Reachability and stabilizability for positive nonlinear systems on time scales

Optimization ◽  
2021 ◽  
pp. 1-16
Author(s):  
Z. Bartosiewicz
Keyword(s):  
Nonlinear Systems ◽  
Time Scales

Adaptive optimal control of unknown nonlinear systems with different time scales

2017 ◽  
Vol 238 ◽  
pp. 179-190 ◽  
Author(s):  
Zhi-Jun Fu ◽  
Wen-Fang Xie ◽  
Subhash Rakheja ◽  
Dong-Dong Zheng
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Time Scales ◽  
Adaptive Optimal Control ◽  
Different Time Scales

On the Equivalence of Normal Form Theory and Multiple Time Scale Method

2007 ◽  
Author(s):  
Fengxia Wang ◽  
Anil K. Bajaj
Keyword(s):  
Nonlinear Systems ◽  
Normal Form ◽  
Differential Equations ◽  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Perturbation Scheme ◽  
Normal Form Theory ◽  
Weakly Nonlinear ◽  
Form Theory

Multiple time scales technique has long been an important method for the analysis of weakly nonlinear systems. In this technique, a set of multiple time scales are introduced that serve as the independent variables. The evolution of state variables at slower time scales is then determined so as to make the expansions for solutions in a perturbation scheme uniform in natural and slower times. Normal form theory has also recently been used to approximate the dynamics of weakly nonlinear systems. This theory provides a way of finding a coordinate system in which the dynamical system takes the “simplest” form. This is achieved by constructing a series of near-identity nonlinear transformations that make the nonlinear systems as simple as possible. The “simplest” differential equations obtained by the normal form theory are topologically equivalent to the original systems. Both methods can be interpreted as nonlinear perturbations of linear differential equations. In this work, the equivalence of these two methods for constructing periodic solutions is proven, and it is explained why some studies have found the results obtained by the two techniques to be inconsistent.

On stabilisability of nonlinear systems on time scales

2013 ◽  
Vol 86 (1) ◽  
pp. 139-145 ◽  
Author(s):  
Zbigniew Bartosiewicz ◽  
Ewa Piotrowska
Keyword(s):  
Nonlinear Systems ◽  
Time Scales

Reduction of MIMO nonlinear systems on homogeneous time scales

2010 ◽  
Vol 43 (14) ◽  
pp. 1249-1254 ◽  
Author(s):  
Ülle Kotta ◽  
Branislav Rehak ◽  
Malgorzata Wyrwas
Keyword(s):  
Nonlinear Systems ◽  
Time Scales ◽  
Mimo Nonlinear Systems

SYMBOLIC DYNAMICS, COARSE GRAINING AND THE MONITORING OF COMPLEX SYSTEMS

2011 ◽  
Vol 21 (12) ◽  
pp. 3465-3475 ◽  
Author(s):  
VASILEIOS BASIOS ◽  
DÓNAL MAC KERNAN
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Complex Systems ◽  
Error Estimates ◽  
Time Scales ◽  
Symbolic Dynamics ◽  
Prediction Error ◽  
Probabilistic Approach ◽  
Coarse Graining ◽  
Complex Nonlinear Systems

Coarse graining techniques and their associated symbolic dynamics are reviewed with a focus on probabilistic aspects of complex dynamical systems. The probabilistic approach initiated by Nicolis and coworkers has been elaborated. One of the major issues when dealing with the dynamics of complex nonlinear systems, the fact that the inherent time-scales of the unfolding phenomena are not well separated, is brought into focus. Recent results related to this interdependence, which is one of the most characteristic aspects of complexity and a major challenge in prediction, error estimates and monitoring of nonlinear complex systems, are discussed.

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