Generating Chaos from Two Three-Dimensional Rigorous Linear Systems via a Novel Switching Control Approach

2016 ◽  
Vol 26 (13) ◽  
pp. 1650212 ◽  
Author(s):  
Changchun Sun ◽  
Qicheng Xu
Keyword(s):  
Equilibrium Point ◽  
Linear Systems ◽  
Three Dimensional ◽  
Constant Term ◽  
Switching Control ◽  
Numerical Examples ◽  
Absolute Value ◽  
Control Approach ◽  
Switching Law ◽  
Dynamical Behaviors

By constructing two three-dimensional (3D) rigorous linear systems, a novel switching control approach for generating chaos from two linear systems is presented. Two 3D linear systems without any constant term have only one common equilibrium point that is the origin. By employing an absolute-value switching law, chaos can be generated by switching between two linear systems. Basic dynamical behaviors of the systems are investigated in detail. Numerical examples illustrate the effectiveness of the presented approach.

Generating a Double-Scroll Attractor by Connecting a Pair of Mutual Mirror-Image Attractors via Planar Switching Control

2017 ◽  
Vol 27 (13) ◽  
pp. 1750197 ◽  
Author(s):  
Changchun Sun ◽  
Zhongtang Chen ◽  
Qicheng Xu
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Three Dimensional ◽  
Switching Control ◽  
Mirror Image ◽  
Image System ◽  
Sign Function ◽  
Control Approach ◽  
Switching Law ◽  
Dynamical Behaviors

An original three-dimensional (3D) smooth continuous chaotic system and its mirror-image system with eight common parameters are constructed and a pair of symmetric chaotic attractors can be generated simultaneously. Basic dynamical behaviors of two 3D chaotic systems are investigated respectively. A double-scroll chaotic attractor by connecting the pair of mutual mirror-image attractors is generated via a novel planar switching control approach. Chaos can also be controlled to a fixed point, a periodic orbit and a divergent orbit respectively by switching between two chaotic systems. Finally, an equivalent 3D chaotic system by combining two 3D chaotic systems with a switching law is designed by utilizing a sign function. Two circuit diagrams for realizing the double-scroll attractor are depicted by employing an improved module-based design approach.

DYNAMICAL ANALYSIS OF A CHAOTIC SYSTEM WITH TWO DOUBLE-SCROLL CHAOTIC ATTRACTORS

2004 ◽  
Vol 14 (03) ◽  
pp. 971-998 ◽  
Author(s):  
WENBO LIU ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Dynamical Analysis ◽  
Chaotic Attractors ◽  
Compound Structure ◽  
Numerical Examples ◽  
Routes To Chaos ◽  
Basic Properties ◽  
Dynamical Behaviors

Dynamical behaviors of a three-dimensional autonomous chaotic system with two double-scroll attractors are studied. Some basic properties such as bifurcation, routes to chaos, periodic windows and compound structure are demonstrated with various numerical examples. System equilibria and their stabilities are discussed, and chaotic features of the attractors are justified numerically.

scholarly journals 3D Multi-Beam and Null Synthesis by Phase-Only Control for 5G Antenna Arrays

Electronics ◽  
2019 ◽  
Vol 8 (6) ◽  
pp. 656 ◽  
Author(s):  
Massimiliano Comisso ◽  
Gabriele Palese ◽  
Fulvio Babich ◽  
Francesca Vatta ◽  
Giulia Buttazzoni
Keyword(s):  
Antenna Arrays ◽  
Computational Cost ◽  
Three Dimensional ◽  
Arbitrary Geometry ◽  
Numerical Examples ◽  
Control Approach ◽  
Fifth Generation ◽  
Conformal Arrays ◽  
Necessary Constraints ◽  
Low Computational Cost

This paper presents an iterative algorithm for the synthesis of the three-dimensional (3D) radiation pattern generated by an antenna array of arbitrary geometry. The algorithm is conceived to operate in fifth-generation (5G) millimeter-wave scenarios, thus enabling the support of multi-user mobile streaming and massive peer-to-peer communications, which require the possibility to synthesize 3D patterns with wide null regions and multiple main beams. Moreover, the proposed solution adopts a phase-only control approach to reduce the complexity of the feeding network and is characterized by a low computational cost, thanks to the closed-form expressions derived to estimate the phase of each element at the generic iteration. These expressions are obtained from the minimization of a weighted cost function that includes all the necessary constraints. To finally check its versatility in a 5G environment, the developed method is validated by numerical examples involving planar and conformal arrays, considering desired patterns with different numbers of main beams and nulls.

Chaos Generated by a Class of 3D Three-Zone Piecewise Affine Systems with Coexisting Singular Cycles

2020 ◽  
Vol 30 (14) ◽  
pp. 2050209
Author(s):  
Kai Lu ◽  
Wenjing Xu ◽  
Qigui Yang
Keyword(s):  
Mathematical Proof ◽  
Three Dimensional ◽  
Piecewise Affine Systems ◽  
Heteroclinic Cycles ◽  
Affine Systems ◽  
Numerical Examples ◽  
Piecewise Affine ◽  
Dynamical Behaviors ◽  
Nonsmooth Systems ◽  
Existence Conditions

It is a significant and challenging task to detect both the coexistence of singular cycles, mainly homoclinic and heteroclinic cycles, and chaos induced by the coexistence in nonsmooth systems. By analyzing the dynamical behaviors on manifolds, this paper proposes some criteria to accurately locate the coexistence of homoclinic cycles and of heteroclinic cycles in a class of three-dimensional (3D) piecewise affine systems (PASs), respectively. It further establishes the existence conditions of chaos arising from such coexistence, and presents a mathematical proof by analyzing the constructed Poincaré map. Finally, the simulations for two numerical examples are provided to validate the established results.

scholarly journals UAV Formation Shape Control via Decentralized Markov Decision Processes

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 91
Author(s):  
Md Ali Azam ◽  
Hans D. Mittelmann ◽  
Shankarachary Ragi
Keyword(s):  
Control Problem ◽  
Shape Control ◽  
Formation Control ◽  
Three Dimensional ◽  
Geographical Region ◽  
Dynamic Programming Method ◽  
Theoretic Approach ◽  
Control Approach ◽  
Uav Swarm ◽  
Markov Decision

In this paper, we present a decentralized unmanned aerial vehicle (UAV) swarm formation control approach based on a decision theoretic approach. Specifically, we pose the UAV swarm motion control problem as a decentralized Markov decision process (Dec-MDP). Here, the goal is to drive the UAV swarm from an initial geographical region to another geographical region where the swarm must form a three-dimensional shape (e.g., surface of a sphere). As most decision-theoretic formulations suffer from the curse of dimensionality, we adapt an existing fast approximate dynamic programming method called nominal belief-state optimization (NBO) to approximately solve the formation control problem. We perform numerical studies in MATLAB to validate the performance of the above control algorithms.

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