A new neural network-based approach for self-tuning control of nonlinear SISO discrete-time systems

This article presents a new neural network-based approach for self-tuning control of nonlinear single-input single-output (SISO) discrete-time dynamic systems. According to the approach, a neural network ARMAX (NN-ARMAX) model of the system is identified and continuously updated, using an online training algorithm. Control design is accomplished by solving an optimal discrete-time linear quadratic tracking problem using an observer-type linear state-space Kalman innovation model, which is built from the parameters of a local linear version of the NN-ARMAX model. The state-feedback control law is implemented using the Kalman state, which is calculated without estimating the noise covariance properties. The proposed control approach is shown to be very effective and outperforms the self-tuning control approach based on a linear ARMAX model on two simulation examples.     

不确定非线性系统全局渐近自适应神经网络控制

针对一类控制增益为一般函数形式的不确定仿射非线性系统,提出一种能够确保全局渐近稳定的自适应神经控制(adaptiveneural control,ANC)方法.为了保证神经网络逼近的适用性,设计一种可变控增益的比例微分(proportionaldifferential,PD)控制器以全局镇定被控对象.利用状态变换解决由未知控制增益函数导致的控制奇异问题.提出一种连续的自适应鲁棒控制项实现闭环系统的渐近跟踪.与现有的全局渐近跟踪ANC方法相比较,本文方法不仅简化了PD增益的选择,而且减轻了控制输入的颤振问题.仿真结果表明了本文方法的有效性.     

Robust adaptive control for a class of uncertain non-affine nonlinear systems using affine-type neural networks

A robust adaptive control is proposed for a class of single-input single-output non-affine nonlinear systems. In order to approximate the unknown nonlinear function, a novel affine-type neural network is used, and then to compensate the approximation error and external disturbance a robust control term is employed. By Lyapunov stability analysis for the closed-loop system, it is proved that tracking errors asymptotically converge to zero. Moreover, an observer is designed to estimate the system states because all the states may not be available for measurements. Furthermore, the adaptation laws of neural networks and the robust controller are given out based on the Lyapunov stability theory. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed control method.     

Adaptive neural network dynamic surface control for perturbed nonlinear time-delay systems

This paper proposes an adaptive neural network control method for a class of perturbed strict-feedback nonlinear systems with unknown time delays. Radial basis function neural networks are used to approximate unknown intermediate control signals. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown time delay terms have been compensated. Dynamic surface control technique is used to overcome the problem of "explosion of complexity" in backstepping design procedure. In addition, the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system is proved. A main advantage of the proposed controller is that both problems of "curse of dimensionality" and "explosion of complexity" are avoided simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the approach.     

未知非线性系统自适应改进RBF滑模控制

针对一类未知的非线性系统,利用输入/输出线性化将其变换为部分线性可控系统,通过RBF神经网络对未知非线性函数进行逼近,提出了一种基于RBF神经网络的自适应滑模控制,并设计了自适应滑模控制器;提出了一种连续函数,很好地减少了抖振现象,使得闭环系统状态一致稳定最终有界。实验结果验证了方法的有效性。     

An observer-based adaptive neural network tracking control of robotic systems

Robotic systems have inherently nonlinear phenomena as joints undergo sliding and/or rotating. This in turn requires that the system running states be predicted correctly. This paper makes a full analysis of the robot states by applying observer-based adaptive wavelet neural network (OBAWNN) tracking control scheme to tackle these phenomena such as system uncertainties, multiple time-delayed state uncertainties, and external disturbances such that the closed loop system signals must obey uniform ultimate boundedness and achieve H^∞ tracking performance. The recurrent adaptive wavelet neural network model is used to approximate the dynamics of the robotic system, while an observer-based adaptive control scheme is to stabilize the system. The advantage of employing adaptive wavelet neural dynamics is that we can utilize the neuron information by activation functions to on-line tune the hidden-to-output weights, and the adaptation parameters to estimate the robot parameters and the bounds of the gains of delay states directly using linear analytical results. It is shown that the stability of the closed-loop system is guaranteed by some sufficient conditions derived from Lyapunov criterion and Riccati-inequality. Finally, a numerical example of a three-links rolling cart is given to illustrate the effectiveness of the proposed control scheme.     

Dynamic structure adaptive neural fuzzy control for MIMO uncertain nonlinear systems

This paper proposes a novel dynamic structure neural fuzzy network (DSNFN) to address the adaptive tracking problems of multiple-input-multiple-output (MIMO) uncertain nonlinear systems. The proposed control scheme uses a four-layer neural fuzzy network (NFN) to estimate system uncertainties online. The main feature of this DSNFN is that it can either increase or decrease the number of fuzzy rules over time based on tracking errors. Projection-type adaptation laws for the network parameters are derived from the Lyapunov synthesis approach to ensure network convergence and stable control. A hybrid control scheme that combines the sliding-mode control and the adaptive bound estimation control with different weights improves system performance by suppressing the influence of external disturbances and approximation errors. As the employment of the DSNFN, high-quality tracking performance could be achieved in the system. Furthermore, the trained network avoids the problems of overfitting and underfitting. Simulations performed on a two-link robot manipulator demonstrate the effectiveness of the proposed control scheme.     

非线性系统RBF神经网络多步预测控制

针对较强非线性的控制问题, 提出一种以RBF 神经网络为模型的多步预测控制方法. 构建多步预测模型, 并给出预测误差关于控制序列的雅可比矩阵的计算方法. 利用Levenberg-Marquardt(L-M) 算法设计滚动优化策略, 过误差修正参考输入的方法实现了反馈校正, 证明了控制系统的稳定性. 仿真结果表明所提出的控制方法效果较好.

     

MLP-based adaptive neural control of nonlinear time-delay systems with the unknown hysteresis

In this note, the authors study the tracking problem for uncertain nonlinear time-delay systems with unknown non-smooth hysteresis described by the generalised Prandtl–Ishlinskii (P-I) model. A minimal learning parameters (MLP)-based adaptive neural algorithm is developed by fusion of the Lyapunov–Krasovskii functional, dynamic surface control technique and MLP approach without constructing a hysteresis inverse. Unlike the existing results, the main innovation can be summarised as that the proposed algorithm requires less knowledge of the plant and independent of the P-I hysteresis operator, i.e. the hysteresis effect is unknown for the control design. Thus, the outstanding advantage of the corresponding scheme is that the control law is with a concise form and easy to implement in practice due to less computational burden. The proposed controller guarantees that the tracking error converges to a small neighbourhood of zero and all states of the closed-loop system are stabilised. A simulation example demonstrates the effectiveness of the proposed scheme.     

Backstepping adaptive fuzzy control of uncertain nonlinear systems against actuator faults

A class of unknown nonlinear systems subject to uncertain actuator faults and external disturbances will be studied in this paper with the help of fuzzy approximation theory. Using backstepping technique, a novel adaptive fuzzy control approach is proposed to accommodate the uncertain actuator faults during operation and deal with the external disturbances though the systems cannot be linearized by feedback. The considered faults are modeled as both loss of effectiveness and lock-in-place （stuck at some unknown place）. It is proved that the proposed control scheme can guarantee all signals of the closed-loop system to be semi-globally uniformly ultimately bounded and the tracking error between the system output and the reference signal converge to a small neighborhood of zero, though the nonlinear functions of the controlled system as well as the actuator faults and the external disturbances are all unknown. Simulation results demonstrate the effectiveness of the control approach.     

非线性系统神经网络自适应控制的发展现状及展望

简要回顾了神经网络控制及其应用的发展历程,重点论述了人们在连续、离散时间非线性系统的神经网络以及神经模糊稳定自适应控制研究方面所取得的主要进展,探讨了神经网络自适应控制研究方面存在的主要问题及解决问题的基本途径.作为当前解决神经网络自适应控制问题的途径之一,介绍了近来人们对二阶模糊神经网络以及量子神经网络的研究.最后,总结并指出了这一领域下一步的发展方向和有待解决的新课题.     

An adaptive variable structure control for a class of nonlinear systems

Motivated by the recent advance in adaptive output-feedback control for a class of nonlinear systems which can be transformed into the so-called output-feedback form [7,10,11], an adaptive structure controller is proposed in this paper to solve the nonlinear model reference adaptive control problem. It is shown that an asymptotic output tracking performance can be achieved for this class of nonlinear system even if some nonlinearity is not available or some unknown parameters are fast time-varying.     

Robust adaptive neural control of uncertain pure-feedback nonlinear systems

In this paper, a robust adaptive neural control design approach is presented for a class of uncertain pure-feedback nonlinear systems. To reduce the complexity of the both controller structure and computation, only one neural network is used to approximate the lumped unknown function of the system at the last step of the recursive design process. By this approach, the complexity growing problem existing in conventional methods can be eliminated completely. Stability analysis shows that all the closed-loop system signals are uniformly ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results demonstrate the effectiveness and merits of the proposed approach.     

具有零动态的SISO仿射非线性系统的神经网络自适应跟踪控制

针对具有零动态的SISO仿射非线性系统提出了一种神经网络直接自适应跟踪控制方法.采用梯度下降算法最小化未知理想控制器与神经网络控制器的误差代价函数以获得参数自适应律,控制器中无需另加鲁棒控制项.基于Lyapunov稳定性定理证明了在该控制器的作用下能保证输出跟踪误差及相应闭环系统的所有状态最终一致有界及神经网络参数的收敛性.仿真结果验证了该文方法的有效性.     

Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics

A neural network-based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unmodeled dynamics. By on-line approximating the unknown nonlinear functions and unmodeled dynamics by radial basis function (RBF) networks, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. It is proved that with the proposed control law, the closed-loop system is stable and the tracking error converges to zero in the presence of unmodeled dynamics and unknown nonlinearity. A simulation example is presented to demonstrate the method.     

Adaptive NN control of uncertain nonlinear pure-feedback systems

This paper is concerned with the control of nonlinear pure-feedback systems with unknown nonlinear functions. This problem is considered difficult to be dealt with in the control literature, mainly because that the triangular structure of pure-feedback systems has no affine appearance of the variables to be used as virtual controls. To overcome this difficulty, implicit function theorem is firstly exploited to assert the existence of the continuous desired virtual controls. NN approximators are then used to approximate the continuous desired virtual controls and desired practical control. With mild assumptions on the partial derivatives of the unknown functions, the developed adaptive NN control schemes achieve semi-global uniform ultimate boundedness of all the signals in the closed-loop. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.     

On near optimal neural control of multiple-input nonlinear systems

It has been a common consensus that general techniques for stabilization of nonlinear systems are available only for some special classes of nonlinear systems. Control design for nonlinear systems with uncertain components is usually carried out on a per system basis, especially when physical control constraints, and certain control performance measures such as optimum time control are imposed. Elegant adaptive control techniques are difficult to apply to this type of problems. A new neural network based control design is proposed and presented in this paper to deal with a special class of uncertain nonlinear systems with multiple inputs. The desired system dynamics are analyzed and utilized in the process of the proposed intelligent control design. The theoretical results are provided to justify the design procedures. The simulation study is conducted on a second-order bilinear system with two inputs and uncertainties on its parameters. The simulation results indicate that the proposed design approach is effective.     

An ISS-modular approach for adaptive neural control of pure-feedback systems

Controlling non-affine non-linear systems is a challenging problem in control theory. In this paper, we consider adaptive neural control of a completely non-affine pure-feedback system using radial basis function (RBF) neural networks (NN). An ISS-modular approach is presented by combining adaptive neural design with the backstepping method, input-to-state stability (ISS) analysis and the small-gain theorem. The difficulty in controlling the non-affine pure-feedback system is overcome by achieving the so-called “ISS-modularity” of the controller-estimator. Specifically, a neural controller is designed to achieve ISS for the state error subsystem with respect to the neural weight estimation errors, and a neural weight estimator is designed to achieve ISS for the weight estimation subsystem with respect to the system state errors. The stability of the entire closed-loop system is guaranteed by the small-gain theorem. The ISS-modular approach provides an effective way for controlling non-affine non-linear systems. Simulation studies are included to demonstrate the effectiveness of the proposed approach.