LOCALIZATION OF COMPACT INVARIANT SETS OF DISCRETE-TIME NONLINEAR SYSTEMS

2011 ◽  
Vol 21 (07) ◽  
pp. 2057-2065 ◽  
Author(s):  
ANATOLY N. KANATNIKOV ◽  
ALEXANDER P. KRISHCHENKO
Keyword(s):  
Nonlinear Systems ◽  
Iterative Algorithm ◽  
Discrete Time ◽  
Invariant Sets ◽  
Localization Problem ◽  
Extremum Condition

In this paper, we examine the localization problem of compact invariant sets of discrete-time nonlinear systems. The localization procedure consists in applying the iterative algorithm based on the extremum condition. An analysis of a location of compact invariant sets of the Henon system is realized for all values of its parameters.

LOCALIZATION OF COMPACT INVARIANT SETS OF NONLINEAR SYSTEMS WITH APPLICATIONS TO THE LANFORD SYSTEM

2006 ◽  
Vol 16 (11) ◽  
pp. 3249-3256 ◽  
Author(s):  
ALEXANDER P. KRISHCHENKO ◽  
KONSTANTIN E. STARKOV
Keyword(s):  
Nonlinear Systems ◽  
Iterative Algorithm ◽  
Periodic Orbits ◽  
Invariant Sets ◽  
Localization Problem ◽  
First Order ◽  
Extremum Condition

In this paper, we examine the localization problem of compact invariant sets of systems with the differentiable right-side. The localization procedure consists in applying the iterative algorithm based on the first order extremum condition originally proposed by one of authors for periodic orbits. Analysis of a location of compact invariant sets of the Lanford system is realized for all values of its bifurcational parameter.

scholarly journals Computing invariant sets of discrete-time nonlinear systems via state immersion

2020 ◽  
Vol 53 (2) ◽  
pp. 5505-5510
Author(s):  
Zheming Wang ◽  
Raphaël M. Jungers ◽  
Chong-Jin Ong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Invariant Sets

Maximal compact positively invariant sets of discrete-time nonlinear systems

2011 ◽  
Vol 44 (1) ◽  
pp. 12521-12525
Author(s):  
Alexander P. Krishchenko ◽  
Anatoly N. Kanatnikov
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Invariant Sets ◽  
Positively Invariant Sets

scholarly journals A Nearer Optimal and Faster Trained Value Iteration ADP for Discrete-Time Nonlinear Systems

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 14933-14944
Author(s):  
Junping Hu ◽  
Gen Yang ◽  
Zhicheng Hou ◽  
Gong Zhang ◽  
Wenlin Yang ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Value Iteration
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