Adaptive neural control for a class of uncertain nonlinear systems with unknown time delay

A neural network (NN)‐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 unknown time delay. By approximating on‐line the unknown nonlinear functions with a three‐layer feedforward NN, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. The control law is delay independent and possible controller singularity problem is avoided. It is proved that with the proposed neural control law, all the signals in the closed‐loop system are semiglobally bounded in the presence of unknown time delay and unknown nonlinearity. A simulation example is presented to demonstrate the method. Copyright © 2008 John Wiley & Sons, Ltd.     

船舶航向控制的多滑模鲁棒自适应设计

针对带有未知虚拟控制增益和常参数不确定的非匹配不确定船舶航向非线性控制问题,设计了一种新的多滑模鲁棒自适应控制算法.该算法利用神经网络来逼近系统模型的不确定性;应用逐步递推的多滑模控制算法降低了控制器的复杂性;尤其是采用Nussbaum函数处理系统中符号未知的问题,避免了可能存在的控制器奇异值问题;然后借助Lyapunov稳定性分析方法,理论分析证明了所得闭环系统全局一致最终有界,且跟踪误差收敛到零.仿真试验结果表明,该方法具有较好的控制效果.     

Neural Network Identification Based Multivariable Feedback Linearization Robust Control for a Two-Link Manipulator

Regarding to the variations of the load and unmodeled dynamic, robot manipulators are known as a nonlinear dynamic system. Overcoming such problems like uncertainties and nonlinear characteristics in the model of two-link manipulator is the principal goal of this paper. To approach to this aim, a neural network is combined with a linear robust control in which the result has the advantages of, the first, approximated nonlinear elements and the second, the guaranteed robustness. To design the proposed controller, at first, multivariable feedback linearization is employed to convert the nonlinear model to linear one. Second, the unknown parameters of the system are identified by neural network based on a new proposed learning rule. Third, Mixed linear feedback-H_?∞? robust control method is proposed to stabilize the closed loop system. The closed loop system based on the proposed controller is analyzed and some numerical simulations are performed. Results show suitable responses of the closed loop system.     

Multi machine power system excitation control design via theories of feedback linearization control and nonlinear robust control

The dynamics of a large-scale power system are both nonlinear and interconnected. The equilibrium of such a system is typically unknown and uncertain, and the controllers within are also subject to physical limitations. In this paper, a new application of nonlinear robust control is presented for power system control design. It is assumed that the controllers are designed as a part of generator excitation system design. First, a customized exact feedback linearization scheme is developed for the power system under investigation. This new linearization scheme allows one to transform the power system with a single-axis system model into a linear uncertain system with an unknown equilibrium. Based on the latest development of nonlinear robust control theory, a novel control design is then applied to stabilize the resulting linearized uncertain system. Finally, a nonlinear decentralized excitation control is obtained by the inverse transformation. Compared with existing control schemes, the proposed control is free from such common deficiencies of power system nonlinear controllers as network dependence and equilibrium dependence. Detailed stability analysis and engineering judgment in the control design are provided. The results of simulation studies are presented.     

Distributed learning consensus control based on neural networks for heterogeneous nonlinear multiagent systems

This paper considers a novel distributed iterative learning consensus control algorithm based on neural networks for the control of heterogeneous nonlinear multiagent systems. The system's unknown nonlinear function is approximated by suitable neural networks; the approximation error is countered by a robust term in the control. Two types of control algorithms, both of which utilize distributed learning laws, are provided to achieve consensus. In the provided control algorithms, the desired reference is considered to be an unknown factor and then estimated using the associated learning laws. The consensus convergence is proven by the composite energy function method. A numerical simulation is ultimately presented to demonstrate the efficacy of the proposed control schemes.     

基于干扰观测器的一类不确定仿射非线性系统有限时间收敛backstepping控制

针对一类不确定仿射非线性系统的跟踪控制问题,提出一种基于干扰观测器的有限时间收敛backstepping控制方法.为增强小脑模型(CMAC)泛化和学习能力,将非对称高斯函数和模糊理论相结合,给出非对称模糊CMAC结构,设计干扰观测器实现系统未知复合干扰在线准确逼近;基于非对称模糊CMAC干扰观测器,给出有限时间收敛backstepping控制器设计步骤,利用Lyapunov稳定理论证明闭环系统稳定性,其中采用非线性微分器获取虚拟控制量滤波和微分信息以避免backstepping设计中的微分“膨胀问题”,设计辅助系统修正因微分器带来的误差对系统跟踪性能影响,引入基于障碍型函数的自适应滑模鲁棒项抑制复合干扰估计偏差对跟踪误差的影响;将所提方法应用于无人机飞行控制仿真实验,结果表明所提方法的有效性.     

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.      

Contact Friction Compensation for Robots Using Genetic Learning Algorithms

In this paper, the issues of contact friction compensation for constrained robots are presented. The proposed design consists of two loops. The inner loop is for the inverse dynamics control which linearizes the system by canceling nonlinear dynamics, while the outer loop is for friction compensation. Although various models of friction have been proposed in many engineering applications, frictional force can be modeled by the Coulomb friction plus the viscous force. Based on such a model, an on-line genetic algorithm is proposed to learn the friction coefficients for friction model. The friction compensation control input is also implemented in terms of the friction coefficients to cancel the effect of unknown friction. By the guidance of the fitness function, the genetic learning algorithm searches for the best-fit value in a way like the natural surviving laws. Simulation results demonstrate that the proposed on-line genetic algorithm can achieve good friction compensation even under the conditions of measurement noise and system uncertainty. Moreover, the proposed control scheme is also found to be feasible for friction compensation of friction model with Stribeck effect and position-dependent friction model.     

Model Predictive Control of Nonlinear Discrete Time Systems with Guaranteed Stability

This paper presents the design of a new robust model predictive control algorithm for nonlinear systems represented by a linear model with unstructured uncertainty. The linear model is obtained by linearizing the nonlinear system at an operating point and the difference between the nonlinear and linear model is considered as a Lipschitz nonlinear function. The controller is designed for the linear model, which fulfills the stabilization condition for the nonlinear term. Unlike previous studies that have not considered a valid Lipschitz matrix of nonlinear term in the design process, we propose an algorithm in this paper in which it is considered. Therefore, the closed loop stability of the nonlinear system is guaranteed. A novel SOS optimization problem to determine design parameters is introduced, which leads to improved closed‐loop performance in comparison to a trial and error tuning procedure. Furthermore, an algorithm is presented to enlarge the region of attraction for the nonlinear closed‐loop system. Stability is improved by checking some additional conditions if which the system may be unstable if not considered. The validity of the proposed algorithm is confirmed by examples.     

Operator-based robust nonlinear control system design for MIMO nonlinear plants with unknown coupling effects

In this article, operator-based robust nonlinear control system design for multi-input multi-output (MIMO) plants with unknown coupling effects is considered. That is, by using operator-based robust nonlinear control design, coupling effects existing in the MIMO nonlinear plants can be decoupled based on a feedback design and robust right coprime factorisation approach, the coupling effects caused by controllers and plant outputs can be stabilised by using definition of Lipschitz operator and contraction mapping theorem, and output tracking performance can be realised by a tracking design scheme. Finally, a simulation example about temperature control process of 3-input/3-output aluminum plate is given to support the theoretical analysis.     

未知相对度非线性系统的一阶D型迭代学习控制

The classical D-type iterative learning control law depends crucially on the relative degree of the controlled system, high order differential iterative learning law must be taken for systems with high order relative degree. It is very difficult to ascertain the relative degree of the controlled system for uncertain nonlinear systems. A first-order D-type iterative learning control design method is presented for a class of nonlinear systems with unknown relative degree based on dummy model in this paper. A dummy model with relative degree 1 is constructed for a class of nonlinear systems with unknown relative degree. A first-order D-type iterative learning control law is designed based on the dummy model, so that the dummy model can track the desired trajectory perfectly, and the controlled system can track the desired trajectory within a certain error. The simulation example demonstrates the feasibility and effectiveness of the presented method.     

Neural network robust control of a 3-DOF hydraulic manipulator with asymptotic tracking

Multiaxial hydraulic manipulators are complicated systems with highly nonlinear dynamics and various modeling uncertainties, which hinders the development of high-performance controller. In this paper, a neural network feedforward with a robust integral of the sign of the error (RISE) feedback is proposed for high precise tracking control of hydraulic manipulator systems. The established nonlinear model takes three-axis dynamic coupling, hydraulic actuator dynamics, and nonlinear friction effects into consideration. A radial basis function neural network (RBFNN) is synthesized to approximate the uncertain system dynamics and external disturbance, which can greatly reduce the dependence on accurate system model. In addition, a continuous RISE feedback law is judiciously integrated to deal with the residual unknown dynamics. Since the major unknown dynamics can be estimated by the RBFNN and then compensated in the feedforward design, the high-gain feedback issue in RISE feedback control will be avoided. The proposed RISE-based neural network robust controller theoretically guarantees an excellent semi-global asymptotic stability. Comparative simulation is performed on a 3-DOF hydraulic manipulator, and the obtained results verify the effectiveness of the proposed controller.     

Integrated guidance and control of elastic flight vehicle based on robust MPC

Integrated guidance and control of an elastic flight vehicle based on constrained robust model predictive control is proposed. The design is based on a partial state feedback control law that minimizes a cost function within the framework of linear matrix inequalities. It is shown that the solution of the defined optimization problem stabilizes the nonlinear plant. Nonlinear kinematics and dynamics are taken into account, and internal stability of the closed‐loop nonlinear system is guaranteed. The performance and effectiveness of the proposed integrated guidance and control against non‐maneuvering and weaving targets are evaluated using computer simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental comparison of PID vs. PID plus nonlinear controller for subsea robots

This paper presents a new approach for designing simple nonlinear robust controllers for underwater vehicles. The paper presents several in-water experiments performed on the VORTEX vehicle developed by IFREMER. We first introduce some general modeling considerations of underwater vehicles, then we present the VORTEX dynamic model and some of the special features of the VORTEX vehicle that are important for control. Among these, low sampling rates for sensor and actuator nonlinearities are considered. The main aim of this paper is to experimentally investigate the benefits of adding an easy-to-tune nonlinear control loop to the actual linear compensator in order to improve the stability and the disturbance rejection properties of the closed-loop system. The advantage of this method is two-fold. First the additional nonlinear loop does not modify the original linear (PID) regulator. Second the design of this additional loop does not rely on the system model and is simple to tune. The results presented in this paper were obtained using the VORTEX vehicle both in simulation and during real experiments; they demonstrate the advantages of using a PID with this nonlinear loop over a simple PID control.     

基于DSC后推法的非线性系统的鲁棒自适应NN控制

针对一类具有不确定系统函数和方向未知的不确定增益函数的非线性系统, 提出了一种鲁棒自适应神经网络控制算法. 本算法采用RBF神经网络(Radial based function neural network, RBF NN)逼近模型不确定性, 外界干扰和建模误差采用非线性阻尼项进行补偿, 将动态面控制(Dynamic surface control, DSC)与后推方法结合, 消除了反推法的计算膨胀问题, 降低了控制器的复杂性; 尤其是采用Nussbaum函数处理系统中方向未知的不确定虚拟控制增益函数, 不仅可以避免可能存在的控制器奇异值问题, 而且还能使得整个系统的在线学习参数显著减少, 与DSC方法优点结合, 使得控制算法的计算量大为减少, 便于计算机实现. 稳定性分析证明了所得闭环系统是半全局一致最终有界(Semi-global uniformly ultimately bounded, SGUUB)的, 并且跟踪误差可以收敛到原点的一个较小邻域. 最后, 计算机仿真结果表明了本文所提出控制器的有效性.     

Robust Decentralized Adaptive Fuzzy Control of Large‐Scale Nonaffine Nonlinear Systems With Strong Interconnection and Application to Automated Highway Systems

A novel decentralized adaptive fuzzy controller is developed for a class of large‐scale uncertain nonaffine nonlinear systems in this paper. Incorporating the benefits of fuzzy systems, implicit function theorem, and robust control technique, the interconnections between subsystems are extended to general unknown nonlinear functions. No a priori knowledge of lower and upper bounds on lumped uncertainties is required to implement each local controller. The resulting closed‐loop large‐scale system is proved to be asymptotically stable. The controller design is applicable to an automated highway system and simulation results confirm its practical usefulness.     

基于深度学习的四旋翼无人机地面效应补偿降落控制设计

针对四旋翼无人机在降落控制过程中地面效应对控制性能有较大影响的问题,在地面效应复杂,难以建立机理模型的约束下,提出一种基于深度学习的新型非线性鲁棒控制策略.利用深度神经网络的学习能力,建立无人机降落过程中未知地面效应的补偿模型;结合super-twisting控制设计,实现对降落过程中未知地面效应的快速抑制和无人机降落的精确控制;通过Lyapunov分析法和谱归一化法,证明降落过程中闭环系统的稳定性和无人机位置误差的有限时间收敛特性.实时飞行实验结果表明,所提出的控制策略具有较好的控制效果.     

A New Robust Adaptive Neural Network Backstepping Control for Single Machine Infinite Power System With TCSC

For a single machine infinite power system with thyristor controlled series compensation (TCSC) device, which is affected by system model uncertainties, nonlinear time-delays and external unknown disturbances, we present a robust adaptive backstepping control scheme based on the radial basis function neural network (RBFNN). The RBFNN is introduced to approximate the complex nonlinear function involving uncertainties and external unknown disturbances, and meanwhile a new robust term is constructed to further estimate the system residual error, which removes the requirement of knowing the upper bound of the disturbances and uncertainty terms. The stability analysis of the power system is presented based on the Lyapunov function, which can guarantee the uniform ultimate boundedness (UUB) of all parameters and states of the whole closed-loop system. A comparison is made between the RBFNN-based robust adaptive control and the general backstepping control in the simulation part to verify the effectiveness of the proposed control scheme.      

Adaptive Fault‐Tolerant Control of Uncertain MIMO Systems with Reduced Requirement on Desired Trajectory Under Unknown Control Direction

This paper aims at investigating the tracking control problem for a class of multi‐input multi‐output (MIMO) nonlinear systems with non‐square control gain matrix subject to unknown control direction and uncertain desired trajectory. By using the artificial neural network (NN) reconstructs the target trajectory with actual disguised trajectory, we are able to design a practical and stable tracking control scheme without the need for the unavailable desired trajectory. Nussbaum‐type function is incorporated in the control law to handle the unknown control direction. The remarkable feature of the proposed scheme is that it is robust against modeling uncertainties and tolerant to actuation faults, yet guarantees that the closed‐loop system is stable in the sense of ultimately uniformly bounded (UUB). The effectiveness of the proposed control schemes are illustrated through simulation results.     

Adaptive Iterative Learning Control for a Class of Nonlinear Time-varying Systems with Unknown Delays and Input Dead-zone

This paper presents an adaptive iterative learning control (AILC) scheme for a class of nonlinear systems with unknown time-varying delays and unknown input dead-zone. A novel nonlinear form of dead-zone nonlinearity is presented. The assumption of identical initial condition for iterative learning control (ILC) is removed by introducing boundary layer function. The uncertainties with time-varying delays are compensated for by using appropriate Lyapunov-Krasovskii functional and Young0s inequality. Radial basis function neural networks are used to model the time-varying uncertainties. The hyperbolic tangent function is employed to avoid the problem of singularity. According to the property of hyperbolic tangent function, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while keeping all the closedloop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.