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In this paper, a new model of evolving networks is proposed based on the dynamical behaviors of nodes in the network. The probability that an existing node in the current network receives a new link from the newly added node is proportional to the defined "activity" of that particular node, which is equivalent to the energy signal of the system from a control theory point of view. This network is found to have the scale-free feature with the degree distribution in a power-law form. This model provides another explanation for the emergence of scale-free networks in many real-world examples.

In this paper, we study the complete synchronization of a class of time-varying delayed coupled chaotic systems using feedback control. In terms of Linear Matrix Inequalities, a sufficient condition is obtained through using a Lyapunov-Krasovskii functional and differential equation inequalities. The conditions can be easily verified and implemented. We present two simulation examples to illustrate the effectiveness of the proposed method.

Existing approaches for tunnel face stability analysis usually apply for circular cross-sections and solutions for tunnel face stability evaluation with city gate cross-sections by kinematic approach of limit analysis have not been reported. The present study developed a kinematic approach on tunnel face stability analysis for city gate sections by using spatial discretization technique. The proposed discretization-based kinematic approach applies to shallow tunnel stability analysis with cover depth ratio less than 5 by comparison with finite element limit analysis (FELA). The required support pressure increases with the increase of tunnel width, straight wall height and the central angle of the circular arch.

In the realm of nonlinear control, feedback linearization via differential geometric techniques has been a concept of paramount importance. However, the applicability of this approach is quite limited, in the sense that a detailed knowledge of the system nonlinearities is required. In practice, most physical chaotic systems have inherent unknown nonlinearities, making real-time control of such chaotic systems still a very challenging area of research. In this paper, we propose using the recurrent high-order neural network for both identifying and controlling unknown chaotic systems, in which the feedback linearization technique is used in an adaptive manner. The global uniform boundedness of parameter estimation errors and the asymptotic stability of tracking errors are proved by the Lyapunov stability theory and the LaSalle–Yoshizawa theorem. In a systematic way, this method enables stabilization of chaotic motion to either a steady state or a desired trajectory. The effectiveness of the proposed adaptive control method is illustrated with computer simulations of a complex chaotic system.

This paper introduces a frequency domain approach together with some techniques and methodologies for the computation and analysis of bifurcations and limit cycles arising in nonlinear dynamical systems. The frequency domain approach discussed in this paper originates from the classical feedback control systems theory, which has been proven to be successful and efficient for the computation and analysis of regular as well as singular bifurcations and stable as well as unstable limit cycles. While describing these techniques and methods, two representative yet distinct applications of the approach are studied in detail: The graphical analysis of multiple parametric bifurcation curves and the numerical computation of multiple limit cycles. Compared to the classical time domain methods, both the advantages and the limitations of the frequency domain approach are analyzed and discussed. It is believed that this frequency domain approach to the study of nonlinear dynamics has great potential and promising future in both theory and applications.

By applying the undetermined coefficient method, this paper finds homoclinic and heteroclinic orbits in the Chen system. It analytically demonstrates that the Chen system has one heteroclinic orbit of Ši'lnikov type that connects two nontrivial singular points. The Ši'lnikov criterion guarantees that the Chen system has Smale horseshoes and the horseshoe chaos. In addition, there also exists one homoclinic orbit joined to the origin. The uniform convergence of the series expansions of these two types of orbits are proved in this paper. It is shown that the heteroclinic and homoclinic orbits together determine the geometric structure of Chen's attractor.

This paper addresses the distributed aggregative optimization challenge in uncertain multiple Euler- Lagrange (EL) systems, where each EL agent's local objective function depends on its own position and the aggregation of all EL agents' positions. The goal is to control all EL agents to reach their optimal positions as defined by the aggregative optimization problem. Two distributed aggregative optimization algorithms are proposed for uncertain EL systems, which are based on distinct optimization-control strategies, namely the open-loop optimization-control strategy and the closed-loop optimization-control strategy. To address the model uncertainty in EL systems, an auxiliary second-order system is introduced, integrating with adaptive compensation and tracking techniques to mitigate the uncertainty. Given the unique structure of the aggregative optimization problem, two distributed estimation protocols are developed for handling the aggregation terms in the optimization problem. Specifically, in the open-loop optimization-control strategy, the optimization gradient is derived from the position information of the auxiliary system; whereas, in the closed-loop optimization-control strategy, the optimization gradient relies on the real-time position of the EL system. The convergence of both algorithms is rigorously proved. Unlike existing studies that mainly concentrate on distributed optimization algorithms based on either open-loop or closed-loop strategies, this paper is dedicated to conducting a comprehensive comparative analysis of open-loop and closed-loop optimization-control strategies, with a special emphasis on the robustness of the closed-loop strategy in counteracting external disturbances and variations. Finally, the proposed distributed aggregative optimization algorithms are applied to the optimal localization problem of networked marine vehicles with parameter uncertainties. Comprehensive simulation comparisons are conducted to verify the theoretical results.

In this paper, a new and systematic method for designing robust digital controllers for uncertain nonlinear systems with structured uncertainties is presented. In the proposed method, a controller is designed in terms of the optimal linear model representation of the nominal system around each operating point of the trajectory, while the uncertainties are decomposed such that the uncertain nonlinear system can be rewritten as a set of local linear models with disturbed inputs. Applying conventional robust control techniques, continuous-time robust controllers are first designed to eliminate the effects of the uncertainties on the underlying system. Then, a robust digital controller is obtained as the result of a digital redesign of the designed continuous-time robust controller using the state-matching technique. The effectiveness of the proposed controller design method is illustrated through some numerical examples on complex nonlinear systems––chaotic systems.

In this paper, topology monitoring of growing networks is studied. When some new nodes are added into a network, the topology of the network is changed, which needs to be monitored in many applications. Some auxiliary systems (network monitors) are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied to designing such network monitors. Based on the Lyapunov function method via constructing a potential or energy function decreasing along any solution of the system, and the LaSalle's invariance principle, which is a generalization of the Lyapunov function method, some sufficient conditions for achieving topology monitoring are obtained. Illustrative examples are provided to demonstrate the effectiveness of the new method.

This paper investigates the problem of coordinated tracking of a linear multi-agent system subject to actuator magnitude saturation and dead zone characteristic with input additive uncertainties and disturbances. Distributed consensus and swarm tracking protocols are developed from a low-and-high gain feedback approach. Under the assumption that each agent is asymptotically null controllable with bounded controls, it is shown that robust semi-global consensus tracking and swarm tracking of the multi-agent system can always be reached provided that the networks are connected. Numerical examples are provided to illustrate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.

Drilling optimization problems in oilfields are usually formulated and solved by using deterministic mathematical models, in which uncertain (indeterminate) factors or random issues are not taken into consideration. However, it has been widely experienced that random factors (such as those from soil layers, drill bits, and surface equipment) greatly affect the drilling performance. This paper introduces a new stochastic model for describing such random effects. This model, when used to optimization design, is more practical and provides a better characterization for real oilfield situations as compared with other deterministic models, and has been demonstrated to be more efficient in solving real design problems of drilling optimizations.

Article Free Access Share on A heuristic approach to determine the gains of a fuzzy PID controller Authors: Dave Misir University of Houston, 4800 Calhoun, Houston, TX University of Houston, 4800 Calhoun, Houston, TXView Profile , Heidar A. Malki University of Houston, 4800 Calhoun, Houston, TX University of Houston, 4800 Calhoun, Houston, TXView Profile , Guanrong Chen University of Houston, 4800 Calhoun, Houston, TX University of Houston, 4800 Calhoun, Houston, TXView Profile Authors Info & Claims SAC '96: Proceedings of the 1996 ACM symposium on Applied ComputingFebruary 1996 Pages 609–613https://doi.org/10.1145/331119.331468Online:18 February 1996Publication History 5citation793DownloadsMetricsTotal Citations5Total Downloads793Last 12 Months3Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF