Nonlinear system control using a self-organizing functional-linked neuro-fuzzy network

This study presents a self-organizing functional-linked neuro-fuzzy network (SFNN) for a nonlinear system controller design. An online learning algorithm, which consists of structure learning and parameter learning of a SFNN, is presented. The structure learning is designed to determine the number of fuzzy rules and the parameter learning is designed to adjust the parameters of membership function and corresponding weights. Thus, an adaptive self-organizing functional-linked neuro-fuzzy control (ASFNC) system, which is composed of a computation controller and a robust compensator, is proposed. In the computation controller, a SFNN observer is utilized to approximate the system dynamic and the robust compensator is designed to eliminate the effect of the approximation error introduced by the SFNN observer upon the system stability. Finally, to show the effectiveness of the proposed ASFNC system, it is applied to a chaotic system. The simulation results demonstrate that favorable control performance can be achieved by the proposed ASFNC scheme without any knowledge of the control plants and without requiring preliminary offline tuning of the SFNN observer.     

Neural-network-based adaptive robust precision motion control of linear motors with asymptotic tracking performance

High precision motion control of permanent magnet linear motors (PMLMs) is limited by undesired nonlinear dynamics, parameter variations, and unstructured uncertainties. To tackle these problems, this paper presents a neural-network-based adaptive robust precision motion control scheme for PMLMs. The presented controller contains a robust feedback controller and an adaptive compensator. The robust controller is designed based on the robust integral of the sign of the error method, and the adaptive compensator consists of a neural network component and a parametric component. Moreover, a composite learning law is designed for the parameter adaption in the compensator to further enhance the control performance. Rigorous stability analysis is provided by using the Lyapunov theory, and asymptotic tracking is theoretically achieved. The effectiveness of the proposed method is verified by comparative simulations and experiments on a PMLM-driven motion stage.

     

考虑摩擦特性的柔性关节空间机器人自适应CMAC神经网络鲁棒控制

讨论了关节摩擦力矩影响下,具有柔性铰关节的漂浮基空间机器人系统的动力学控制问题.设计了基于高斯基函数的小脑神经网络(CMAC)鲁棒控制器和摩擦力矩补偿器.用奇异摄动理论对系统的动力学模型进行快慢变子系统分解,针对快变子系统,设计力矩微分反馈控制器来抑制机械臂关节柔性引起的振动;对于慢变子系统,设计了基于自适应CMAC神...     

Adaptive exponential-reaching sliding-mode control for antilock braking systems

Most commercial antilock braking system (ABS) is based on a look-up table. The table is calibrated through laboratory experiments and engineering field tests under specified road conditions, but it is not adaptive. To attack this problem, this paper proposes an adaptive exponential-reaching sliding-mode control (AERSMC) system for an ABS. The proposed AERSMC system is composed of an equivalent controller and an exponential compensator. The equivalent controller uses a functional-linked wavelet neural network (FWNN) to online approximate the system uncertainties and the exponential compensator is designed to eliminate the effect of the approximation error introduced by the FWNN uncertain observer with an exponential-reaching law. In addition, the adaptive laws online-tune the controller parameters in the sense of Lyapunov function to guarantee the system stability. Finally, the simulation results verify that the proposed AERSMC system can achieve favorable slip tracking performance and is robust against parameter variations in the plant.     

Discrete adaptive fuzzy control for asymptotic tracking of robotic manipulators

This paper presents a novel discrete adaptive fuzzy controller for electrically driven robot manipulators. It addresses how to overcome the nonlinearity, uncertainties, discretizing error and approximation error of the fuzzy system for asymptotic tracking control of robotic manipulators. The proposed controller is model-free in the form of discrete Mamdani fuzzy controller. The parameters of fuzzy controller are adaptively tuned using an adaptive mechanism derived by stability analysis. A robust control term is used to compensate the approximation error of the fuzzy system for asymptotic tracking of a desired trajectory. The controller is robust against all uncertainties associated with the robot manipulator and actuators. It is easy to implement since it requires only the joint position feedback. Compared with fuzzy controllers which employ all states to guarantee stability, the proposed controller is very simpler. Stability analysis and simulation results show its efficiency in the tracking control.     

A particle swarm optimization approach for fuzzy sliding mode control for tracking the robot manipulator

In this paper, an optimal fuzzy sliding mode controller is used for tracking the position of robot manipulator, is presented. In the proposed control, initially by using inverse dynamic method, the known sections of a robot manipulator’s dynamic are eliminated. This elimination is done due to reduction over structured and unstructured uncertainties boundaries. In order to overcome against existing uncertainties for the tracking position of a robot manipulator, a classic sliding mode control is designed. The mathematical proof shows the closed-loop system in the presence of this controller has the global asymptotic stability. Then, by applying the rules that are obtained from the design of classic sliding mode control and TS fuzzy model, a fuzzy sliding mode control is designed that is free of undesirable phenomena of chattering. Eventually, by applying the PSO optimization algorithm, the existing membership functions are adjusted in the way that the error tracking robot manipulator position is converged toward zero. In order to illustrate the performance of the proposed controller, a two degree-of-freedom robot manipulator is used as the case study. The simulation results confirm desirable performance of optimal fuzzy sliding mode control.     

Chaos synchronization of coupled neurons under electrical stimulation via robust adaptive fuzzy control

This paper presents a robust adaptive fuzzy controller to synchronize two gap junction coupled chaotic FitzHugh–Nagumo (FHN) neurons under external electrical stimulation. A variable universe adaptive fuzzy approximator is used to approximate the nonlinear uncertain function of the synchronization error system. Based on the Lyapunov stability theory, the obtained adaptive laws of fuzzy algorithm not only guarantee the stability of the closed loop error system, but also attenuate the influence of matching error and external disturbance on synchronization error to an arbitrarily desired level. Chaos synchronization is obtained by proper choice of the control parameters. The simulation results demonstrate the effectiveness of the proposed control method.     

Robust optimal attitude control of hexarotor robotic vehicles

Multirotor aerial robotic vehicles attract much attention due to their increased load capacity and high maneuverability. In this paper, a robust optimal attitude controller is proposed for a kind of multirotor helicopters—hexarotors. It consists of a nominal optimal controller and a robust compensator. The nominal controller is designed based on the linear quadratic regulation (LQR) method to achieve desired tracking of the nominal system, and the robust compensator is added to restrain the influence of uncertainties. The key contributions of this work are twofold: firstly, the closed-loop control system is robust against coupling and nonlinear dynamics, parametric uncertainties, and external disturbances; secondly, a decoupled and linear time-invariant control architecture making it ideal for real-time implementation. The attitude tracking errors are proven to be ultimately bounded with specified boundaries. Simulation and experimental results on the hexarotor demonstrate the effectiveness of the proposed attitude control method.     

Optimal nonlinear observers for chaotic synchronization with message embedded

This paper presents an optimal nonlinear observer for synchronizing the transmitter-receiver pair with guaranteed optimal performance. In the proposed scheme, a generalized nonlinear state-space observer via uniform matrix transformations is constructed to estimate the transmitter state and the information signal, simultaneously. A nonlinear optimal design approach is used to synchronize chaotic systems. Solving the Hamilton–Jacobi–Bellman (H–J–B) equations we can obtain a linear optimal feedback scheme for piecewise-linear chaotic systems. Moreover, a robust scheme derived from the H _∞ optimization theory improves the synchronization performance of general nonlinear chaotic systems by suppressing the influence of their high order residual terms. Finally, two numerical simulation examples are illustrated by the chaotic Chua’s circuit system and the Lorenz chaotic system to demonstrate the effectiveness of our scheme.     

模糊—神经网络控制算法及其在离心力—振动复合环境试验系统中的应用

针对离心－振动复合环境试验系统所存在的耦合性、非线性和不确定性提出了一种模糊－神经网络控制算法,利用被控对象输入输出信息离线、在线相结合学习系统的动态特性,对时变、非线性系统进行跟踪控制,并研究了该算法在系统中的实现方法。实现表明了控制系统具有良好的跟踪能力。该算法也适用于快速变化这类系统的实时控制。     

Robust trajectory tracking control for a laboratory helicopter

This paper presents a robust nonlinear control strategy to deal with the trajectory tracking control problem for a laboratory helicopter. The helicopter model is considered as a nominal one with uncertainties such as unmodeled nonlinear dynamics, parametric uncertainties, and external disturbances. The proposed control approach incorporates the feedback linearization technique (FLT) and the signal compensation technique. The FLT is first applied to achieve the linearization of the nominal nonlinear model for reducing the conservation of the robust compensator design. A nominal controller based on the linear quadratic regulation method is designed for the linearized nominal system, whereas a robust compensator is introduced to restrain the influences of the uncertainties. It is shown that the trajectory tracking errors of the closed-loop system are ultimately bounded, and the boundaries can be specified by choosing the controller parameters. Simulation and experimental results on the lab helicopter verify the effectiveness of the proposed method.     

Decentralized adaptive neural control of nonlinear systems with unknown time delays

In this paper, a novel decentralized adaptive neural control scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear time-delay systems. RBF neural networks (NNs) are used to tackle unknown nonlinear functions, then the decentralized adaptive NN tracking controller is constructed by combining Lyapunov–Krasovskii functions and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. The proposed controller guarantees semi-global uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop large-scale system, while the tracking errors converge to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters for each subsystem is reduced to one, and three problems of “computational explosion,” “dimension curse” and “controller singularity” are solved, respectively. Finally, a numerical simulation is presented to demonstrate the effectiveness and performance of the proposed scheme.     

Robust adaptive sliding mode control of MEMS gyroscope using T–S fuzzy model

In this paper, a multi-input multi-output Takagi–Sugeno (T–S) fuzzy model is proposed to represent the nonlinear model of micro-electro mechanical systems (MEMS) gyroscope and improve the tracking and compensation performance. A robust adaptive sliding mode control with on-line identification for the upper bounds of external disturbances and an adaptive estimator for the model uncertainty parameters are proposed in the Lyapunov framework. The adaptive algorithm of model uncertainty parameters could compensate the error between the optimal T–S model and the designed T–S model, and decrease the chattering of the sliding surface. Based on Lyapunov methods, these adaptive laws can guarantee that the system is asymptotically stable. For the purpose of comparison, the designed controller is also implemented on the nonlinear model of MEMS gyroscope. Numerical simulations are investigated to verify the effectiveness of the proposed control scheme on the T–S model and the nonlinear model.     

Dynamic model based nonlinear tracking control of a planar parallel manipulator

Based on the dynamic model, a novel nonlinear tracking controller is developed to overcome the nonlinear dynamics and friction of a planar parallel manipulator. The dynamic model is formulated in the active joint space, and the active joint friction is described with the Coulomb + viscous friction model. A nonlinear tracking controller is designed to eliminate the tracking error by using the power function. The nonlinear tracking controller is proven to guarantee asymptotic convergence to zero of both the tracking error and error rate with the Barbalat’s lemma. The trajectory tracking experiment of the proposed controller is implemented on an actual five-bar planar parallel manipulator both at the low-speed and high-speed motion. Moreover, the control performances of the proposed controller are compared with the results of the augmented PD (APD) controller.     

Proper uncertainty bound parameter to robust control of electrical manipulators using nominal model

This paper focuses on the uncertainty bound parameter (UBP) to design the robust control of electrical manipulators. The UBP is commonly obtained by considering the worst case of uncertainties in bounding functions. However, too high estimation of UBP may cause saturation of input, higher frequency of chattering in the switching control laws, and thus a bad behavior of the whole system, while too low estimation of UBP may cause a higher tracking error. A proper UBP is preferred to improve the performance of robust control system. A simple, less dependent and proper UBP is proposed based on the nominal model of electrical manipulator and feedbacks of joint accelerations. This work is motivated by recent experimental results in measuring acceleration by optical encoder. Modeling of an electrical manipulator with presence of uncertainties is presented for control purposes. The proposed robust control is justified by stability analysis.     

A new adaptive fuzzy sliding mode observer for a class of MIMO nonlinear systems

In this paper, a new adaptive fuzzy sliding mode (AFSM) observer is proposed which can be used for a class of MIMO nonlinear systems. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. In this method, a fuzzy system is designed to estimate the nonlinear behavior of the observer. The output of fuzzy rules are tuned adaptively, based on the observer error. The output connection matrix is used to combine the observer errors of individual subsystems. A robust term, which is designed based on the sliding mode theory, is added to the observer to compensate the fuzzy estimation error. The estimation error bound is adjusted by an adaptive law. The main advantage of the proposed observer is that, unlike many of the previous works, the measured outputs is not limited to the first entries of a canonical-form state vector. The proposed observer estimates the closed-loop state tracking error asymptotically, provided that the output gain matrix includes Hurwitz coefficients. The chattering is eliminated by using boundary layers around the sliding surfaces and the observer convergence is proved using a Lyapunov-based approach. The proposed method is applied on a real multilink robot manipulator. The performance of the observer shows its effectiveness in the real world.     

Switched exponential state estimation of neural networks based on passivity theory

In this paper, a new exponential state estimation method is proposed for switched Hopfield neural networks based on passivity theory. Through available output measurements, the main purpose is to estimate the neuron states such that the estimation error system is exponentially stable and passive from the control input to the output error. Based on augmented Lyapunov–Krasovskii functional, Jensen’s inequality, and linear matrix inequality (LMI), a new delay-dependent state estimator for switched Hopfield neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. The unknown gain matrix is determined by solving delay-dependent LMIs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

Neural network based robust hybrid control for robotic system: an H �� approach

A novel robust hybrid tracking control for robotic system is proposed. This hybrid control scheme combines computed torque control (CTC) with neural network, variable structure control (VSC) and nonlinear H _?? control methods. It is assumed that the nominal system of robotic system is completely known, which is controlled by using CTC method. Neural network is designed to approximate parameter uncertainties, VSC is used to eliminate the effect of approximation error, and H _?? control is employed to achieve a desired robust tracking performance. Based on Lyapunov stability theorem, it can be guaranteed that all signals in closed loop are bounded and a specified H _?? tracking performance is achieved by employing the proposed robust hybrid control. The validity of the control scheme is shown by computer simulation of a two-link robotic manipulator.     

Linear parameter varying feedforward control synthesis using parameter-dependent Lyapunov function

This paper presents the dynamic feedforward control synthesis for linear parameter varying (LPV) systems. It is assumed that all system matrices are dependent on varying parameters, which are measurable with sensor or observable. The parameters have bounded variation rates. Parameter-dependent Lyapunov function is used for the feedforward control synthesis such that the robust stability is assured for all varying parameters at the time of the operation. The method is formulated in terms of linear matrix inequalities for LPV feedforward controller that guarantees the stability of the transfer matrix having \(L_{2}\) -gain. This compensator is designed by adding on the feedback controller in two degrees of freedom control configuration. This controller can be used for the disturbance attenuation or decreasing the tracking error. The numerical examples and simulations are given to provide the applicability of the proposed solution.