An optimal trajectory planning problem for a single-link, flexible joint manipulator is studied. A global feedback-linearization is first applied to formulate the nonlinear inequality-constrained optimization problem in a suitable way. Then, an exact and explicit structural formula for the optimal solution of the problem is derived and the solution is shown to be unique. It turns out that the optimal trajectory planning and control can be done off-line, so that the proposed method is applicable to both theoretical analysis and real time tele-robotics control engineering.
No abstract is provided for this article.
An adaptive feedback controller is developed based on rigorous Lyapunov argument for an uncertain chaotic Duffing oscillator, in which the three key system parameters are essentially unknown. The proposed method can be easily extended to handle some other chaotic dynamical systems with mild modifications. Simulation results are included to verify the control theory and controller design method.
This paper presents an investigation of dynamics of the coupled nonidentical FHN models with synaptic connection, which can exhibit rich bifurcation behavior with variation of the coupling strength. With the time delay being introduced, the coupled neurons may display a transition from the original chaotic motions to periodic ones, which is accompanied by complex bifurcation scenario. At the same time, synchronization of the coupled neurons is studied in terms of their mean frequencies. We also find that the small time delay can induce new period windows with the coupling strength increasing. Moreover, it is found that synchronization of the coupled neurons can be achieved in some parameter ranges and related to their bifurcation transition. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behavior are clarified.
Our goal is to find a necessary and sufficient condition on the consensus over a random network, generated by i.i.d. stochastic matrices. We show that the consensus problem in three different convergence modes (almost surely, in probability, and in L1) are equivalent, thus have the same necessary and sufficient condition. We obtain the necessary and sufficient condition through the stability in a projected subspace.
Recently, a new hyperchaos generator, obtained by controlling a three-dimensional autonomous chaotic system — Chen's system — with a periodic driving signal, has been found. In this letter, we formulate and study the hyperchaotic behaviors in the corresponding fractional-order hyperchaotic Chen's system. Through numerical simulations, we found that hyperchaos exists in the fractional-order hyperchaotic Chen's system with order less than 4. The lowest order we found to have hyperchaos in this system is 3.4. Finally, we study the synchronization problem of two fractional-order hyperchaotic Chen's systems.
The network homology Hk-core decomposition proposed in this article is similar to the k-core decomposition based on node degrees of the network. The C. elegans neural network and the cat cortical network are used as examples to reveal the symmetry of the deep structures of such networks. First, based on the concept of neighborhood in mathematics, some new concepts are introduced, including such as node-neighbor subnetwork and Betti numbers of the neighbor subnetwork, among others. Then, the Betti numbers of the neighbor subnetwork of each node are computed, which are used to perform Hk-core decomposition of the network homology. The construction process is as follows: the initial network is referred to as the H0-core; the H1-core is obtained from the H0-core by deleting some nodes of certain properties; the H2-core is obtained from the H1-core by deleting some nodes or edges of certain properties; the H3-core is obtained from the H2-core by deleting some nodes of certain properties or by retaining the nodes of certain properties, and so on, which will be described in detail in the main text. Throughout the process, the index of node involved in deleting edge needs to be updated in every step. The Hk-core decomposition is easy to implement in parallel. It has a wide range of applications in many fields such as network science, data science, computational topology, and artificial intelligence. In this article, we also show how to use it to simplify homology calculation, e.g. for the C. elegans neural network, whereas the results of decomposition are the H1-core, the H2-core, and the H3-core. Thus, the simplexes consisting of four highest-order cavities in the H3-core subnetwork can also be directly obtained.
A new fuzzy logic controller is designed, which can enhance the efficiency of a control process. This controller employs the implication logic to determine the weights of the defuzzification of the control signals. To verify its performance, the new controller is applied to stabilizing a torsion pendulum. Compared with the traditional fuzzy control approach, simulation shows that the new design can improve the control performance with shorter settling time.
Based on two basic characteristics of continuous-time autonomous chaotic systems, namely being globally bounded while having a positive Lyapunov exponent, this paper develops a universal and practical anti-control approach to design a general continuous-time autonomous chaotic system via Lyapunov exponent placement. This self-unified approach is verified by mathematical analysis and validated by several typical systems designs with simulations. Compared to the common trial-and-error methods, this approach is semi-analytical with feasible guidelines for design and implementation. Finally, using the Shilnikov criteria, it is proved that the new approach yields a heteroclinic orbit in a three-dimensional autonomous system, therefore the resulting system is indeed chaotic in the sense of Shilnikov.
This paper establishes some generalized synchronization (GS) theorems for a coupled discrete array of difference systems (CDADS) and a coupled continuous array of differential systems (CCADS). These constructive theorems provide general representations of GS in CDADS and CCADS. Based on these theorems, one can design GS-driven CDADS and CCADS via appropriate (invertible) transformations. As applications, the results are applied to autonomous and nonautonomous coupled Chen cellular neural network (CNN) CDADS and CCADS, discrete bidirectional Lorenz CNN CDADS, nonautonomous bidirectional Chua CNN CCADS, and nonautonomously bidirectional Chen CNN CDADS and CCADS, respectively. Extensive numerical simulations show their complex dynamic behaviors. These theorems provide new means for understanding the GS phenomena of complex discrete and continuously differentiable networks.
This Letter improves the Chen–Lai chaotification algorithm for discrete-time systems from multiple-input to single-input state feedback, while preserving its mathematical rigor.
This paper initiates a saturated function series approach for chaos generation. The systematic saturated function series methodology developed here can create multiscroll chaotic attractors from a three-dimensional (3D) linear autonomous system with a simple saturated function series controller, including one-directional n-scroll, two-directional n/spl times/m-grid scroll, and 3-D n/spl times/m/spl times/l-grid scroll chaotic attractors. The dynamical behaviors and chaos generation mechanism of multiscroll systems are further investigated by analyzing the system trajectories. In particular, a two-dimensional (2D) Poincare/spl acute/ return map is rigorously derived for verifying the chaotic behaviors of the double-scroll chaotic attractor, which is a basic generator of various multiscroll chaotic attractors investigated in the paper.
In this paper, assuming that each node is incident with two or more fault-free links, we show that an n-dimensional alternating group graph can tolerate up to 4n −13 link faults, where n ⩾4, while retaining a fault-free Hamiltonian cycle. The proof is computer-assisted. The result is optimal with respect to the number of link faults tolerated. Previously, without the assumption, at most 2n −6 link faults can be tolerated for the same problem and the same graph.
No abstract is provided for this article.
This is an essay to present some personal views onsystemsandnetworkswith respect to their similarities and differences as well as their relationships.
We develop a three-phase design scheme for fuzzy modeling using input-output training data. The first step is to establish an approximate rule base using a clustering method, then the selective rule activation technique is applied to resize the rule base, and finally the parameters are fine-tuned by the backpropagation algorithm. Simulation results show that this scheme generates a good fuzzy model that can successfully predict the system output and the rules selected by the selective rule activation technique are appropriate for generalizing different sets of data.
When chaotic systems are realized with finite precisions in digital computers, their dynamical properties are often found to be entirely different from the original versions in the continuous setting. In the literature, there does not seem to be much work on quantitative analysis of such degradation of digitized chaos and how to reduce its negative influence on chaos-based digital systems. Focusing on 1D piecewise linear chaotic maps (PWLCM), this paper reports some findings on a new series of dynamical indicators, which can quantitatively reflect the degradation effects on a digital PWLCM realized with a fixed-point finite precision. On top of that, the paper introduces a new method for studying digital chaos from an algorithmic point of view. In addition, the theoretical results obtained in this paper should be very helpful for the consideration of reducing negative influence of dynamical degradation in real design of various digital chaotic systems. As typical examples, the proposed dynamical indicators are applied to the performance comparison of different remedies for improving dynamical degradation, cryptanalysis of digital chaotic ciphers based on 1D PWLCM, and design of chaotic pseudo-random number generators with desired characteristics.
