Research

13 pages, 2586 KiB

Open AccessArticle

Synchronization of Complex Dynamical Networks with Stochastic Links Dynamics

by Juanxia Zhao, Yinhe Wang, Peitao Gao, Shengping Li and Yi Peng

Entropy 2023, 25(10), 1457; https://doi.org/10.3390/e25101457 - 17 Oct 2023

Cited by 1 | Viewed by 801

The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem [...] Read more.

The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network’s topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

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18 pages, 3273 KiB

Open AccessArticle

Formation with Non-Collision Control Strategies for Second-Order Multi-Agent Systems

by Eduardo Aranda-Bricaire and Jaime González-Sierra

Entropy 2023, 25(6), 904; https://doi.org/10.3390/e25060904 - 06 Jun 2023

Cited by 1 | Viewed by 921

Abstract

This article tackles formation control with non-collision for a multi-agent system with second-order dynamics. The nested saturation approach is proposed to solve the well-known formation control problem, allowing us to delimit the acceleration and velocity of each agent. On the other hand, repulsive [...] Read more.

This article tackles formation control with non-collision for a multi-agent system with second-order dynamics. The nested saturation approach is proposed to solve the well-known formation control problem, allowing us to delimit the acceleration and velocity of each agent. On the other hand, repulsive vector fields (RVFs) are developed to avoid collisions among the agents. For this purpose, a parameter depending on the distances and velocities among the agents is designed to scale the RVFs adequately. It is shown that when the agents are at risk of collision, the distances among them are always greater than the safety distance. Numerical simulations and a comparison with a repulsive potential function (RPF) illustrate the agents’ performance. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

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14 pages, 6265 KiB

Open AccessArticle

Exploring the Role of Indirect Coupling in Complex Networks: The Emergence of Chaos and Entropy in Fractional Discrete Nodes

by Ernesto Zambrano-Serrano, Miguel Angel Platas-Garza, Cornelio Posadas-Castillo, Adrian Arellano-Delgado and César Cruz-Hernández

Entropy 2023, 25(6), 866; https://doi.org/10.3390/e25060866 - 29 May 2023

Viewed by 1051

Abstract

Understanding the dynamics of complex systems defined in the sense of Caputo, such as fractional differences, is crucial for predicting their behavior and improving their functionality. In this paper, the emergence of chaos in complex dynamical networks with indirect coupling and discrete systems, [...] Read more.

Understanding the dynamics of complex systems defined in the sense of Caputo, such as fractional differences, is crucial for predicting their behavior and improving their functionality. In this paper, the emergence of chaos in complex dynamical networks with indirect coupling and discrete systems, both utilizing fractional order, is presented. The study employs indirect coupling to produce complex dynamics in the network, where the connection between the nodes occurs through intermediate fractional order nodes. The temporal series, phase planes, bifurcation diagrams, and Lyapunov exponent are considered to analyze the inherent dynamics of the network. Analyzing the spectral entropy of the chaotic series generated, the complexity of the network is quantified. As a final step, we demonstrate the feasibility of implementing the complex network. It is implemented on a field-programmable gate array (FPGA), which confirms its hardware realizability. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

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14 pages, 398 KiB

Open AccessArticle

Optimum k-Nearest Neighbors for Heading Synchronization on a Swarm of UAVs under a Time-Evolving Communication Network

by Rigoberto Martínez-Clark, Javier Pliego-Jimenez, Juan Francisco Flores-Resendiz and David Avilés-Velázquez

Entropy 2023, 25(6), 853; https://doi.org/10.3390/e25060853 - 26 May 2023

Cited by 2 | Viewed by 1117

Abstract

Heading synchronization is fundamental in flocking behaviors. If a swarm of unmanned aerial vehicles (UAVs) can exhibit this behavior, the group can establish a common navigation route. Inspired by flocks in nature, the k-nearest neighbors algorithm modifies the behavior of a group member [...] Read more.

Heading synchronization is fundamental in flocking behaviors. If a swarm of unmanned aerial vehicles (UAVs) can exhibit this behavior, the group can establish a common navigation route. Inspired by flocks in nature, the k-nearest neighbors algorithm modifies the behavior of a group member based on the k closest teammates. This algorithm produces a time-evolving communication network, due to the continuous displacement of the drones. Nevertheless, this is a computationally expensive algorithm, especially for large groups. This paper contains a statistical analysis to determine an optimal neighborhood size for a swarm of up to 100 UAVs, that seeks heading synchronization using a simple P-like control algorithm, in order to reduce the calculations on every UAV, this is especially important if it is intended to be implemented in drones with limited capabilities, as in swarm robotics. Based on the literature of bird flocks, that establishes that the neighborhood of every bird is fixed around seven teammates, two approaches are treated in this work: (i) the analysis of the optimum percentage of neighbors from a 100-UAV swarm, that is necessary to achieve heading synchronization, and (ii) the analysis to determine if the problem is solved in swarms of different sizes, up to 100 UAVs, while maintaining seven nearest neighbors among the members of the group. Simulation results and a statistical analysis, support the idea that the simple control algorithm behaves like a flock of starlings. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

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17 pages, 1192 KiB

Open AccessArticle

Formation and Flocking Control Algorithms for Robot Networks with Double Integrator Dynamics and Time-Varying Formations

by Carlos Montañez-Molina, Javier Pliego-Jiménez and Rigoberto Martínez-Clark

Entropy 2023, 25(6), 834; https://doi.org/10.3390/e25060834 - 23 May 2023

Viewed by 1041

Abstract

In this work, we study the problem of designing control laws that achieve time-varying formation and flocking behaviors in robot networks where each agent or robot presents double integrator dynamics. To design the control laws, we adopt a hierarchical control approach. First, we [...] Read more.

In this work, we study the problem of designing control laws that achieve time-varying formation and flocking behaviors in robot networks where each agent or robot presents double integrator dynamics. To design the control laws, we adopt a hierarchical control approach. First, we introduce a virtual velocity, which is used as a virtual control input for the position subsystem (outer loop). The objective of the virtual velocity is to achieve collective behaviors. Then, we design a velocity tracking control law for the velocity subsystem (inner loop). An advantage of the proposed approach is that the robots do not require the velocity of their neighbors. Additionally, we address the case in which the second state of the system is not available for feedback. We include a set of simulation results to show the performance of the proposed control laws. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

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13 pages, 927 KiB

Open AccessArticle

Attitude Synchronization of a Group of Rigid Bodies Using Exponential Coordinates

by Miguel Sidón-Ayala, Javier Pliego-Jiménez and César Cruz-Hernandez

Entropy 2023, 25(6), 832; https://doi.org/10.3390/e25060832 - 23 May 2023

Cited by 1 | Viewed by 925

Abstract

Currently, managing a group of satellites or robot manipulators requires coordinating their motion and work in a cooperative way to complete complex tasks. The attitude motion coordination and synchronization problems are challenging since attitude motion evolves in non-Euclidean spaces. Moreover, the equation of [...] Read more.

Currently, managing a group of satellites or robot manipulators requires coordinating their motion and work in a cooperative way to complete complex tasks. The attitude motion coordination and synchronization problems are challenging since attitude motion evolves in non-Euclidean spaces. Moreover, the equation of motions of the rigid body are highly nonlinear. This paper studies the attitude synchronization problem of a group of fully actuated rigid bodies over a directed communication topology. To design the synchronization control law, we exploit the cascade structure of the rigid body’s kinematic and dynamic models. First, we propose a kinematic control law that induces attitude synchronization. As a second step, an angular velocity-tracking control law is designed for the dynamic subsystem. We use the exponential coordinates of rotation to describe the body’s attitude. Such coordinates are a natural and minimal parametrization of rotation matrices which almost describe every rotation on the Special Orthogonal group

S O (3)

. We provide simulation results to show the performance of the proposed synchronization controller. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

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17 pages, 15346 KiB

Open AccessArticle

Electronic Implementation of a Deterministic Small-World Network: Synchronization and Communication

by Daniel Reyes-De la Cruz, Rodrigo Méndez-Ramírez, Adrian Arellano-Delgado and César Cruz-Hernández

Entropy 2023, 25(5), 709; https://doi.org/10.3390/e25050709 - 25 Apr 2023

Cited by 2 | Viewed by 1166

Abstract

In this paper, synchronization and encrypted communication transmissions of analog and digital messages in a deterministic small-world network (DSWN) are presented. In the first instance, we use a network with 3 coupled nodes in a nearest-neighbor (NN) topology, then the amount of nodes [...] Read more.

In this paper, synchronization and encrypted communication transmissions of analog and digital messages in a deterministic small-world network (DSWN) are presented. In the first instance, we use a network with 3 coupled nodes in a nearest-neighbor (NN) topology, then the amount of nodes is increased until reaching a DSWN with 24 nodes. The synchronization and encrypted communication transmissions using a DSWN are presented experimentally by using Chua’s chaotic circuit as node, in both analog and digital electronic implementations, where for the continuous version (CV) we use operational amplifiers (OA), and in the discretized version (DV) we use Euler’s numerical algorithm implemented in an embedded system by using an Altera/Intel FPGA and external digital-to-analog converters. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

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11 pages, 5187 KiB

Open AccessFeature PaperArticle

Master–Slave Outer Synchronization in Different Inner–Outer Coupling Network Topologies

by Adrian Arellano-Delgado, Rosa Martha López-Gutiérrez, Miguel Ángel Murillo-Escobar and Cornelio Posadas-Castillo

Entropy 2023, 25(5), 707; https://doi.org/10.3390/e25050707 - 24 Apr 2023

Cited by 1 | Viewed by 1198

Abstract

In this work, the problem of master–slave outer synchronization in different inner–outer network topologies is presented. Specifically, the studied inner–outer network topologies are coupled in master–slave configuration, where some particular scenarios concerning inner–outer topologies are addressed in order to disclose a suitable coupling [...] Read more.

In this work, the problem of master–slave outer synchronization in different inner–outer network topologies is presented. Specifically, the studied inner–outer network topologies are coupled in master–slave configuration, where some particular scenarios concerning inner–outer topologies are addressed in order to disclose a suitable coupling strength to achieve outer synchronization. The novel MACM chaotic system is used as a node in the coupled networks, which presents robustness in its bifurcation parameters. Extensive numerical simulations are presented where the stability of the inner–outer network topologies is analyzed through a master stability function approach. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

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27 pages, 4072 KiB

Open AccessArticle

Network Synchronization of MACM Circuits and Its Application to Secure Communications

by Rodrigo Méndez-Ramírez, Adrian Arellano-Delgado and Miguel Ángel Murillo-Escobar

Entropy 2023, 25(4), 688; https://doi.org/10.3390/e25040688 - 19 Apr 2023

Cited by 2 | Viewed by 1358

Abstract

In recent years, chaotic synchronization has received a lot of interest in applications in different fields, including in the design of private and secure communication systems. The purpose of this paper was to achieve the synchronization of the Méndez–Arellano–Cruz–Martínez (MACM) 3D chaotic system [...] Read more.

In recent years, chaotic synchronization has received a lot of interest in applications in different fields, including in the design of private and secure communication systems. The purpose of this paper was to achieve the synchronization of the Méndez–Arellano–Cruz–Martínez (MACM) 3D chaotic system coupled in star topology. The MACM electronic circuit is used as chaotic nodes in the communication channels to achieve synchronization in the proposed star network; the corresponding electrical hardware in the slave stages receives the coupling signal from the master node. In addition, a novel application to the digital image encryption process is proposed using the coupled-star-network; and the switching parameter technique is finally used to transmit an image as an encrypted message from the master node to the slave coupled nodes. Finally, the cryptosystem is submitted to statistical tests in order to show the effectiveness in multi-user secure image applications. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

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16 pages, 3474 KiB

Open AccessArticle

Bio-Inspired Autonomous Navigation and Formation Controller for Differential Mobile Robots

by Alejandro Juarez-Lora and Alejandro Rodriguez-Angeles

Entropy 2023, 25(4), 582; https://doi.org/10.3390/e25040582 - 28 Mar 2023

Viewed by 1263

Abstract

This article proposes a decentralized controller for differential mobile robots, providing autonomous navigation and obstacle avoidance by enforcing a formation toward trajectory tracking. The control system relies on dynamic modeling, which integrates evasion forces from obstacles, formation forces, and path-following forces. The resulting [...] Read more.

This article proposes a decentralized controller for differential mobile robots, providing autonomous navigation and obstacle avoidance by enforcing a formation toward trajectory tracking. The control system relies on dynamic modeling, which integrates evasion forces from obstacles, formation forces, and path-following forces. The resulting control loop can be seen as a dynamic extension of the kinematic model for the differential mobile robot, producing linear and angular velocities fed to the mobile robot’s kinematic model and thus passed to the low-level wheel controller. Using the Lyapunov method, the closed-loop stability is proven for the non-collision case. Experimental and simulated results that support the stability analysis and the performance of the proposed controller are shown. Full article

(This article belongs to the Special Issue Synchronization in Time-Evolving Complex Networks)

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