Adaptive NN control for a class of strict-feedback discrete-time nonlinear systems

In this paper, both full state and output feedback adaptive neural network (NN) controllers are presented for a class of strict-feedback discrete-time nonlinear systems. Firstly, Lyapunov-based full-state adaptive NN control is presented via backstepping, which avoids the possible controller singularity problem in adaptive nonlinear control and solves the noncausal problem in the discrete-time backstepping design procedure. After the strict-feedback form is transformed into a cascade form, another relatively simple Lyapunov-based direct output feedback control is developed. The closed-loop systems for both control schemes are proven to be semi-globally uniformly ultimately bounded.     

Direct adaptive NN control of a class of nonlinear systems

In this paper, direct adaptive neural-network (NN) control is presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By utilizing a special property of the affine term, the developed scheme,avoids the controller singularity problem completely. All the signals in the closed loop are guaranteed to be semiglobally uniformly ultimately bounded and the output of the system is proven to converge to a small neighborhood of the desired trajectory. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation results are presented to show the effectiveness of the approach.     

Robust adaptive NN control for a class of uncertain discrete-time nonlinear MIMO systems

A robust adaptive NN output feedback control is proposed to control a class of uncertain discrete-time nonlinear multi-input–multi-output (MIMO) systems. The high-order neural networks are utilized to approximate the unknown nonlinear functions in the systems. Compared with the previous research for discrete-time MIMO systems, robustness of the proposed adaptive algorithm is obvious improved. Using Lyapunov stability theorem, the results show all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero by choosing the design parameters appropriately.     

一类非线性离散系统的直接自适应模糊控制

针对一类含延迟非线性离散系统,提出了一种直接自适应模糊控制器设计的新方案．将系统用T-S模糊模型来表示,并基于并行分布补偿(PDC)基本思想设计了一种具有未知参数的模糊控制器,同时采用梯度下降算法对该控制器的参数进行在线辨识．通过输入到状态稳定(ISS)方法,证明了系统输出和参考输出的误差有界且满足一定的平均性能．仿真表明本方法的有效性．     

Robust adaptive control of a class of nonlinear strict-feedback discrete-time systems with exact output tracking

In this paper, adaptive control is studied for a class of single-input–single-output (SISO) nonlinear discrete-time systems in strict-feedback form with nonparametric nonlinear uncertainties of the Lipschitz type. To eliminate the effect of the nonparametric uncertainties in an unmatched manner, a novel future states prediction is designed using states information at previous steps to compensate for the effect of uncertainties at the current step. Utilizing the predicted future states, constructive adaptive control is developed to compensate for the effects of both parametric and nonparametric uncertainties such that global stability and asymptotical output tracking is achieved. The effectiveness of the proposed control law is demonstrated in the simulation.     

Direct adaptive fuzzy control of nonlinear strict-feedback systems

This paper focuses on adaptive fuzzy tracking control for a class of uncertain single-input /single-output nonlinear strict-feedback systems. Fuzzy logic systems are directly used to approximate unknown and desired control signals and a novel direct adaptive fuzzy tracking controller is constructed via backstepping. The proposed adaptive fuzzy controller guarantees that the output of the closed-loop system converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. A main advantage of the proposed controller is that it contains only one adaptive parameter that needs to be updated online. Finally, an example is used to show the effectiveness of the proposed approach.     

An indirect model reference robust fuzzy adaptive control for a class of SISO nonlinear systems

In this paper we are interested in robust adaptive fuzzy control of nonlinear SISO systems in the presence of parametric uncertainties. The plant model structure is represented by the Takagi-Sugeno (T-S) type fuzzy system. An indirect adaptive fuzzy controller based on model reference control scheme is proposed to provide asymptotic tracking of reference signal. The controller parameters are computed at each time. The plant state tracks asymptotically the state of the reference model for any bounded reference input signal. Inverted pendulum and mass spring damper are used to check the performance of the proposed controller.     

一类严格反馈非线性系统的间接自适应模糊控制

针对一类不确定严格反馈非线性系统,设计了间接自适应模糊控制方法．该方法用模糊逻辑系统逼近设计过程中的未知函数,基于时变宽度死区对模糊逻辑系统中的未知参数进行自适应调节,并对时变死区宽度设计了自适应律．证明了该方法能使闭环系统的所有信号有界,且可使跟踪误差收敛到原点的小邻域内．仿真算例验证了该方法的有效性．     

Hybrid-based adaptive NN backstepping control of strict-feedback systems

Hybrid-based adaptive NN backstepping tracking control designs for both the single-input/single-output (SISO) and the square multi-input/multi-output (MIMO) strict-feedback systems with unknown system nonlinearities are presented. Each virtual/actual controller in these designs contains four main parts: a single-layer radial basis function neural network (RBFNN) for re-parameterizing the unknown nonlinearity to render the adaptive control applicable; an adaptive linearizing controller for compensating the resembled nonlinearities; a supervisory agent which hands over temporarily the control authority to the fourth part of a robust controller during the singularity. The proposed design ensures the semiglobal uniform ultimate boundedness (SGUUB) of all the closed-loop signals and compared with existing schemes has a wider applicability with a simpler structure. Simulation results demonstrating the validity of the proposed design are given in the final section.     

Linear adaptive control of a class of SISO nonaffine nonlinear systems

This paper addresses the problem of linear adaptive control for a class of uncertain continuous-time single-input single-output (SISO) nonaffine nonlinear dynamic systems. Using the implicit function theory, the existence of an ideal controller which can achieve control objectives is firstly demonstrated. However, this ideal controller cannot be known and computed even if the system model is well known. The aim of our work is to construct this unknown ideal controller using a simple linear controller with the free parameters updated online by a stable adaptation mechanism designed to minimise the error between the unknown ideal controller and the used linear controller. Since the mathematical model of the system is assumed unknown in this work, the proposed control scheme can be regarded as a simple model free controller for the studied class of nonaffine systems. We prove that the closed-loop system is stable and all the signals are bounded. An application of the proposed linear adaptive controller for a nonaffine system is illustrated through the simulation results to demonstrate the effectiveness of the proposed control scheme.     

Neural-network-based robust adaptive control for a class of nonlinear systems

In this study, a robust adaptive control (RAC) system is developed for a class of nonlinear systems. The RAC system is comprised of a computation controller and a robust compensator. The computation controller containing a radial basis function (RBF) neural network is the principal controller, and the robust compensator can provide the smooth and chattering-free stability compensation. The RBF neural network is used to approximate the system dynamics, and the adaptive laws are derived to on-line tune the parameters of the neural network so as to achieve favorable estimation performance. From the Lyapunov stability analysis, it is shown that all signals in the closed-loop RBAC system are uniformly ultimately bounded. To investigate the effectiveness of the RAC system, the design methodology is applied to control two nonlinear systems: a wing rock motion system and a Chua’s chaotic circuit system. Simulation results demonstrate that the proposed RAC system can achieve favorable tracking performance with unknown of the system dynamics.     

基于神经网络的严反馈块非线性系统的鲁棒控制

针对非匹配不确定性的严反馈块非线性系统,基于神经网络提出一种鲁棒控制方法．利用Lyapunov稳定性定理推导出RBF神经网络的全调节律,用于处理系统中的非线性参数不确定性,提高了神经网络的在线逼近能力;采用神经网络和鲁棒控制方法,利用已知信息的同时,对控制系数矩阵未知时的设计问题进行处理,避免了控制器可能的奇异问题;引入非线性跟踪微分器,解决了Backstepping设计中的“计算膨胀”问题．运用Lyapunov稳定性定理证明了闭环系统的所有信号均最终一致有界．     

Improved robust backstepping adaptive control for nonlinear discrete-time systems without overparameterization

This paper reports a robust backstepping adaptive controller for output tracking of nonlinear discrete-time systems. The result improves the previous one in Zhang, Wen, and Soh [(2001). Robust adaptive control for nonlinear discrete-time systems without overparameterization. Automatica, 37, 551-558] by removing the lower bound constraints on the system nonlinearities.     

一类不确定非线性离散系统的模糊自适应控制器设计

针对一类不确定非线性离散系统,提出一种带有自动可调伸缩因子的模糊自适应控制方法.该控制器设计方法的优点是模糊逻辑系统的逼近精度不再依赖于模糊逻辑系统的结构和规则数目,参数自适应律调节与被逼近函数的特征和逼近精度有关,因此能有效减少在线估计的参数数目,且设计方法能够保证闭环系统的所有状态半全局一致终极有界.最后,通过数值仿真算例表明所提出方法的有效性.     

一类非线性MIMO系统的直接自适应模糊鲁棒控制

针对一类未知的非线性MIMO系统, 本文提出了一种直接自适应模糊鲁棒控制设计方法. 理论分析和仿真实验都已证明, 该方法确保闭环系统全局稳定, 获得H_∞跟踪性能指标, 外部干扰、模糊逻辑逼近误差和输入对输出的交叉耦合可衰减到给定的水平, 系统鲁棒性好.     

Optimal higher order learning adaptive control approach for a class of SISO nonlinear systems

In this paper,an optimal higher order learning adaptive control approach is developed for a class of SISO nonlinear systems.This design is model-free and depends directly on pseudo-partial-derivatives derived on-line from the input and output information of the system.A novel weighted one-step-ahead control criterion function is proposed for the control law.The convergence analysis shows that the proposed control law can guarantee the convergence under the assumption that the desired output is a set point.Simulation examples are provided for nonlinear systems to illustrate the better performance of the higher order learning adaptive control.     

严格反馈非线性系统的自适应模糊控制

针对一类不确定非线性系统,基于backstepping方法提出了一种新的鲁棒自适应模糊控制器设计方案。该方案通过引入最优逼近误差的自适应补偿项和新的鲁棒项,削减建模误差和参数估计误差的影响,从而在稳定性分析中取消了要求逼近误差平方可积或逼近误差的上确界已知的条件。理论分析证明了闭环系统状态有界,跟踪误差收敛到零的较小邻域内。仿真结果表明了该方法的有效性。     

Optimal higher order learning adaptive control approach for a class of SISO nonlinear systems

1IntroductionMany dynamic systems to be controlled have constant orslowly_varying uncertain parameters .Adaptive control is apopular approachtothe control ofsuchsystems [1] .Inthepast two decades ,significant progress has been made in theresearch and design of adaptive control systems [2,3] .Fairly complete and comprehensive guidelines are nowavailable for both design and implementation of adaptivecontrollers inthe cases where the systemunder control canbe adequately modeled as a linear dynami…