An analytic solution to the limit cycle control problem for multi-modal and 2-dimensional piecewise affine systems

2017 ◽  
Author(s):  
Tatsuya Kai ◽  
Kousuke Izumi
Keyword(s):  
Control Problem ◽  
Limit Cycle ◽  
Analytic Solution ◽  
Piecewise Affine Systems ◽  
Affine Systems ◽  
Piecewise Affine

scholarly journals Homoclinic Orbits in Several Classes of Three-Dimensional Piecewise Affine Systems with Two Switching Planes

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3285
Author(s):  
Yanli Chen ◽  
Lei Wang ◽  
Xiaosong Yang
Keyword(s):  
Analytic Solution ◽  
Three Dimensional ◽  
Homoclinic Orbits ◽  
Heteroclinic Cycle ◽  
Sufficient Condition ◽  
Piecewise Affine Systems ◽  
Affine Systems ◽  
Analytic Proof ◽  
Piecewise Affine ◽  
Cycle Plays

The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affine systems with two switching planes regardless of the symmetry. An analytic proof is provided using the concrete expression forms of the analytic solution, stable manifold, and unstable manifold. Meanwhile, a sufficient condition for the existence of two homoclinic orbits is also obtained. Furthermore, two concrete piecewise affine asymmetric systems with two homoclinic orbits have been constructed successfully, demonstrating the method’s effectiveness.

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