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This paper presents a novel approach to real-time obstacle avoidance based on Dynamical Systems (DS) that ensures impenetrability of multiple convex shaped objects. The proposed method can be applied to perform obstacle avoidance in Cartesian and Joint spaces and using both autonomous and non-autonomous DS-based controllers. Obstacle avoidance proceeds by modulating the original dynamics of the controller. The modulation is parameterizable and allows to determine a safety margin and to increase the robot’s reactiveness in the face of uncertainty in the localization of the obstacle. The method is validated in simulation on different types of DS including locally and globally asymptotically stable DS, autonomous and non-autonomous DS, limit cycles, and unstable DS. Further, we verify it in several robot experiments on the 7 degrees of freedom Barrett WAM arm.

Chaotic dynamics is ubiquitous in nature. Traditionally, a good model representation of a certain system can help in predicting this system’s future behavior. However, for a complex system, a physics-based model may not be easy to construct given the complexity of a system, in particular, those that exhibit chaotic behavior. Furthermore, due to the aperiodic nature of the motion and finite precision, a model-based prediction may only have relatively high accuracy over a short-time horizon, before significant growth of error occurs in the prediction. In this article, the authors explore an alternate modeling approach, which is based on data-driven modeling, to explore forecasting viability for systems that display chaotic dynamics. Specifically, a deep recurrent neural network architecture, a neural machine, is constructed for forecasting temporal evolution of different chaotic systems. Data obtained from simulations with well-known nonlinear dynamical system prototypes serve as training data for the chosen neural network. In practice, this simulation data may be replaced with field data. The trained system is studied to examine the forecasting ability. Two ordinary differential dynamical systems, namely the Lorenz’63 system and the Lorenz’96 system, and a partial differential system, the Kuramoto–Sivashinsky equation, are studied, and the numerical experiments conducted are presented here to demonstrate the forecasting viability of the constructed neural network.

The aim of the research is to describe a mass media social effect in the form of several levels of hierarchy. At the first level of hierarchy, the object of study is an adjacency matrix. Its elements appear to be the expert assessments of specialists obtained in paired comparisons of some factors. The second level represents the adjacency matrices of the components of the studied object, formed from the elements of the adjacency matrix of the first hierarchy level. The third level is represented by contiguous components of the second hierarchy level in the form of weighted oriented graphs and links between them. The fourth level details the interrelated components of the studied object presented as orographs of the third hierarchy levels. The computational experiment is conducted to test the stability of the detailed structure of the fourth hierarchy level. Implicit interactions between factors are studied by simplicial analysis. Mass media effect on mass audience is determined to manifests itself in social activity of people through the \"plausible information\" factor.

This work proposes an efficient approach to solve the problem of training a regressive neural network efficiently. Regressive networks are characterized by delay lines possibly in both the input and the output feedback. Each delay line is connected to the network with synaptic weights and thus increases the number of parameters that must be optimized by the training algorithm. Training algorithms such as the Levenberg–Marquardt, normally used to train neural networks, are prone to local minima entrapment, and for this reason, a strategy to initialize the training procedure correctly is needed. To solve this problem, the continuous flock of starling optimization algorithm, a highly explorative optimizer based on swarm intelligence, is used. The proposed approach is tested and validated on an experimental benchmark featuring a second-order nonlinear dynamic system.

Choosing state variables in a state-space representation of a nonlinear dynamical system is a nonunique procedure for a given input–output relationship and therefore a potentially challenging task. It can be even more challenging when there are piecewise-defined restoring forces, as in bilinear hysteresis or Bouc–Wen models, which are just two of many such engineering mechanics models. Using various piecewise-smooth models, we make use of flow- and effort-controlled system concepts, common to bond graph theory, to initiate our state variable selection task, and we view numerical simulation as being within the framework of hybrid dynamical systems. In order to develop accurate and efficient time integration, we incorporate MATLAB’s state event location algorithm, which is a mathematically sound numerical solver that deserves to be better known in the engineering mechanics community. We show that different choices of state variables can affect state event implementation, which in turn can significantly affect accuracy and efficiency, as judged by tolerance proportionality and work–accuracy diagrams. Programming details of state event location are included to facilitate application to other models involving piecewise-defined restoring forces. In particular, one version of the Bouc–Wen–Baber–Noori (BWBN) class of models is implemented as a demonstration.

The transportation system has a certain capacity. The needs of the transportation system need to be predicted. The predictions made are the basis for providers to prepare existing transportation facilities. Through this paper, we propose a system to predict the capacity requirements of the transportation system using a dynamic systems approach. We use the Stella application as a dynamic system modeling tool. It was found that using the dynamic systems approach, the relationship between variables that form complexity can be modelled.

This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science.

This work aims to provide a broad overview of computational techniques belonging to the area of artificial intelligence tailored for identification of nonlinear dynamical systems. Both parametric and nonparametric identification problems are considered. The examined computational intelligence techniques for parametric identification deal with genetic algorithm, particle swarm optimization, and differential evolution. Special attention is paid to the parameters estimation for a rich class of nonlinear dynamical models, including the Bouc–Wen model, chaotic systems, the Jiles–Atherton model, the LuGre model, the Prandtl–Ishlinskii model, the Preisach model, and the Wiener–Hammerstein model. On the other hand, genetic programming and artificial neural networks are discussed for nonparametric identification applications. Once the identification problem is formulated, a detailed illustration of the considered computational intelligence techniques is provided, together with a comprehensive examination of relevant applications in the fields of structural mechanics and engineering. Possible directions for future research are also addressed.

Rotationally coherent Lagrangian vortices are formed by tubes of deforming fluid elements that complete equal bulk material rotation relative to the mean rotation of the deforming fluid volume. We show that the initial positions of such tubes coincide with tubular level surfaces of the Lagrangian-averaged vorticity deviation (LAVD), the trajectory integral of the normed difference of the vorticity from its spatial mean. The LAVD-based vortices are objective, i.e. remain unchanged under time-dependent rotations and translations of the coordinate frame. In the limit of vanishing Rossby numbers in geostrophic flows, cyclonic LAVD vortex centres are precisely the observed attractors for light particles. A similar result holds for heavy particles in anticyclonic LAVD vortices. We also establish a relationship between rotationally coherent Lagrangian vortices and their instantaneous Eulerian counterparts. The latter are formed by tubular surfaces of equal material rotation rate, objectively measured by the instantaneous vorticity deviation (IVD). We illustrate the use of the LAVD and the IVD to detect rotationally coherent Lagrangian and Eulerian vortices objectively in several two- and three-dimensional flows.

The Einstein static (ES) universe has played a major role in various emergent scenarios recently proposed in order to cure the problem of the initial singularity of the standard model of cosmology. In the model we address, we study the existence and stability of an ES universe in the context of f ( R ,  T ) modified theories of gravity. Considering specific forms of the f ( R ,  T ) function, we seek for the existence of solutions representing ES state. Using dynamical system techniques along with numerical analysis, we find two classes of solutions: the first one is always unstable of the saddle type, while the second is always stable so that its dynamical behavior corresponds to a center equilibrium point. The importance of the second class of solutions is due to the significant role they play in constructing non-singular emergent models in which the universe could have experienced past-eternally a series of infinite oscillations about such an initial static state after which it enters, through a suitable physical mechanism, to an inflationary era. Considering specific forms for the functionality of f ( R ,  T ), we show that this theory is capable of providing cosmological solutions which admit emergent universe (EU) scenarios. We also investigate homogeneous scalar perturbations for the mentioned models. The stability regions of the solutions are parametrized by a linear equation of state (EoS) parameter and other free parameters that will be introduced for the models. Our results suggest that modifications in f ( R ,  T ) gravity would lead to stable solutions which are unstable in f ( R ) gravity model.