Response to comment on ‘Persistent inputs and the standard H2 multivariable control problem’ by K. Park and J.J. Bongiorno Jr

Layered networks are used in a nonlinear adaptive control problem. The plant is an unknown feedback-linearizable discrete-time system, represented by an input-output model. A state space model of the plant is obtained to define the zero dynamics, which are assumed to be stable. A linearizing feedback control is derived in terms of some unknown nonlinear functions. To identify these functions, it is assumed that they can be modelled by layered neural networks. The weights of the networks are updated and used to generate the control. A local convergence result is given. Computer simulations verify the theoretical result.     

Neural networks-based adaptive control for a class of nonlinear bioprocesses

The paper studies the design and analysis of a neural adaptive control strategy for a class of square nonlinear bioprocesses with incompletely known and time-varying dynamics. In fact, an adaptive controller based on a dynamical neural network used as a model of the unknown plant is developed. The neural controller design is achieved by using an input–output feedback linearization technique. The adaptation laws of neural network weights are derived from a Lyapunov stability property of the closed-loop system. The convergence of the system tracking error to zero is guaranteed without the need of network weights convergence. The resulted control method is applied in a depollution control problem in the case of a wastewater treatment bioprocess, belonging to the square nonlinear class, for which kinetic dynamics are strongly nonlinear, time varying and not exactly known.     

基于状态观测器的迟滞非线性系统输出反馈控制

利用Preisach模型与其边界线之间的映射关系建立了容易在线更新的迟滞模型．将模型和径向基网络相结合，针对一类动态多映射迟滞非线性系统设计了输出反馈控制器．应用LyaPunov定理得到系统控制律和神经网络权值更新律，从而保证了闭环系统的跟踪误差及网络权值偏差收敛到原点的某个有界邻域内．     

Robust adaptive control of uncertain non-linear systems using neural networks

This paper presents a robust adaptive output feedback control design method for uncertain non-affine non-linear systems, which does not rely on state estimation. The approach is applicable to systems with unknown but bounded dimensions and with known relative degree. A neural network is employed to approximate the unknown modelling error. In fact, a neural network is considered to approximate and adaptively make ineffective unknown plant non-linearities. An adaptive law for the weights in the hidden layer and the output layer of the neural network are also established so that the entire closed-loop system is stable in the sense of Lyapunov. Moreover, the robustness of the system against the approximation error of neural network is achieved with the aid of an additional adaptive robustifying control term. In addition, the tracking error is guaranteed to be uniformly and asymptotically stable, rather than uniformly ultimately bounded, by using this additional control term. The proposed control algorithm is relatively straightforward and no restrictive conditions on the design parameters for achieving the systems stability are required. The effectiveness of the proposed scheme is shown through simulations of a non-affine non-linear system with unmodelled dynamics, and is compared with a second-sliding mode controller.     

Iterative learning of model reference adaptive controller for uncertain nonlinear systems with only output measurement

In this paper, a model reference adaptive control strategy is used to design an iterative learning controller for a class of repeatable nonlinear systems with uncertain parameters, high relative degree, initial output resetting error, input disturbance and output noise. The class of nonlinear systems should satisfy some differential geometric conditions such that the plant can be transformed via a state transformation into an output feedback canonical form. A suitable error model is derived based on signals filtered from plant input and output. The learning controller compensates for the unknown parameters, uncertainties and nonlinearity via projection type adaptation laws which update control parameters along the iteration domain. It is shown that the internal signals remain bounded for all iterations. The output tracking error will converge to a profile which can be tuned by design parameters and the learning speed is improved if the learning gain is large.     

Feedback linearisation control of an induction machine augmented by single-hidden layer neural networks

We consider adaptive output feedback control methodology of highly uncertain nonlinear systems with both parametric uncertainties and unmodelled dynamics. The approach is also applicable to systems of unknown, but bounded dimension. However, the relative degree of the regulated output is assumed to be known. This new control strategy is proposed to address the tracking problem of an induction motor based on a modified field-oriented control method. The obtained controller is then augmented by an online neural network that serves as an approximator for the neglected dynamics and modelling errors. The network weight adaptation rule is derived from the Lyapunov stability analysis, that guarantees boundedness of all the error signals of the closed-loop system. Computer simulations of an output feedback controlled induction machine, augmented via single-hidden-layer neural networks, demonstrate the practical potential of the proposed control algorithm.     

Multiple model-based event-triggered adaptive control of a class of discrete-time nonlinear systems

In this study, the problem of event-triggered-based adaptive control (ETAC) for a class of discrete-time nonlinear systems with unknown parameters and nonlinear uncertainties is considered. Both neural network (NN) based and linear identifiers are used to approximate the unknown system dynamics. The feedback output signals are transmitted, and the parameters and the NN weights of the identifiers are tuned in an aperiodic manner at the event sample instants. A switching mechanism is provided to evaluate the approximate performance of each identifier and decide which estimated output is utilised for the event-triggered controller design, during any two events. The linear identifier with an auxiliary output and an improved adaptive law is introduced so that the nonlinear uncertainties are no longer assumed to be Lipschitz. The number of transmission times are significantly reduced by incorporating multiple model schemes into ETAC. The boundedness of both the parameters of identifiers and the system outputs is demonstrated though the Lyapunov approach. Simulation results demonstrate the effectiveness of the proposed method.     

一般严格反馈型非线性系统的自适应控制

研究一般严格反馈型非线性系统的控制问题．假设系统的对象模型、状态均未知,只有输出是可测的．应用自适应模糊神经推断系统辨识对象模型,状态观测器设计为Luenberger型,控制器由反步控制、变结构控制和3层神经网络直接控制综合而成．理论分析和仿真研究都说明此方案能够有效地控制只有输出可测的一般严格反馈型非线性系统．     

Direct adaptive controller for nonaffine nonlinear systems using self-structuring neural networks

A direct adaptive state-feedback controller is proposed for highly nonlinear systems. We consider uncertain or ill-defined nonaffine nonlinear systems and employ a neural network (NN) with flexible structure, i.e., an online variation of the number of neurons. The NN approximates and adaptively cancels an unknown plant nonlinearity. A control law and adaptive laws for the weights in the hidden layer and output layer of the NN are established so that the whole closed-loop system is stable in the sense of Lyapunov. Moreover, the tracking error is guaranteed to be uniformly asymptotically stable (UAS) rather than uniformly ultimately bounded (UUB) with the aid of an additional robustifying control term. The proposed control algorithm is relatively simple and requires no restrictive conditions on the design constants for the stability. The efficiency of the proposed scheme is shown through the simulation of a simple nonaffine nonlinear system.     

Feedback-Linearization-Based Neural Adaptive Control for Unknown Nonaffine Nonlinear Discrete-Time Systems

A new feedback-linearization-based neural network (NN) adaptive control is proposed for unknown nonaffine nonlinear discrete-time systems. An equivalent model in affine-like form is first derived for the original nonaffine discrete-time systems as feedback linearization methods cannot be implemented for such systems. Then, feedback linearization adaptive control is implemented based on the affine-like equivalent model identified with neural networks. Pretraining is not required and the weights of the neural networks used in adaptive control are directly updated online based on the input–output measurement. The dead-zone technique is used to remove the requirement of persistence excitation during the adaptation. With the proposed neural network adaptive control, stability and performance of the closed-loop system are rigorously established. Illustrated examples are provided to validate the theoretical findings.      

非线性系统的神经网络鲁棒自适应跟踪控制

针对一类具有未知非线性函数和未知虚拟系数非线性函数的二阶非线性系统,提出了一种神经网络鲁棒自适应输出跟踪控制方法.用李雅普诺夫稳定性分析方法证明了本文的神经网络自适应控制器能够使受控系统内的所有信号均为有界.选择的神经网络权值调整规律可以防止自适应控制中的参数漂移.     

管式聚合反应器温度分布的动态建模与广义PI控制

针对阳离子聚合反应器的温度分布建模与控制问题,提出了一种基于B样条神经网络的广义PI控制方法.首先采用B样条复合网络建立分布函数的动态和静态模型,并基于该模型,将分布函数的跟踪问题等效为动态权值向量的时间域跟踪问题.最后给出一种新型的广义PI控制方法,实现对给定温度分布的跟踪控制.同时,为了更好地抑制未知干扰、参数摄动以及模型不匹配等问题,模型权值状态、模型输出与实测温度分布所对应的权值误差都被引入到反馈控制回路,因此能够大大增强系统的鲁棒性与抗干扰能力.仿真结果表明该方法的可行性.     

基于控制性能的MIMO非线性系统动态面控制

针对一类不确定非线性MIMO(multiple-input multiple-output)系统,在动态面控制方法的基础上,提出了自适应跟踪控制方案.通过引入性能函数和输出误差转换,保证输出信号具有指定的跟踪速度、跟踪误差、最大超调量.为了避免控制奇异问题,采用神经网络直接逼近期望控制信号.该方案无需估计神经网络的权值,仅对1个参数进行自适应律设计.理论证明了闭环系统所有信号有界,仿真结果验证了所提方案的有效性.     

Adaptive neural output feedback finite-time command filtered backstepping control for nonlinear systems with full-state constraints

In this paper, an adaptive neural finite-time control method via barrier Lyapunov function, command filtered backstepping, and output feedback is proposed to solve the tracking problem of uncertain high-order nonlinear systems with full-state constraints and input saturation. By utilizing the neural network (NN) to approximate unknown nonlinear functions, the finite-time command filters are used to filtering the virtual control signals and get the intermediate control signals in a finite time in the backstepping process. Because there are errors between the output of finite-time command filters and the virtual control signals, the error compensation signals are added to eliminate the influence of filtering errors. Based on the proposed control scheme, the states of the system can be constrained in the predetermined region, all signals in the system are bounded in finite time, and the tracking error can converge to the desired region in finite time. At last, a simulation example is given to show the effectiveness of the proposed control method.     

NN‐Based Output‐Feedback Control for Stochastic Nonlinear Systems with Unknown Control Directions

This paper addresses the neural network‐based output‐feedback control problem for a class of stochastic nonlinear systems with unknown control directions. The restrictions on the drift and diffusion terms are removed and the conditions on unknown control directions are relaxed. By introducing a proper coordinate transformation, and combining dynamic surface control (DSC) technique with radial basis function neural network (RBF NN) approximation approach, we construct an adaptive output‐feedback controller to guarantee the closed‐loop system to be mean square semi‐globally uniformly ultimately bounded (M‐SGUUB). A simulation example demonstrates the effectiveness of the proposed scheme.     

NONLINEAR NETWORK STRUCTURES FOR FEEDBACK CONTROL

A framework is given for controller design using Nonlinear Network Structures, which include both neural networks and fuzzy logic systems. These structures possess a universal approximation property that allows them to be used in feedback control of unknown systems without requirements for linearity in the system parameters or finding a regression matrix. Nonlinear nets can be linear or nonlinear in the tunable weight parameters. In the latter case weight tuning algorithms are not straightforward to obtain. Feedback control topologies and weight tuning algorithms are given here that guarantee closed-loop stability and bounded weights. Extensions are discussed to force control, backstepping control, and output feedback control, where dynamic nonlinear nets are required.     

An RBF neural network-based adaptive control for SISO linearisable nonlinear systems

An RBF neural network-based adaptive control is proposed for Single-Input and Single-Output (SISO) linearisable nonlinear systems in this paper. It is shown that a SISO nonlinear system is first linearised by using the differential geometric approach in the state space, and the linearised nonlinear system is then treated as a partially known system. The known dynamics are used to design a nominal feedback controller to stabilise the nominal system, and an adaptive RBF neural network-based compensator is then designed to compensate for the effects of uncertain dynamics. The main function of the RBF neural network in this work is to adaptively learn the upper bound of the system uncertainty, and the output of the neural network is then used to adaptively adjust the gain of the compensator so that the strong robustness with respect to unknown dynamics can be obtained, and the tracking error between the plant output and the desired reference signal can asymptotically converge to zero. A simulation example is performed in support of the proposed scheme.     

高频增益未知的受扰非线性系统输出反馈控制

针对一类具有未知定常参数,包括未知高频增益的受扰非线性最小相位系统,给出了一种鲁棒自适应输出反馈控制策略．系统所受的干扰假设有界,但其界值是未知的．通过采用自适应策略来对其界值进行在线估计,控制算法并不需要高频增益符号的先验知识．同时,系统中的非线性项并不要求满足增长性条件和匹配条件．算法使得估计参数量达到了最小,保证了闭环系统所有信号的有界性,同时使得跟踪误差渐近收敛于零．     

基于神经网络的一类非线性系统自适应跟踪控制

提出一种非线性系统的自适应神经跟踪控制方案。通过利用RBF神经网络对未知非线性系统建模,并用一个滑模控制项消除网络建模误差和外部干扰的影响,从而能够保证闭环系统的全局稳定性和输出跟踪误差渐近收敛于零。     

基于遗传算法学习的复合神经网络自适应温度控制系统

针对一类温度控制系统中存在的非线性和参数不确定等问题,提出一种复合神经网络自适应控制结构.在控制系统中构造了神经网络正模型来再现被控对象的动态特性,用神经网络控制器实现优化控制律的非线性映射.文中选用了被控对象80组历史数据作为样本集,并利用遗传算法的全局搜索能力及高效率来训练多层前向神经网络的权系数.最后用升降温工艺曲线作为输入对温度控制系统进行仿真.仿真结果表明,应用遗传算法能够提高神经网络的学习效率.保证神经网络全局快速收敛,从而克服了传统的误差反传学习算法的一些缺点.证明了采用这种神经网络自适应控制结构.使神经网络控制器的输出可以适应对象参数和环境的变化.使温度控制系统具有很好的学习和自适应控制能力,取得了良好的控制效果.