering that implicitly identifies the time-varying system inverse along the trajectory being tracked. By feeding the error signal through the copied inverse filter, it results in a rapidly convergent inversion-based ILC. This approach is compared to a nonlinear extension of the data-driven ILC that uses system adjoint as the learning filter. The developed algorithm is validated through simulation on a fully actuated 2 DOF Furuta pendulum.

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