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This paper discusses the consensus tracking problem for a class of nonlinear multi-agent systems (MASs) with output constraints, unmodeled dynamics, nonsymmetric input dead-zones and actuator failures under directed graphs, and proposes an adaptive cooperative neural dynamic surface control (DSC) strategy. Using the properties of invertible nonlinear mapping and Gaussian function, output constraints and non-strict feedback terms are separately dealt with. A measurable dynamic signal produced by an auxiliary first-order system is used to eliminate the influence of unmodeled dynamics on the system. Two input models of input dead-zone and actuator failure are linearized, each follower control signal is constructed via DSC. All the signals of the closed-loop system are proved to be cooperative semi-globally uniformly ultimately bounded, and all the followers can accomplish a desired consensus results. Finally, the simulation results are provided to illustrate the availability of the presented adaptive control approach.

In this paper, adaptive optimal control is proposed for a class of strict-feedback nonlinear systems with unmodeled dynamics and output constraints. The controller design procedure contains two parts. In the first part, to satisfy output constraints, nonlinear mapping is used to transform constrained system into a novel one without output constraints. A dynamical signal is utilized to deal with unmodeled dynamics. A feedforward controller is designed using the dynamics surface control technique. In the second part, an auxiliary dynamical system is introduced to optimize cost function, and neural-network based adaptive dynamic programming(ADP) is employed to approximate the optimal cost function and the optimal control law. It is proved that the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB) and the output constraints are not triggered by theoretical analysis. Two simulation examples are provided to illustrate the effectiveness of the proposed scheme.

In this paper, an adaptive quantized fuzzy dynamic surface control (DSC) stratergy is investigated for a class of nonlinear systems with input unmodeled dynamics and output constraints. A challenge lies in that the input-quantized actuator is considered to possess both unknown control gain and nonlinear input unmodeled dynamics. By quantized controller design and DSC technique, combining normalized signal, integral Lyapunov functions, Nussbaum functions and the adaptive laws, the obstacle caused by quantization and multiple uncertainties is effectively overcome. The designed novel quantizer has the advantages of both the existing uniform quantizer and hysteresis quantizer, which can avoid the chattering and reduce the quantization error no matter the control volume is large or small. By defining a group of transformation based on a logarithmic one to one mapping, time-varying output constraints is satisfied. It is shown that all the signals are bounded, and the output signal is constrained within the preset range.

In this work, the problem of adaptive neural dynamic surface control (DSC) with the minimum adjustable parameters is discussed for a class of multi-input multi-output (MIMO) pure-feedback nonlinear systems with unmodeled dynamics and output constraints. An auxiliary signal designed by the characteristics of unmodeled dynamics is used to handle the dynamical uncertainties. The unknown continuous black-box functions produced in the controller design process are approximated by using radial basis function neural networks (RBFNNs). Based on an one-to-one nonlinear mapping(NM), the MIMO nonaffine nonlinear system with output constraints is transformed into a novel block-structure MIMO nonaffine nonlinear system without output constraints. Based on the transformed system and modified DSC, robust adaptive neural tracking control scheme is developed. Through theoretical analysis, all the signals in the closed-loop system are shown to be semi-globally uniformly ultimately bounded (SGUUB). A numerical example is provided to demonstrate the effectiveness of the proposed design strategy.

This paper solves the problem of adaptive neural dynamic surface control (DSC) for a class of full state constrained stochastic nonlinear systems with unmodeled dynamics. The concept of the state constraints in probability is first proposed and applied to the stability analysis of the system. The full state constrained stochastic nonlinear system is transformed to the system without state constraints through a nonlinear mapping. The unmodeled dynamics is dealt with by introducing a dynamic signal and the adaptive neural dynamic surface control method is explored for the transformed system. It is proved that all signals of the closed-loop system are bounded in probability and the error signals are semi-globally uniformly ultimately bounded(SGUUB) in mean square or the sense of four-moment. At the same time, the full state constraints are not violated in probability. The validity of the proposed control scheme is demonstrated through the simulation examples.

The broad-spectrum bacteriostatic properties of hops (Humulus lupulus L.) components have been widely recognized. In this study, chitosan was selected as raw material, and silane was introduced by covalent and non-covalent bonding to yield a chitosan-based hydrogel film loaded with hops β-acids. The structure of the obtained film was explored by Fourier infrared transform spectroscopy (FTIR), scanning electron microscopy (SEM) and X-ray diffraction (XRD). Mechanical performance assay revealed that the tensile strength (TS) of the film increased to 4.14 MPa after modification with silicon. The film had an inhibitory effect on Escherichia coli and Staphylococcus aureus after loading with hops β-acids, with minimum inhibitory concentration (MIC) and minimum bactericidal concentration (MBC) of 100 μg/mL and 400 μg/mL, respectively, against E. coli, and MIC and MBC of 50 μg/mL and 200 μg/mL, respectively, against S. aureus. Release experiments with β-acids indicated that nano-silica promoted cumulative and delayed release of β-acids due to the formation of covalent bonds with silicon. In addition, the obtained film displayed a remarkable ability to block ultraviolet rays. Results of antibacterial activity assay and SEM observations revealed that β-acids led to disruption of membrane integrity and cell death. Molecular docking study of β-acids was performed against β-lactamases, FabI, FabH from both E. coli and S. aureus. This study lays the foundation for further exploration of the antibacterial mechanism of hops β-acids and points towards the possibility of using β-acids-loaded hydrogel films as an antiseptic material in the food industry.

This paper is concerned with adaptive output feedback tracking control for a class of uncertain nonlinear systems with quantized input and unmodeled dynamics as well as output constraints. Quantized reduced-order K-filters are designed to observe parts of unmeasured states. The considered system is of two types of uncertainties. To deal with these uncertainties, we adopts global exponential stability technique of the state unmodeled dynamics with a Lyapunov description and the fuzzy approximation approach to those uncertain functions. To avoid the chattering of the quantized control signal, a hysteretic quantizer is introduced, and by designing a novel control law based on dynamic surface control (DSC) method, many assumptions of the quantized system in early literatures are removed. Combining quantized DSC with an one to one mapping from output error to the first dynamic surface, the robust quantized adaptive controller is constructed to guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error is restricted within the prescribed output constraints. A numerical simulation example shows the effectiveness of the proposed approach.

We obtain several estimates for bilinear forms with exponential sums with binomials m x k + n x l . In particular we show the existence of nontrivial cancellations between such sums when the coefficients m and n vary over rather sparse sets of general nature.

In this paper, adaptive neural dynamic surface control(DSC) is developed for a class of constrained strict-feedback nonlinear systems with input unmodeled dynamics. By introducing a one to one nonlinear mapping, the output constrained strict-feedback system in the presence of unmodeled dynamics is transformed into a novel unconstrained strict-feedback system. Neural networks (NNs) are employed to approximate unknown nonlinear continuous functions. A normalization signal and an updating parameter are used to handle the uncertain term which input unmodeled dynamics brings about in the design final step. By adding the normalization signal to the whole Lyapunov function and using the defined compact set in stability analysis, all the signals in the closed-loop system are proved to be semi-globally uniformly ultimately bounded (SGUUB), and output constraint is not violated. Two numerical examples are used to illustrate the effectiveness of the proposed adaptive DSC method in handling input unmodeled dynamics.

We give nontrivial upper bounds in various ranges for Kloosterman sums of the form ∑ ′ n ∈ S ( x , y ) exp ⁡ ( 2 π i a n ‾ / m ) , where m , a are integers with m ≥ 2 , ( a , m ) = 1 , and S ( x , y ) is the set of y-smooth numbers up to x. We also obtain a better bound on average over m as ∑ m ∼ M max ( a , m ) = 1 ⁡ | ∑ ′ n ∈ S ( x , y ) exp ⁡ ( 2 π i a n ‾ / m ) | , where m ∼ M means M m ≤ 2 M .

This paper addresses a decentralized fuzzy adaptive control scheme for stochastic large-scale systems in the presence of stochastic input unmodeled dynamics, which is a novel problem on the research of unmodeled dynamics. The stochastic nonlinear input unmodeled dynamics is restricted to be stochastic input-to-state stable. We introduce changing supply function to deal with the stochastic input unmodeled dynamics and construct the corresponding small gain condition. Due to partial states unavailable for measurement and control gains unknown, we design reduced-order K-filters to estimate the unmeasurable states only. First type fuzzy systems are adopted to approximate the whole of the black-box functions and the unknown continuous system functions, which can degrade the complexity of calculation and simply the K-filters’ structure. Utilizing the changing supply function, dynamic surface control (DSC) method and Chebyshev’s inequality, a strict stability analysis in probability is made. The analysis shows that the control laws can guarantee all the signals to be semi-globally uniformly ultimately bounded (SGUUB) in mean square or the sense of four-moment. Simulation results illustrate the effectiveness of the approach.

This paper is concerned with the adaptive control problem of a class of output feedback nonlinear systems with unmodeled dynamics and output constraint. Two dynamic surface control design approaches based on integral barrier Lyapunov function are proposed to design controller ensuring both desired tracking performance and constraint satisfaction. The radial basis function neural networks are utilized to approximate unknown nonlinear continuous functions. K-filters and dynamic signal are introduced to estimate the unmeasured states and deal with the dynamic uncertainties, respectively. By theoretical analysis, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded, while the output constraint is never violated. Simulation results demonstrate the effectiveness of the proposed approaches.

In this paper, the problem of adaptive neural network (NN) dynamic surface control (DSC) is discussed for a class of strict-feedback nonlinear systems with full state constraints and unmodeled dynamics. By introducing a one to one nonlinear mapping, the strict-feedback system with full state constraints is transformed into a novel pure-feedback system without state constraints. Radial basis function (RBF) neural networks (NNs) are used to approximate unknown nonlinear continuous functions. Unmodeled dynamics is dealt with by introducing a dynamical signal. Using modified DSC and introducing integral-type Lyapunov function, adaptive NN DSC is developed. Using Young’s inequality, only one parameter is adjusted at each recursive step in the design. It is shown that all the signals in the closed-loop system are semi-global uniform ultimate boundedness (SGUUB), and the full state constraints are not violated. Simulation results are provided to verify the effectiveness of the proposed approach.

In this paper, adaptive prescribed performance output feedback control is investigated for a class of nonlinear systems with unmodeled dynamics. Neural networks are used to approximate the unknown nonlinear functions. MT-filters are employed to estimate the unmeasured states. The unmodeled dynamics is dealt with by introducing an available dynamic signal. Adaptive output feedback dynamic surface control and parameter adaptive laws are proposed based on introducing the prescribed performance function and output error transformation. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Simulation results are provided to demonstrate the effectiveness of the proposed approach.

Text By using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function, a hybrid mean value problem involving certain Hardy sum and Kloosterman sum is studied. Two exact computational formulae are given, through which the cancellation phenomenon is revealed. Video For a video summary of this paper, please visit https://youtu.be/d-X81xErU7Q .

This paper addresses the sliding mode control problem for uncertain MIMO linear Markovian jump systems. Firstly, by using the linear matrix inequality approach, sufficient conditions are proposed to guarantee the stochastically asymptotical stability of the system on the sliding surfaces. Secondly, an equivalent control based sliding mode control is proposed, such that the closed-loop system can be driven onto the desired sliding surfaces in a finite time. Finally, combining with multi-step state transition probability, the reaching and sliding probabilities are derived for situations where the control force may not be strong enough to ensure the fully asymptotical stability. Simulation results are presented to illustrate the effectiveness of the proposed design method.

Text With the aids of elementary methods, the fourth power mean value of the analogous general Kloosterman sums C ( m , n , k , χ ; q ) is studied, and an explicit formula is obtained. It shows that C ( m , n , k , χ ; q ) enjoys good mean value distribution properties. Video For a video summary of this paper, please visit https://youtu.be/FZmy08BTpH8 .

This paper addresses a novel anti-disturbance dynamical tracking problem for a class of MIMO systems subject to unknown disturbances and nonlinear dynamics. Different from some traditional anti-disturbance results, T-S fuzzy models are firstly employed to describe the nonlinear disturbances, in which a disturbance observer based on T-S exogenous models is designed under different conditions to estimate the unknown nonlinear disturbances for the plants with known and unknown nonlinearities, respectively. By integrating the estimates of disturbance with PI-type control input, a composite controller based on convex optimization theory is proposed to ensure the system stability and convergence of the tracking error to zero. Meanwhile, the favorable disturbance estimation and attenuation performance can also be achieved by the designed convex optimization algorithm. Finally, the effectiveness of the proposed control schemes is verified by simulations for flight control systems with three different types of nonlinear disturbances.

In this paper, centralized and decentralized adaptive fuzzy output feedback control schemes are investigated for a class of stochastic nonlinear interconnected large-scale systems with dynamic uncertainties and unmeasured states. Fuzzy systems are used to approximate the unknown nonlinear functions. Decentralized 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 (DSC) technique with backstepping design, the condition in which the approximation errors are assumed to be bounded is avoided. Using the defined compact set in the stability analysis, the unknown smooth interconnections and black box functions are effectively dealt with. Using It o ? formula and Chebyshev's inequality, it is shown 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 demonstrate the effectiveness of the proposed approach.

The paper addresses a practical issue for adaptive synchronization in master–slave large-scale systems with constant channel time-delay., and a novel adaptive synchronization control scheme is proposed to guarantee the synchronization errors asymptotically converge to the origin, in which the matching condition as in the related literatures is not necessary. The real value of channel time-delay can be estimated online by a proper adaptation mechanism, which removes the conditions that the channel time-delay should be known exactly as in existing works. Finally, simulation results demonstrate the effectiveness of the approach.

This paper is concerned with the centralized and decentralized adaptive output feedback control problem for a class of uncertain interconnected nonlinear systems with unmodeled dynamics and unmeasured states. The known requirement of the upper bounds of dynamic disturbances and coupling terms in the considered system is avoided. Decentralized observers are constructed based on the K-filters to estimate the unmeasured states of each subsystem. In the design of adaptive output feedback dynamic surface control, the unknown nonlinear functions are directly approximated by neural networks, while the coupling terms being lumped together with those unknown continuous functions produced in deduction are approximated as a whole. Using the defined compact set in the stability analysis, some unknown nonlinear continuous functions are dealt with effectively. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Simulation results are provided to illustrate the effectiveness of the proposed approach.

In this paper, two adaptive output feedback control schemes are proposed for a class of nonlinear systems with unmodeled dynamics and unmeasured states as well as unknown high-frequency gain. Radial basis function (RBF) neural networks (NNs) 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 introducing the dynamic surface control (DSC) method, the bounded condition of the approximation error is removed, and the tracking control is achieved. Moreover, the number of adjustable parameters and the complexity of the design are both reduced. By theoretical analysis, the closed-loop system is shown to be semi-globally uniformly ultimately bounded (SGUUB). Simulation results are provided to illustrate the effectiveness of the proposed approach.

In this paper, a novel adaptive control scheme is investigated based on the backstepping design for a class of stochastic nonlinear systems with unmodeled dynamics and time-varying state delays. The radial basis function neural networks are used to approximate the unknown nonlinear functions obtained by using Ito differential formula and Young׳s inequality. The unknown time-varying delays and the unmodeled dynamics are dealt with by constructing appropriate Lyapunov–Krasovskii functions and introducing available dynamic signal. It is proved that all signals in the closed-loop system are bounded in probability and the error signals are semi-globally uniformly ultimately bounded (SGUUB) in mean square or the sense of four-moment. Simulation results illustrate the effectiveness of the proposed design.

In this paper, robust adaptive control is proposed for a class of pure-feedback nonlinear systems with unmodeled dynamics and unknown gain signs using radial basis function neural networks (RBFNNs). Dynamic uncertainties are dealt with using a dynamic signal. The unknown virtual gain signs are solved using the Nussbaum functions. Using mean value theorem and Young's inequality, only one learning parameter needs to be tuned online at each step of recursion. It is proved that the proposed design scheme can guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results demonstrate the effectiveness of the proposed approach.

The state feedback control scheme combined with backstepping, neural network and adaptive control is proposed for the tracking control problem of a class of nonlinear systems with uncertain input delay and disturbances. A filter and a virtual observer are constructed to produce the auxiliary signal. Neural networks are employed to estimate the unknown continuous functions. The tracking error is proved to ultimately converge to an adequately small compact set. The theoretical result is illustrated through a simulation example.

The tracking control problem is studied for a class of uncertain non-affine systems. Based on the principle of sliding mode control (SMC), using the neural networks (NNs) and the property of the basis function, a novel adaptive design scheme is proposed. A novel Lyapunov function, which depends on both system states and control input variable, is used for the development of the control law and the adaptive law. The approach overcomes the drawback in the literature. In addition, the lumped disturbances are taken in account. By theoretical analysis, it is proved that tracking errors asymptotically converge to zero. Finally, simulation results demonstrate the effectiveness of the proposed approach.

An adaptive control scheme combined with backstepping, radial basis function (RBF) neural networks is proposed for the output tracking control problem of a class of MIMO nonlinear systems with input delay and disturbances. Neural networks are employed to estimate the unknown continuous functions. The control scheme ensures that the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB). The tracking error is proved to be bounded and ultimately converges to an adequately small compact set. The feasibility is investigated by a simulation example.

The main purpose of this paper is using the analytic methods to study the hybrid mean value involving the character sums, general quadratic Gauss sums and general Kloosterman sums, and give several interesting mean value formulae.

An output feedback control scheme combined with backstepping, radial basis function (RBF) neural networks, and adaptive control is proposed for the stabilization of nonlinear system with input delay and disturbances. A filter and a virtual observer are constructed to substitute the immeasurable system state. By using state transformation, the original system is converted to the system without input delay. Neural networks are employed to estimate the unknown continuous functions. The control scheme ensures that the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB).

A control scheme combined with backstepping, radius basis function (RBF) neural networks and adaptive control is proposed for the stabilization of nonlinear system with input and state delay. By using state transformation, the original system is converted to the system without input delay. The RBF neural network is employed to estimate the unknown continuous function. The controller is designed for the converted system so that the closed-loop system is bounded. According to the relation between the original system and the converted one, the state of the original system is proved to be bounded. The control scheme ensures that the closed-loop system is semi-globally uniformly ultimately bounded.

In this paper, adaptive neural control is proposed for a class of uncertain multi-input multi-output (MIMO) nonlinear state time-varying delay systems in a triangular control structure with unknown nonlinear dead-zones and gain signs. The design is based on the principle of sliding mode control and the use of Nussbaum-type functions in solving the problem of the completely unknown control directions. The unknown time-varying delays are compensated for using appropriate Lyapunov-Krasovskii functionals in the design. The approach removes the assumption of linear functions outside the deadband as an added contribution. By utilizing the integral Lyapunov function and introducing an adaptive compensation term for the upper bound of the residual and optimal approximation error as well as the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the approach.

The problem of stable adaptive fuzzy control for a class of interconnected systems with unknown control gains is studied in this paper. By using fuzzy modeling method, a design scheme of an adaptive fuzzy controller is proposed. The design is capable of incorporating linguistic and numerical information into controllers. By theoretical analysis, the closed-loop adaptive fuzzy control system is proved to be globally stable in the sense that all signals involved are bounded, with tracking errors converging to a neighborhood of zero.

A decentralized adaptive fuzzy control scheme for a class of large-scale nonlinear systems is proposed in this paper. The design is based on the principle of sliding mode control and the approximation capability of fuzzy systems. The control architecture employs decentralized fuzzy systems to adaptively compensate for plant uncertainties. By using the Lyapunov function method, the control algorithm is proved to be globally stable, with tracking errors converging to a neighborhood of zero.