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Summary In this article, the issue of adaptive finite‐time dynamic surface control (DSC) is discussed for a class of parameterized nonlinear systems with full state constraints. Using the property ...

Summary In this paper, the issue of adaptive neural control is discussed for a class of stochastic nonstrict‐feedback constrained nonlinear systems with input and state unmodeled dynamics. A dynami...

We obtain a new bound on the average value of the error term in the asymptotic formula for the number of k‐free numbers in arithmetic progressions. In particular, we improve the results of J. Gibson (2014) and C. Hooley (1975).

Summary In this paper, we are concerned with the problem of adaptive output‐feedback tracking control for nonlinear systems with input quantization, unmodeled dynamics, and output constraints. A no...

Summary This paper focuses on the problem of adaptive control for a class of pure‐feedback nonlinear systems with full‐state time‐varying constraints and unmodeled dynamics. By introducing a one‐to...

Summary Stochastic adaptive dynamic surface control is presented for a class of uncertain multiple‐input–multiple‐output (MIMO) nonlinear systems with unmodeled dynamics and full state constraints ...

Summary This paper proposes an adaptive neural‐network control design for a class of output‐feedback nonlinear systems with input delay and unmodeled dynamics under the condition of an output const...

Summary In this paper, the problem of adaptive neural control is discussed for a class of strict-feedback time-varying delays nonlinear systems with full-state constraints and unmodeled dynamics, as well as distributed time-varying delays. The considered nonlinear system with full-state constraints is transformed into a nonlinear system without state constraints by introducing a one-to-one asymmetric nonlinear mapping. Based on modified backstepping design and using radial basis function neural networks to approximate the unknown smooth nonlinear function and using a dynamic signal to handle dynamic uncertainties, a novel adaptive backstepping control is developed for the transformed system without state constraints. The uncertain terms produced by state time delays and distributed time delays are compensated for by constructing appropriate Lyapunov-Krasovskii functionals. All signals in the closed-loop system are proved to be semiglobally uniformly ultimately bounded. A numerical example is provided to illustrate the effectiveness of the proposed design scheme.

In this paper, an adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmeasured states and four kinds of uncertainties including uncertain nonlinear function, dynamic disturbance, input unmodeled dynamics, and stochastic inverse dynamics. The unmeasured states are estimated by K-filters, and stochastic inverse dynamics is dealt with by constructing a changing supply function. The considered input unmodeled dynamic subsystem possesses nonlinear feature, and a dynamic normalization signal is introduced to counteract the unstable effect produced by the input unmodeled dynamics. Combining dynamic surface control technique with stochastic input-to-state stability, small-gain condition, and Chebyshev's inequality, the designed robust adaptive controller can guarantee that all the signals in the closed-loop system are bounded in probability, and the error signals are semi-globally uniformly ultimately bounded in mean square or the sense of four-moment. Simulation results are provided to verify the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.

This paper explores the probability problems on terminal sliding mode control of second-order nonlinear continuous Markovian jump systems. An equivalent control based terminal sliding mode control scheme is proposed that can guarantee the systems' finite time mean-square stability. By introducing a multi-step transition conditional probability, the novel reaching and sliding probabilities are derived for the situations where the control force is not strong enough. This indicates that the reaching and sliding probabilities are both monotonically bounded non-decreasing non-negative piecewise right-continuous functions of the control parameter. A numerical example is given to show the feasibility of the theoretical results.

Summary In this paper, adaptive output feedback tracking control is developed for a class of stochastic nonlinear systems with dynamic uncertainties and unmeasured states. Neural networks are used to approximate the unknown nonlinear functions. K-filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By combining dynamic surface control technique with backstepping, the condition in which the approximation error is assumed to be bounded is avoided. Using It o formula and Chebyshev's inequality, it is shown that all signals in the closed-loop system are bounded in probability, and the error signals are semi-globally uniformly ultimately bounded in mean square or the sense of four-moment. Simulation results are provided to illustrate the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.

To reveal the mysterious and still controversial mechanism of high ionization efficiency during helicon discharges, this work focuses particularly on the role of second-order derivative in radial density profile, both analytical and numerically. It is found that: (i) the radially localized potential well that plays a critical role in resonance power absorption from antenna to plasma is localized where the second-order derivative vanishes, (ii) the power absorption increases for positive second-order derivative, decreases for negative second-order derivative, and maximizes where second-order derivative becomes zero, (iii) the power absorption decreases near plasma core and increases near plasma edge when the radial location of vanishing second-order derivative moves outwards, which is also a process of Trivelpiece-Gould mode overwhelming helicon mode. These findings can be very interesting for helicon plasma applications that require certain power distribution or heat flux configuration, e. g. material processing, which can be controlled by adjusting the profile and zero-crossing location of second-order radial density gradient.

The Duobuza gold-rich porphyry copper district is located in the Bangongco metallogenetic belt in the Bangongco-Nujiang suture zone south of the Qiangtang terrane. Two main gold-rich porphyry copper deposits (Duobuza and Bolong) and an occurrence (135 Line) were discovered in the district. The porphyry-type mineralization is associated with three Early Cretaceous ore-bearing granodiorite porphyries at Duobuza, 135 Line and Bolong, and is hosted by volcanic and sedimentary rocks of the Middle Jurassic Yanshiping Formation and intermediate-acidic volcanic rocks of the Early Cretaceous Meiriqie Group. Simultaneous emplacement and isometric distribution of three ore-forming porphyries is explained as multi-centered mineralization generated from the same magma chamber. Intense hydrothermal alteration occurs in the porphyries and at the contact zone with wall rocks. Four main hypogene alteration zones are distinguished at Duobuza. Early-stage alteration is dominated by potassic alteration with extensive secondary biotite, K-feldspar and magnetite. The alteration zone includes dense magnetite and quartz-magnetite veinlets, in which Cu-Fe-bearing sulfides are present. Propylitic alteration occurs in the host basic volcanic rocks. Extensive chloritization-silicification with quartz-chalcopyrite or quartz-molybdenite veinlets superimposes on the potassic alteration. Final-stage argillic alteration overlaps on all the earlier alteration. This alteration stage is characterized by destruction of feldspar to form illite, dickite and kaolinite, with accompanying veinlets of quartz + chalcopyrite + pyrite and quartz + pyrite assemblages. Cu coexists with Au, which indicates their simultaneous precipitation. Mass balance calculations show that ore-forming elements are strongly enriched during the above-mentioned three alteration stages.