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Summary: This article addresses the problem of global adaptive finite‐time control for a class of p‐normal nonlinear systems via an event‐triggered strategy. A state feedback controller is first designed for the nominal system by adding a power integrator method. Then, by the skillful design of adaptive dynamic gain mechanism, a novel event‐triggered controller is constructed for uncertain nonlinear system without homogeneous growth condition. It is proved that the global finite‐time stabilization of p‐normal nonlinear systems is guaranteed and the Zeno phenomenon is excluded. Finally, two examples are presented to indicate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Summary: In this article, an adaptive neural fault‐tolerant decentralized tracking control problem is investigated for switched stochastic large‐scale uncertain nonlinear systems, in which time‐varying delay and unknown control coefficient are under consideration. By incorporating the quadratic Lyapunov function and Lyapunov Krasovskii function into the backstepping approach, an adaptive neural fault‐tolerant decentralized control strategy is proposed, which ensures that signals in the closed‐loop system are stable in probability and the tracking error converges to a small neighborhood of the origin under arbitrary switching. At last, to verify the presented strategy is feasible, a simulation example is given. [ABSTRACT FROM AUTHOR]

This article investigates the consensus tracking problem with predefined transient and steady performance requirements for a class of nonstrict‐feedback nonlinear multi‐agent systems (MASs) with input quantization under a directed graph. Based on prescribed performance error transformation methods and command filtered backstepping techniques, a novel observer‐based adaptive control protocol is proposed, where neural observers are designed to estimate unmeasurable states and radial basis function neural networks are constructed to compensate command filter errors. The proposed protocol can be applied to a more general class of nonlinear MASs with nonstrict‐feedback nonlinear dynamics and unmeasurable states information. It is strictly proved that all signals in the whole MAS are semi‐globally uniformly ultimately bounded and both the transient and steady performances of the consensus tracking errors satisfy prescribed performance requirements. Finally, three numerical examples are presented to validate the effectiveness of the proposed protocol. [ABSTRACT FROM AUTHOR]

The contribution of this investigation lies in solving a sampled‐data output feedback stabilization problem for a class of upper‐triangular stochastic nonlinear systems in p$$ p $$‐normal structure with unavailable states and uncertain time‐varying input delay. A reduced‐order observer with the available sampled output detection is developed for the focused system to estimate its unavailable states, and under such observer, a sampled‐data output feedback stabilizer is constructed by combining the backstepping and adding a power integral techniques. Through selecting the appropriate Lyapunov–Krasovskii functionals, we can demonstrate that the adverse influences caused by the uncertain time‐varying delays in the resulting closed‐loop system can be restricted effectively by the constructed stabilizer, and further, by following the stochastic differential theories, the global stability of the considered resulting closed‐loop system can be analyzed under the suitable design parameters and allowable sampling period. Finally, two examples are given to verify the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

SUMMARY A generalized refined Arnoldi method based on the weighted inner product is presented for computing PageRank. The properties of the generalized refined Arnoldi method were studied. To speed up the convergence performance for computing PageRank, we propose to change the weights adaptively where the weights are calculated based on the current residual corresponding to the approximate PageRank vector. Numerical results show that the proposed Arnoldi method converges faster than existing methods, in particular when the damping factor is large. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

To achieve predefined‐time trajectory tracking control of a flexible‐joint space robot(FJSR) with actuator constraints, a nonsingular predefined‐time dynamic surface control scheme is developed. The input saturation caused by actuator constraints is addressed via the designed predefined‐time anti‐saturation compensator. On this basis, two different control laws are designed for such high‐order nonlinear systems by utilizing the backstepping technique, and a novel nonlinear filter is constructed to filter the virtual control signals, thus avoiding the "differential expansion" phenomenon. Moreover, a singularity‐free auxiliary function is designed to solve the singularity issue generated by the derivative of fractional power terms in the predefined‐time control algorithm framework. The closed‐loop system is proven to be semi‐globally predefined‐timely uniformly ultimately bounded (SGPTUUB) via constructing the suitable Lyapunov function. The difference and effectiveness of the two designed control laws are illustrated by the conducted simulations. Both of them allow the FJSR system to track the desired trajectory in a reasonably predefined time. [ABSTRACT FROM AUTHOR]