Backstepping sliding mode control for uncertain strict-feedback nonlinear systems using neural-network-based adaptive gain scheduling

A neural-network-based adaptive gain scheduling backstepping sliding mode control（NNAGS-BSMC） approach for a class of uncertain strict-feedback nonlinear system is proposed.First, the control problem of uncertain strict-feedback nonlinear systems is formulated. Second, the detailed design of NNAGSBSMC is described. The sliding mode control（SMC） law is designed to track a referenced output via backstepping technique.To decrease chattering result from SMC, a radial basis function neural network（RBFNN） is employed to construct the NNAGSBSMC to facilitate adaptive gain scheduling, in which the gains are scheduled adaptively via neural network（NN）, with sliding surface and its differential as NN inputs and the gains as NN outputs. Finally, the verification example is given to show the effectiveness and robustness of the proposed approach. Contrasting simulation results indicate that the NNAGS-BSMC decreases the chattering effectively and has better control performance against the BSMC.

Uniformed model of networked control systems with long time delay

Feedback control systems wherein the control loops are closed through a real-time network are called networked control systems （NCS）. The defining feature of an NCS is that information is exchanged using a network among control system components. Two new concepts including long time delay and short time delay are proposed. The sensor is almost always clock driven. The controller or the actuator is either clock driven or event driven. Four possible driving modes of networked control systems are presented. The open loop mathematic models of networked control systems with long time delay are developed when the system is driven by anyone of the four different modes. The uniformed modeling method of networked control systems with long time delay is proposed. The simulation results are given in the end.

Stabilization of Networked Control Systems Using a Mixed-Mode Based Switched Delay System Method

The phenomenon of mixed-mode is one of the most important characteristics of switched delay systems. If a networked control system(NCS) with network induced delays and packet dropouts(NIDs & PDs) is recast as a switched delay system, it is imperative to consider the effects of mixed-modes in the stability analysis for an NCS. In this paper, with the help of the interpolatory quadrature formula and the average dwell time method, stabilization of NCSs using a mixed-mode based switched delay system method is investigated based on a novel constructed Lyapunov-Krasovskii functional. With the Finsler's lemma, new exponential stabilizability conditions with less conservativeness are given for the NCS. Finally, an illustrative example is provided to verify the effectiveness of the developed results.

Finite-time robust control of uncertain fractional-order Hopfield neural networks via sliding mode control

The finite-time control of uncertain fractional-order Hopfield neural networks is investigated in this paper. A switched terminal sliding surface is proposed for a class of uncertain fractional-order Hopfield neural networks. Then a robust control law is designed to ensure the occurrence of the sliding motion for stabilization of the fractional-order Hopfield neural networks. Besides, for the unknown parameters of the fractional-order Hopfield neural networks, some estimations are made. Based on the fractional-order Lyapunov theory, the finite-time stability of the sliding surface to origin is proved well. Finally, a typical example of three-dimensional uncertain fractional-order Hopfield neural networks is employed to demonstrate the validity of the proposed method.

SYNCHRONIZATION OF MASTER-SLAVE MARKOVIAN SWITCHING COMPLEX DYNAMICAL NETWORKS WITH TIME-VARYING DELAYS IN NONLINEAR FUNCTION VIA SLIDING MODE CONTROL

In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities （LMIs）. Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkin＇s formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

Robust control for a class of nonlinear networked systems with stochastic communication delays via sliding mode conception

This paper deals with the robust control problem for a class of uncertain nonlinear networked systems with stochastic communication delays via sliding mode conception （SMC）. A sequence of variables obeying Bernoulli distribution are employed to model the randomly occurring communication delays which could be different for different state variables. A discrete switching function that is different from those in the existing literature is first proposed. Then, expressed as the feasibility of a linear matrix inequality （LMI） with an equality constraint, sufficient conditions are derived in order to ensure the globally mean-square asymptotic stability of the system dynamics on the sliding surface. A discrete-time SMC controller is then synthesized to guarantee the discrete-time sliding mode reaching condition with the specified sliding surface. Finally, a simulation example is given to show the effectiveness of the proposed method.

Spatiotemporal chaos synchronization of an uncertain network based on sliding mode control

The sliding mode control method is used to study spatiotemporal chaos synchronization of an uncertain network.The method is extended from synchronization between two chaotic systems to the synchronization of complex network composed of N spatiotemporal chaotic systems.The sliding surface of the network and the control input are designed.Furthermore,the effectiveness of the method is analysed based on the stability theory.The Burgers equation with spatiotemporal chaos behavior is taken as an example to simulate the experiment.It is found that the synchronization performance of the network is very stable.

Neural network based adaptive sliding mode control of uncertain nonlinear systems

The purpose of this paper is the design of neural network-based adaptive sliding mode controller for uncertain unknown nonlinear systems. A special architecture adaptive neural network, with hyperbolic tangent activation functions, is used to emulate the equivalent and switching control terms of the classic sliding mode control （SMC）. Lyapunov stability theory is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as of all other signals in the closed loop. In addition to keeping the stability and robustness properties of the SMC, the neural network-based adaptive sliding mode controller exhibits perfect rejection of faults arising during the system operating. Simulation studies are used to illustrate and clarify the theoretical results.

An Adaptive Sliding Mode Tracking Controller Using BP Neural Networks for a Class of Large-scale Nonlinear Systems

A new type controller, BP neural-networks-based sliding mode controller is developed for a class of large-scale nonlinear systems with unknown bounds of high-order interconnections in this paper. It is shown that decentralized BP neural networks are used to adaptively learn the uncertainty bounds of interconnected subsystems in the Lyapunov sense, and the outputs of the decentralized BP neural networks are then used as the parameters of the sliding mode controller to compensate for the effects of subsystems uncertainties. Using this scheme, not only strong robustness with respect to uncertainty dynamics and nonlinearities can be obtained, but also the output tracking error between the actual output of each subsystem and the corresponding desired reference output can asymptotically converge to zero. A simulation example is presented to support the validity of the proposed BP neural-networks-based sliding mode controller.

ROBUST SLIDING MODE DECENTRALIZED CONTROL FOR A CLASS OF NONLINEAR INTERCONNECTED LARGE-SCALE SYSTEM WITH NEURAL NETWORKS

A new decentralized robust control method is discussed for a class of nonlinear interconnected largescale system with unknown bounded disturbance and unknown nonlinear function term. A decentralized control law is proposed which combines the approximation method of neural network with sliding mode control. The decentralized controller consists of an equivalent controller and an adaptive sliding mode controller. The sliding mode controller is a robust controller used to reduce the track error of the control system. The neural networks are used to approximate the unknown nonlinear functions, meanwhile the approximation errors of the neural networks are applied to the weight value updated law to improve performance of the system. Finally, an example demonstrates the availability of the decentralized control method.

Neural Network Based Terminal Sliding Mode Control for WMRs Affected by an Augmented Ground Friction With Slippage Effect

Wheeled mobile robots(WMRs) encounter unavoidable slippage especially on the low adhesion terrain such that the robots stability and accuracy are reduced greatly.To overcome this drawback,this article presents a neural network(NN) based terminal sliding mode control(TSMC) for WMRs where an augmented ground friction model is reported by which the uncertain friction can be estimated and compensated according to the required performance.In contrast to the existing friction models,the developed augmented ground friction model corresponds to actual fact because not only the effects associated with the mobile platform velocity but also the slippage related to the wheel slip rate are concerned simultaneously.Besides,the presented control approach can combine the merits of both TSMC and radial basis function(RBF) neural networks techniques,thereby providing numerous excellent performances for the closed-loop system,such as finite time convergence and faster friction estimation property.Simulation results validate the proposed friction model and robustness of controller;these research results will improve the autonomy and intelligence of WMRs,particularly when the mobile platform suffers from the sophisticated unstructured environment.

Outer synchronization of uncertain small-world networks via adaptive sliding mode control

The outer synchronization of irregular coupled complex networks is inves- tigated with nonidentical topological structures. The switching gain is estimated by an adaptive technique, and a sliding mode controller is designed to satisfy the sliding con- dition. The outer synchronization between two irregular coupled complex networks with different initial conditions is implemented via the designed controllers with the corre- sponding parameter update laws. The chaos synchronization of two small-world networks consisting of N uncertain identical Lorenz systems is achieved to demonstrate the appli- cations of the proposed approach.

Robust Sliding Mode Control for Nonlinear Discrete-Time Delayed Systems Based on Neural Network

This paper presents a robust sliding mode controller for a class of unknown nonlinear discrete-time systems in the presence of fixed time delay. A neural-network approximation and the Lyapunov-Krasovskii functional theory into the sliding-mode technique is used and a neural-network based sliding mode control scheme is proposed. Because of the novality of Chebyshev Neural Networks (CNNs), that it requires much less computation time as compare to multi layer neural network (MLNN), is preferred to approximate the unknown system functions. By means of linear matrix inequalities, a sufficient condition is derived to ensure the asymptotic stability such that the sliding mode dynamics is restricted to the defined sliding surface. The proposed sliding mode control technique guarantees the system state trajectory to the designed sliding surface. Finally, simulation results illustrate the main characteristics and performance of the proposed approach.

Neural-Network-Based Terminal Sliding Mode Control for Frequency Stabilization of Renewable Power Systems

This paper addresses a terminal sliding mode control(T-SMC) method for load frequency control(LFC) in renewable power systems with generation rate constraints(GRC).A two-area interconnected power system with wind turbines is taken into account for simulation studies. The terminal sliding mode controllers are assigned in each area to achieve the LFC goal. The increasing complexity of the nonlinear power system aggravates the effects of system uncertainties. Radial basis function neural networks(RBF NNs) are designed to approximate the entire uncertainties. The terminal sliding mode controllers and the RBF NNs work in parallel to solve the LFC problem for the renewable power system. Some simulation results illustrate the feasibility and validity of the presented scheme.

Backstepping sliding mode control with self recurrent wavelet neural network observer for a novel coaxial twelve-rotor UAV

The robust attitude control for a novel coaxial twelve-rotor UAV which has much greater payload capacity,higher drive capability and damage tolerance than a quad-rotor UAV is studied. Firstly,a dynamical and kinematical model for the coaxial twelve-rotor UAV is designed. Considering model uncertainties and external disturbances,a robust backstepping sliding mode control( BSMC) with self recurrent wavelet neural network( SRWNN) method is proposed as the attitude controller for the coaxial twelve-rotor. A combinative algorithm of backstepping control and sliding mode control has simplified design procedures with much stronger robustness benefiting from advantages of both controllers. SRWNN as the uncertainty observer is able to estimate the lumped uncertainties effectively.Then the uniformly ultimate stability of the twelve-rotor system is proved by Lyapunov stability theorem. Finally,the validity of the proposed robust control method adopted in the twelve-rotor UAV under model uncertainties and external disturbances are demonstrated via numerical simulations and twelve-rotor prototype experiments.

Adaptive Sliding Mode Control for Re-entry Attitude of Near Space Hypersonic Vehicle Based on Backstepping Design

Combining sliding mode control method with radial basis function neural network(RBFNN), this paper proposes a robust adaptive control scheme based on backstepping design for re-entry attitude tracking control of near space hypersonic vehicle(NSHV) in the presence of parameter variations and external disturbances. In the attitude angle loop, a robust adaptive virtual control law is designed by using the adaptive method to estimate the unknown upper bound of the compound uncertainties. In the angular velocity loop, an adaptive sliding mode control law is designed to suppress the effect of parameter variations and external disturbances. The main benefit of the sliding mode control is robustness to parameter variations and external disturbances. To further improve the control performance, RBFNNs are introduced to approximate the compound uncertainties in the attitude angle loop and angular velocity loop, respectively. Based on Lyapunov stability theory, the tracking errors are shown to be asymptotically stable. Simulation results show that the proposed control system attains a satisfied control performance and is robust against parameter variations and external disturbances.

FUZZY NEURAL NETWORK CONTROL FOR VIBRATION WAVEFORM SYSTEM OF MOLD

Combining with the characteristic of the fuzzy control and the neural networkcontrol(NNC), a new kind of the fuzzy neural network controller is proposed, and the synthesisdesign method of the control law and fast speed learning algorithm of the parameters of networks areput forward. The output of the controller is composed of two parts, part one is derived on basis ofthe principle of sliding control, the lower order model and the estimated parameters of the plantare only required, part two is derived on basis FNN, it is used to compensate the uncertainties ofthe systems. Because new type of FNN controller extracts from the advantages of the intelligentcontrol and model based sliding mode control, the numbers of adjusting parameters and the structureof FNN are simplified at large, and the practical significance and variation range are attached toeach layer of the network and its connected weights, the control performance and learning speed areincreased at large. The Tightness of the conclusions is verified by the experiment of anelectro-hydraulic position servo system of the mold of the continuous casting machinery.

Decentralized direct adaptive neural network control for a class of interconnected systems

The problem of direct adaptive neural network control for a class of large-scale systems with unknown function control gains and the high-order interconneetions is studied in this paper. Based on the principle of sliding mode control and the approximation capability of multilayer neural networks, a design scheme of decentralized di- rect adaptive sliding mode controller is proposed. The plant dynamic uncertainty and modeling errors are adaptively compensated by adjusted the weights and sliding mode gains on-line for each subsystem using only local informa- tion. According to the Lyapunov method, the closed-loop adaptive control system is proven to be globally stable, with tracking errors converging to a neighborhood of zero. Simulation results demonstrate the effectiveness of the proposed approach.

Fault Estimation and Accommodation for Networked Control Systems with Transfer Delay

在这份报纸，差错评价和差错的一个方法为有转移延期和进程噪音的联网的控制系统(NCS ) 的容忍的控制被介绍。首先，联网的控制系统作为有转移的分离时间的系统推迟的 multiple-input-multiple-output (MIMO ) 被建模，处理噪音，并且为无常建模。在这个模型下面并且在一些条件下面，一个差错评价方法被建议估计系统差错。根据差错评价和滑动模式控制理论的信息，一个差错容忍的控制器被设计恢复系统性能。最后，模拟结果被用来验证方法的效率。