2,312 publications from this institution
We investigate second-order consensus of multiple nonlinear dynamical mobile agents with a virtual leader in a dynamic proximity network. We assume that only a small fraction of agents in the group have access to the information about the position and velocity of the virtual leader through, for example, certain pre-designed communication mechanism such as wireless broadcasting or sensing. To avoid fragmentation, we propose a connectivity-preserving second-order consensus algorithm. Under the assumption that the initial network is connected, we introduce local adaptation strategies for both the weights on the velocity navigational feedback and the velocity coupling strengths that enable all agents to synchronize with the virtual leader even when only one agent is informed, without requiring any knowledge of the agent dynamics. We finally provide some convincing simulation results to illustrate the theoretical results.
Rule 110 is a complex cellular automaton (CA) in Wolfram's system of identification, capable of supporting universal computation. It has been suggested that a universal CA should be on the ‘edge of chaos’, which means that the dynamical behaviour of such a system is neither simple nor chaotic. There is no doubt that the dynamical property of Rule 110 is extremely complex and still not well understood. This paper proves the existence of subsystems on which this rule is chaotic in the sense of Devaney.
For the generalized Serre–Green–Naghdi equations with surface tension, using the methodologies of dynamical systems and singular traveling wave theory developed by Li and Chen [2007] for their traveling wave systems, in different parameter conditions of the parameter space, all possible bounded solutions (solitary wave solutions, kink wave solutions, peakons, pseudo-peakons and periodic peakons as well as compactons) are obtained. More than 26 explicit exact parametric representations are given. It is interesting to find that this fully nonlinear water waves equation coexists with uncountably infinitely many smooth solitary wave solutions or infinitely many pseudo-peakon solutions with periodic solutions or compacton solutions. Differing from the well-known peakon solution of the Camassa–Holm equation, the generalized Serre–Green–Naghdi equations have four new forms of peakon solutions.
No abstract is provided for this article.
No abstract is provided for this article.
Restart strategy helps the covariance matrix adaptation evolution strategy (CMA-ES) to increase the probability of finding the global optimum in optimization, while a single run CMA-ES is easy to be trapped in local optima. In this paper, the continuous non-revisiting genetic algorithm (cNrGA) is used to help CMA-ES to achieve multiple restarts from different sub-regions of the search space. The CMA-ES with on-line search history-assisted restart strategy (HR-CMA-ES) is proposed. The entire on-line search history of cNrGA is stored in a binary space partitioning (BSP) tree, which is effective for performing local search. The frequently sampled sub-region is reflected by a deep position in the BSP tree. When leaf nodes are located deeper than a threshold, the corresponding sub-region is considered a region of interest (ROI). In HR-CMA-ES, cNrGA is responsible for global exploration and suggesting ROI for CMA-ES to perform an exploitation within or around the ROI. CMA-ES restarts independently in each suggested ROI. The non-revisiting mechanism of cNrGA avoids to suggest the same ROI for a second time. Experimental results on the CEC 2013 and 2017 benchmark suites show that HR-CMA-ES performs better than both CMA-ES and cNrGA. A positive synergy is observed by the memetic cooperation of the two algorithms.
Implementing linearly nonseparable Boolean functions (non-LSBF) has been an important and yet challenging task due to the extremely high complexity of this kind of functions and the exponentially increasing percentage of the number of non-LSBF in the entire set of Boolean functions as the number of input variables increases. In this paper, an algorithm named DNA-like learning and decomposing algorithm (DNA-like LDA) is proposed, which is capable of effectively implementing non-LSBF. The novel algorithm first trains the DNA-like offset sequence and decomposes non-LSBF into logic XOR operations of a sequence of LSBF, and then determines the weight-threshold values of the multilayer perceptron (MLP) that perform both the decompositions of LSBF and the function mapping the hidden neurons to the output neuron. The algorithm is validated by two typical examples about the problem of approximating the circular region and the well-known n-bit parity Boolean function (PBF).
Recently, there has been a growing interest in network controllability for determining the number and placement of controllers. In the framework of linear dynamics, this paper regarding the network controllability studies both the formulation of the control input matrix and the influence of the linear nodal dynamics, with precise guidelines derived on how to design the input matrix. This design strategy takes the column vectors of the input matrix as the basis to maximize the controllable subspace. In the one-dimensional case, it is found that nodal dynamics with high degrees of heterogeneity dominate the network topology, but identical nodal dynamics have no effect on the network controllability. In the higher dimensional case, it reveals why controllable network topology and controllable nodal dynamics together are still insufficient to ensure the controllability of the whole network, with a feasible solution to the problem presented based on a suitably designed input matrix. All characteristics of the network topology and nodal dynamics are integrated into the input matrix formulation, which plays an essential role in determining the network controllability.
No abstract is provided for this article.
Multi-agent systems are ubiquitous in the world. Recently, multi-agent systems have received increasing attention from mathematics, physics, engineering sciences, and social science communities. This paper firstly introduces several fundamental concepts and then reviews several representative models of multi-agent systems, including the Boids model, Vicsek model, Couzin-Levin model and its invariants, and various complex dynamical networks. Based on these models, it further investigates the dynamical behaviors of multi-agent systems, such as consensus, convergence, adaptation, and consensus decision-making. Moreover, it briefly reviews the main progress in the control of multi-agent systems. Finally, it looks ahead into some important research topics on multi-agent systems, with regard to modelling, analysis, and control.
No abstract is provided for this article.
The aim of this paper is to study synchronization of a dynamical complex network consisting of nodes being generalized Lorenz chaotic systems and connections are created with transmitted synchronizing signals. Focus is on the robustness of the network synchronization with respect to its connectional structure. This robustness is analyzed theoretically for the case of two nodes with two-sided (bidirectional connections), and numerically for various cases with many nodes. It is shown that unless a certain minimal coherent connectional structure is present in network, the synchronization is always preserved. While for a minimal connectional configuration where the synchronization is global, the resulting synchronization is only semi-global when some redundant connections are added.
Recent progress in symbolic dynamics of cellular automata (CA) shows that many CA exhibit rich and complicated Bernoulli-shift properties, such as positive topological entropy, topological transitivity and even mixing. Noticeably, some CA are only transitive, but not mixing on their subsystems. Yet, for one-dimensional CA, this paper proves that not only the shift transitivity guarantees the CA transitivity but also the CA with transitive non-trivial Bernoulli subshift of finite type have dense periodic points. It is concluded that, for one-dimensional CA, the transitivity implies chaos in the sense of Devaney on the non-trivial Bernoulli subshift of finite types.
