Direct adaptive iterative learning control of nonlinear systems using an output-recurrent fuzzy neural network

In this paper, a direct adaptive iterative learning control (DAILC) based on a new output-recurrent fuzzy neural network (ORFNN) is presented for a class of repeatable nonlinear systems with unknown nonlinearities and variable initial resetting errors. In order to overcome the design difficulty due to initial state errors at the beginning of each iteration, a concept of time-varying boundary layer is employed to construct an error equation. The learning controller is then designed by using the given ORFNN to approximate an optimal equivalent controller. Some auxiliary control components are applied to eliminate approximation error and ensure learning convergence. Since the optimal ORFNN parameters for a best approximation are generally unavailable, an adaptive algorithm with projection mechanism is derived to update all the consequent, premise, and recurrent parameters during iteration processes. Only one network is required to design the ORFNN-based DAILC and the plant nonlinearities, especially the nonlinear input gain, are allowed to be totally unknown. Based on a Lyapunov-like analysis, we show that all adjustable parameters and internal signals remain bounded for all iterations. Furthermore, the norm of state tracking error vector will asymptotically converge to a tunable residual set as iteration goes to infinity. Finally, iterative learning control of two nonlinear systems, inverted pendulum system and Chua's chaotic circuit, are performed to verify the tracking performance of the proposed learning scheme.     

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.     

基于确定学习的机器人任务空间自适应神经网络控制

针对产生回归轨迹的连续非线性动态系统, 确定学习可实现未知闭环系统动态的局部准确逼近. 基于确定学习理论, 本文使用径向基函数(Radial basis function, RBF)神经网络为机器人任务空间跟踪控制设计了一种新的自适应神经网络控制算法, 不仅实现了闭环系统所有信号的最终一致有界, 而且在稳定的控制过程中, 沿着回归跟踪轨迹实现了部分神经网络权值收敛到最优值以及未知闭环系统动态的局部准确逼近. 学过的知识以时不变且空间分布的方式表达、以常值神经网络权值的方式存储, 可以用来改进系统的控制性能, 也可以应用到后续相同或相似的控制任务中, 节约时间和能量. 最后, 用仿真说明了所设计控制算法的正确性和有效性.     

一类非线性系统的神经网络自适应区间观测器设计

本文研究了一类单输入单输出非线性系统的神经网络自适应区间观测器设计问题. 针对由状态和输入所描述的未知非线性函数的界不可测, 现有的区间观测器方法并未有效地处理系统含有参数不确定性的未知非线性函数. 首先, 本文构造两个径向基函数神经网络来逼近未知非线性部分, 进而分别估计系统状态的上下界; 然后, 选择合适的Lyapunov函数, 采用网络权值校正和网络误差选择机制确保所设计的误差动态系统有界和非负性, 并证明了神经网络自适应区间观测器的稳定性; 最后, 通过仿真实例验证了所提出的神经网络自适应区间观测器的有效性.     

An efficient decentralized robust adaptive controller for a class of large-scale non-affine nonlinear systems with strong interactions

This paper proposed a novel combination of decentralized robust adaptive radial basis neural network controller for a class of large-scale nonlinear non-affine systems with unknown subsystems and strong interconnections. Some suitable adaptive rules based on neural network are introduced that make all signals bounded, and also Lyapunov theory guaranteed tracking error signal asymptotically reaches zero. To show the effectiveness of the proposed method, some numerical results are presented. Furthermore, to evaluate the performance of the suggested method, a decentralized adaptive method is adopted from the literature and applied for comparison. Simulation results verify the desirable performance of the proposed controller.     

Adaptive neural control for pure-feedback nonlinear time-delay systems with unknown dead-zone: a Lyapunov-Razumikhin method

This paper addresses the problem of adaptive neural control for a class of uncertain pure-feedback nonlinear systems with multiple unknown state time-varying delays and unknown dead-zone. Based on a novel combination of the Razumikhin functional method, the backstepping technique and the neural network parameterization, an adaptive neural control scheme is developed for such systems. All closed-loop signals are shown to be semiglobally uniformly ultimately bounded, and the tracking error remains in a small neighborhood of the origin. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control schemes.     

Synthesis of the sliding-mode neural network controller for unknown nonlinear discrete-time systems

This paper develops a sliding-mode neural network controller for a class of unknown nonlinear discrete-time systems using a recurrent neural network (RNN). The control scheme is based on a linearized expression of the nonlinear system using a linear neural network (LNN). The control law is proposed according to the discrete L yapunov theory. With a modified real-time recurrent learning algorithm, the RNN as an estimator is used to estimate the unknown part in the control law in on-line fashion. The stability of the control system is guaranteed owing to the on-line learning ability of the RNN algorithm. The proposed control scheme is applied to numerical problems and simulation results that it is very effective.     

State estimation in MIMO nonlinear systems subject to unknown deadzones using recurrent neural networks

This paper deals with the problem of state observation by means of a continuous-time recurrent neural network for a broad class of MIMO unknown nonlinear systems subject to unknown but bounded disturbances and with an unknown deadzone at each input. With respect to previous works, the main contribution of this study is twofold. On the one hand, the need of a matrix Riccati equation is conveniently avoided; in this way, the design process is considerably simplified. On the other hand, a faster convergence is carried out. Specifically, the exponential convergence of Euclidean norm of the observation error to a bounded zone is guaranteed. Likewise, the weights are shown to be bounded. The main tool to prove these results is Lyapunov-like analysis. A numerical example confirms the feasibility of our proposal.     

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control (AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance. To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control (ILC), a new boundary layer function is proposed by employing Mittag-Leffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function (CEF) containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.      

A New Neuro-FDS Definition for Indirect Adaptive Control of Unknown Nonlinear Systems Using a Method of Parameter Hopping

The indirect adaptive regulation of unknown nonlinear dynamical systems is considered in this paper. The method is based on a new neuro-fuzzy dynamical system (neuro-FDS) definition, which uses the concept of adaptive fuzzy systems (AFSs) operating in conjunction with high-order neural network functions (FHONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of an FDS and then the fuzzy rules are approximated by appropriate HONNFs. Thus, the identification scheme leads up to a recurrent high-order neural network (RHONN), which however takes into account the fuzzy output partitions of the initial FDS. The proposed scheme does not require a priori experts' information on the number and type of input variable membership functions making it less vulnerable to initial design assumptions. Once the system is identified around an operation point, it is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The existence of the control signal is always assured by introducing a novel method of parameter hopping, which is incorporated in the weight updating law. Simulations illustrate the potency of the method and comparisons with conventional approaches on benchmarking systems are given. Also, the applicability of the method is tested on a direct current (dc) motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation.     

Linearization and state estimation of unknown discrete-timenonlinear dynamic systems using recurrent neurofuzzy networks

Model-based methods for the state estimation and control of linear systems have been well developed and widely applied. In practice, the underlying systems are often unknown and nonlinear. Therefore, data based model identification and associated linearization techniques are very important. Local linearization and feedback linearization have drawn considerable attention in recent years. In this paper, linearization techniques using neural networks are reviewed, together with theoretical difficulties associated with the application of feedback linearization. A recurrent neurofuzzy network with an analysis of variance (ANOVA) decomposition structure and its learning algorithm are proposed for linearizing unknown discrete-time nonlinear dynamic systems. It can be viewed as a method for approximate feedback linearization, as such it enlarges the class of nonlinear systems that can be feedback linearized using neural networks. Applications of this new method to state estimation are investigated with realistic simulation examples, which shows that the new method has useful practical properties such as model parametric parsimony and learning convergence, and is effective in dealing with complex unknown nonlinear systems.     

控制方向未知的二阶时变非线性系统自适应迭代学习控制

对一类二阶严格反馈时变非线性系统的自适应迭代学习控制问题进行了研究.系统中含有非周期时变参数化不确定性且控制方向未知.首先,提出了一种神经网络估计器,实现了对未知非周期时变非线性函数的逼近.随后,用Nussbaum函数对未知控制方向进行了自适应估计,并综合应用baCkstcpping技术和自适应迭代学习控制技术设计了控制器.所设计的控制器能保证系统所有状态量在Lpe-范数意义下有界,且系统的输出量在LT2-范数意义下收敛到期望轨迹.最后的仿真研究证明了控制器设计方法的有效性.     

Adaptive Neural Network-Based Control for a Class of Nonlinear Pure-Feedback Systems With Time-Varying Full State Constraints

In this paper, an adaptive neural network (NN) control approach is proposed for nonlinear pure-feedback systems with time-varying full state constraints. The pure-feedback systems of this paper are assumed to possess nonlinear function uncertainties. By using the mean value theorem, pure-feedback systems can be transformed into strict feedback forms. For the newly generated systems, NNs are employed to approximate unknown items. Based on the adaptive control scheme and backstepping algorithm, an intelligent controller is designed. At the same time, time-varying Barrier Lyapunov functions (BLFs) with error variables are adopted to avoid violating full state constraints in every step of the backstepping design. All closedloop signals are uniformly ultimately bounded and the output tracking error converges to the neighborhood of zero, which can be verified by using the Lyapunov stability theorem. Two simulation examples reveal the performance of the adaptive NN control approach.      

Prediction and identification using wavelet-based recurrent fuzzy neural networks

This paper presents a wavelet-based recurrent fuzzy neural network (WRFNN) for prediction and identification of nonlinear dynamic systems. The proposed WRFNN model combines the traditional Takagi-Sugeno-Kang (TSK) fuzzy model and the wavelet neural networks (WNN). This paper adopts the nonorthogonal and compactly supported functions as wavelet neural network bases. Temporal relations embedded in the network are caused by adding some feedback connections representing the memory units into the second layer of the feedforward wavelet-based fuzzy neural networks (WFNN). An online learning algorithm, which consists of structure learning and parameter learning, is also presented. The structure learning depends on the degree measure to obtain the number of fuzzy rules and wavelet functions. Meanwhile, the parameter learning is based on the gradient descent method for adjusting the shape of the membership function and the connection weights of WNN. Finally, computer simulations have demonstrated that the proposed WRFNN model requires fewer adjustable parameters and obtains a smaller rms error than other methods.     

Adaptive recurrent neural network control using a structure adaptation algorithm

This paper proposes an adaptive recurrent neural network control (ARNNC) system with structure adaptation algorithm for the uncertain nonlinear systems. The developed ARNNC system is composed of a neural controller and a robust controller. The neural controller which uses a self-structuring recurrent neural network (SRNN) is the principal controller, and the robust controller is designed to achieve L ² tracking performance with desired attenuation level. The SRNN approximator is used to online estimate an ideal tracking controller with the online structuring and parameter learning algorithms. The structure learning possesses the ability of both adding and pruning hidden neurons, and the parameter learning adjusts the interconnection weights of neural network to achieve favorable approximation performance. And, by the L ² control design technique, the worst effect of approximation error on the tracking error can be attenuated to be less or equal to a specified level. Finally, the proposed ARNNC system with structure adaptation algorithm is applied to control two nonlinear dynamic systems. Simulation results prove that the proposed ARNNC system with structure adaptation algorithm can achieve favorable tracking performance even unknown the control system dynamics function.     

控制方向未知的不确定系统预设性能自适应神经网络反演控制

对一类控制方向未知的不确定严格反馈非线性系统的预设性能自适应神经网络反演控制问题进行了研究.系统中含有时变非匹配不确定项且控制方向未知.首先,提出了一种新的误差转化方法,放宽了对初始误差已知的限制;随后,利用径向基函数(radial basis function,RBF)神经网络及跟踪微分器分别实现了对未知函数和虚拟控制量导数的逼近,并综合运用Nussbaum函数和反演控制技术设计了控制器.所设计的控制器能保证系统内所有信号有界且输出误差满足预设的瞬态和稳态性能要求.最后的仿真研究验证了控制器设计方法的有效性.     

输入饱和的一类切换系统神经网络跟踪控制

针对单输入单输出系统研究一种在任意切换下的跟踪控制问题,系统包含未知扰动和输入饱和特性.首先,利用高斯误差函数描述一个连续可导的非对称饱和模型.其次,利用径向基神经网络（Radial basis function neural network,RBF NN）逼近未知的系统动态.最后,基于公共的Lyapunov函数构造状态反馈控制器.设计的控制器避免过多参数调节从而减轻计算负荷.结果展示本文给出的状态反馈控制器可以保证闭环系统的所有信号是半全局一致有界的,并且跟踪误差可收敛到零值小的领域内.最后的仿真结果进一步验证提出方法的有效性.     

Direct adaptive robust NN control for a class of discrete-time nonlinear strict-feedback SISO systems

In this paper, a direct adaptive neural network control algorithm based on the backstepping technique is proposed for a class of uncertain nonlinear discrete-time systems in the strict-feedback form. The neural networks are utilized to approximate unknown functions, and a stable adaptive neural network controller is synthesized. The fact that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded is proven and the tracking error can converge to a small neighborhood of zero by choosing the design parameters appropriately. Compared with the previous research for discrete-time systems, the proposed algorithm improves the robustness of the systems. A simulation example is employed to illustrate the effectiveness of the proposed algorithm.     

A Wiener-type recurrent neural network and its control strategy for nonlinear dynamic applications

This paper presents a Wiener-type recurrent neural network with a systematic identification algorithm and a control strategy for the identification and control of unknown dynamic nonlinear systems. The proposed Wiener-type recurrent network resembles the conventional Wiener model that consists of a dynamic linear subsystem cascaded with a static nonlinear subsystem. The novelties of our network include: (1) the two subsystems are integrated into a single network whose output is expressed by a nonlinear transformation of a linear state-space equation; (2) the characteristics of the trained network can be analyzed by its associated state-space equation using the well-developed theory of linear systems; and (3) the size of the network structure is determined by the number of state variables (or the system order) of the unknown systems to be identified. To effectively identify a given unknown system from its input–output data, we have developed a systematic identification algorithm that consists of an order determination procedure, a parameterization procedure, and an online learning procedure. The false nearest neighbors algorithm was adopted to acquire a minimal embedding dimension from the input–output data as the system order, and then the eigensystem realization algorithm (ERA) was used to initialize a best-fit state-space representation according to the acquired system order. To improve the overall identification performance, we have derived an online parameter learning algorithm based on an ordered derivatives and momentum terms. Subsequently, a simple feedback linear controller was designed to control the unknown dynamic nonlinear systems without much complexity. Computer simulations and comparisons with some existing recurrent networks have conducted to confirm the effectiveness and superiority of the proposed Wiener-type network, identification algorithm and control strategy.     

An algorithmic approach to adaptive state filtering using recurrentneural networks

Practical algorithms are presented for adaptive state filtering in nonlinear dynamic systems when the state equations are unknown. The state equations are constructively approximated using neural networks. The algorithms presented are based on the two-step prediction-update approach of the Kalman filter. The proposed algorithms make minimal assumptions regarding the underlying nonlinear dynamics and their noise statistics. Non-adaptive and adaptive state filtering algorithms are presented with both off-line and online learning stages. The algorithms are implemented using feedforward and recurrent neural network and comparisons are presented. Furthermore, extended Kalman filters (EKFs) are developed and compared to the filter algorithms proposed. For one of the case studies, the EKF converges but results in higher state estimation errors that the equivalent neural filters. For another, more complex case study with unknown system dynamics and noise statistics, the developed EKFs do not converge. The off-line trained neural state filters converge quite rapidly and exhibit acceptable performance. Online training further enhances the estimation accuracy of the developed adaptive filters, effectively decoupling the eventual filter accuracy from the accuracy of the process model.