RESUMO
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 SO(3). We provide simulation results to show the performance of the proposed synchronization controller.
RESUMO
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.
RESUMO
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.
RESUMO
Currently, chaos-based cryptosystems are being proposed in the literature to provide confidentiality for digital images, since the diffusion effect in the Advance Encryption Standard (AES) algorithm is weak. Security is the most important challenge to assess in cryptosystems according to the National Institute of Standard and Technology (NIST), then cost and performance, and finally algorithm and implementation. Recent chaos-based image encryption algorithms present basic security analysis, which could make them insecure for some applications. In this paper, we suggest an integral analysis framework related to comprehensive security analysis, cost and performance, and the algorithm and implementation for chaos-based image cryptosystems. The proposed guideline based on 20 analysis points can assist new cryptographic designers to present an integral analysis of new algorithms. Future comparisons of new schemes can be more consistent in terms of security and efficiency. In addition, we present aspects regarding digital chaos implementation, chaos validation, and key definition to improve the security of the overall cryptosystem. The suggested guideline does not guarantee security, and it does not intend to limit the liberty to implement new analysis. However, it provides for the first time in the literature a solid basis about integral analysis for chaos-based image cryptosystems as an effective approach to improve security.