Adaptive neural integral sliding‐mode control for tracking control of fully actuated uncertain surface vessels

This paper develops a novel adaptive neural integral sliding‐mode control to enhance the tracking performance of fully actuated uncertain surface vessels. The proposed method is built based on an integrating between the benefits of the approximation capability of neural network (NN) and the high robustness and precision of the integral sliding‐mode control (ISMC). In this paper, the design of NN, which is used to approximate the unknown dynamics, is simplified such that just only one simple adaptive rule is needed. The ISMC, which can eliminate the reaching phase and offer higher tracking performance compared to the conventional sliding‐mode control, is designed such that the system robust against the approximation error and stabilize the whole system. The design procedure of the proposed controller is constructed according to the backstepping control technique so that the stability of the closed‐loop system is guaranteed based on Lyapunov criteria. The proposed method is then tested on a simulated vessel system using computer simulation and compared with other state‐of‐the‐art methods. The comparison results demonstrate the superior performance of the proposed approach.     

Direct adaptive control for a class of discrete‐time unknown nonaffine nonlinear systems using neural networks

In this paper, a direct adaptive state‐feedback control approach is developed for a class of nonlinear systems in discrete‐time (DT) domain. We study MIMO unknown nonaffine nonlinear DT systems and employ a two‐layer NN to design the controller. By using the presented method, the NN approximation is able to cancel the nonlinearity of the unknown DT plant. Meanwhile, pretraining is not required, and the weights of NNs used in adaptive control are directly updated online. Moreover, unlike standard NN adaptive controllers yielding uniform ultimate boundedness results, the tracking error is guaranteed to be uniformly asymptotically stable by utilizing Lyapunov's direct method. Two illustrative examples are provided to demonstrate the effectiveness and the applicability of the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Online Adaptive Approximate Optimal Tracking Control with Simplified Dual Approximation Structure for Continuous-time Unknown Nonlinear Systems

This paper proposes an online adaptive approximate solution for the infinite-horizon optimal tracking control problem of continuous-time nonlinear systems with unknown dynamics. The requirement of the complete knowledge of system dynamics is avoided by employing an adaptive identifier in conjunction with a novel adaptive law, such that the estimated identifier weights converge to a small neighborhood of their ideal values. An adaptive steady-state controller is developed to maintain the desired tracking performance at the steady-state, and an adaptive optimal controller is designed to stabilize the tracking error dynamics in an optimal manner. For this purpose, a critic neural network (NN) is utilized to approximate the optimal value function of the Hamilton-Jacobi-Bellman (HJB) equation, which is used in the construction of the optimal controller. The learning of two NNs, i.e., the identifier NN and the critic NN, is continuous and simultaneous by means of a novel adaptive law design methodology based on the parameter estimation error. Stability of the whole system consisting of the identifier NN, the critic NN and the optimal tracking control is guaranteed using Lyapunov theory; convergence to a near-optimal control law is proved. Simulation results exemplify the effectiveness of the proposed method.      

含未知信息的轮式移动机器人编队确定学习控制

本文研究含未知信息的轮式移动机器人(wheeled mobile robots,WMR)的编队控制问题.首先,基于领航–跟随法和虚拟结构法,将WMR编队控制问题转化为跟随机器人对参考虚拟机器人的跟踪控制问题.然后,利用径向基函数神经网络(radial basis function neural networks,RBF NN)对WMR的未知系统动态进行学习,以及根据李雅普诺夫稳定性理论设计了稳定的自适应RBF NN控制器和RBF NN权值估计的学习率.依据确定学习理论,闭环系统内部信号在对回归轨迹实现跟踪控制的过程中满足部分持续激励(persistent excitation,PE)条件.随着PE条件的满足,RBF NN权值估计收敛到其理想权值,实现了对未知闭环系统动态的准确学习.最后,利用学习结果设计了RBF NN学习控制器,保证了控制系统的稳定与收敛,实现了闭环稳定性和改进了控制性能,并通过仿真验证了所提控制方法的正确性和有效性.     

Reinforcement learning neural-network-based controller for nonlinear discrete-time systems with input constraints.

A novel adaptive-critic-based neural network (NN) controller in discrete time is designed to deliver a desired tracking performance for a class of nonlinear systems in the presence of actuator constraints. The constraints of the actuator are treated in the controller design as the saturation nonlinearity. The adaptive critic NN controller architecture based on state feedback includes two NNs: the critic NN is used to approximate the "strategic" utility function, whereas the action NN is employed to minimize both the strategic utility function and the unknown nonlinear dynamic estimation errors. The critic and action NN weight updates are derived by minimizing certain quadratic performance indexes. Using the Lyapunov approach and with novel weight updates, the uniformly ultimate boundedness of the closed-loop tracking error and weight estimates is shown in the presence of NN approximation errors and bounded unknown disturbances. The proposed NN controller works in the presence of multiple nonlinearities, unlike other schemes that normally approximate one nonlinearity. Moreover, the adaptive critic NN controller does not require an explicit offline training phase, and the NN weights can be initialized at zero or random. Simulation results justify the theoretical analysis.     

Neural-Network-Based State Feedback Control of a Nonlinear Discrete-Time System in Nonstrict Feedback Form

In this paper, a suite of adaptive neural network (NN) controllers is designed to deliver a desired tracking performance for the control of an unknown, second-order, nonlinear discrete-time system expressed in nonstrict feedback form. In the first approach, two feedforward NNs are employed in the controller with tracking error as the feedback variable whereas in the adaptive critic NN architecture, three feedforward NNs are used. In the adaptive critic architecture, two action NNs produce virtual and actual control inputs, respectively, whereas the third critic NN approximates certain strategic utility function and its output is employed for tuning action NN weights in order to attain the near-optimal control action. Both the NN control methods present a well-defined controller design and the noncausal problem in discrete-time backstepping design is avoided via NN approximation. A comparison between the controller methodologies is highlighted. The stability analysis of the closed-loop control schemes is demonstrated. The NN controller schemes do not require an offline learning phase and the NN weights can be initialized at zero or random. Results show that the performance of the proposed controller schemes is highly satisfactory while meeting the closed-loop stability.      

Adaptive neural control with fast approximation for uncertain nonlinear systems: A novel composite learning approach

In existing adaptive neural control approaches, only when the regressor satisfies the persistent excitation (PE) or interval excitation (IE) conditions, the constant optimal weights of neural network (NN) can be identified, which can be used to establish uncertainties in nonlinear systems. This paper proposes a novel composite learning approach based on adaptive neural control. The focus of this approach is to make the NN approximate uncertainties in nonlinear systems quickly and accurately without identifying the constant optimal weights of the NN. Hence, the regressor does not need to satisfy the PE or IE conditions. In this paper, regressor filtering scheme is adopted to generate prediction error, and then the prediction error and tracking error simultaneously drive the update of NN weights. Under the framework of Lyapulov theory, the proposed composite learning approach can ensure that approximation error of the uncertainty and tracking error of the system states converge to an arbitrarily small neighborhood of zero exponentially. The simulation results verify the effectiveness and advantages of the proposed approach in terms of fast approximation.     

Robust force/motion control of constrained robots using neural network

A robust neural network (NN) controller is proposed for the simultaneous force/motion control of constrained rigid robots. The NN weights here are tuned on‐line, with no off‐line learning phase required. Most importantly, we can guarantee the boundedness of constraint force errors, joint position tracking errors, and NN weights. When compared with adaptive controllers, we do not require linearity in the unknown parameters, and the tedious computation of the regression matrix. Novel passivity properties of the NN controller are stated and proven. ©1999 John Wiley & Sons, Inc.     

Adaptive radial basis function neural network control with variable variance parameters

The paper presents a direct adaptive control architecture for a class of nonlinear dynamic systems, which are either ill defined or rather complex. The direct adaptive architecture employs radial basis function (RBF) neural network (NN) systems to reconstruct the ideal feedback linearization control. With the modified adaptation algorithm proposed herein, the on-line function approximation capability of the RBF NN a system is enhanced to remove the auxiliary control term and switching element in a conventional RBF-NN-based controller; simultaneously, the tracking performance is upgraded. Global asymptotic stability of the on-line algorithm is established in the Lyapunov sense to guarantee that the tracking error can converge to a small neighbourhood of the origin. Simulation validations for an inverted pendulum system are finally performed to verify the effectiveness of the proposed controller and the theoretical discussion.     

Deterministic learning from neural control for uncertain nonlinear pure‐feedback systems by output feedback

The essence of intelligence lies in the acquisition/learning and utilization of knowledge. However, how to implement learning in dynamical environments for nonlinear systems is a challenging issue. This article investigates the deterministic learning (DL) control problem for uncertain pure‐feedback systems by output feedback, which achieves the human‐like learning and control in a simple way. To reduce the complexity of control design and analysis, first, by combining an appropriate system transformation, the original pure‐feedback system is transformed into a simple normal nonaffine system. An observer is then introduced to estimate the transformed system states. Based on the backstepping and dynamic surface control techniques, a simple adaptive neural control scheme is first developed to guarantee the finite time convergence of the tracking error using only one neural network (NN) approximator. Second, through DL, the exponential convergence of the NN weights is obtained with the satisfaction of partial persistent excitation condition. Thus, locally accurate approximation/learning of the transformed unknown system dynamics is achieved and stored as constant NNs. Finally, by utilizing the stored knowledge, an experience‐based controller is constructed and a novel learning control scheme is further proposed to improve the control performance without any further adaptation online for the estimate neural weights. Simulation results have been given to illustrate that the proposed scheme not only can learn and memorize knowledge like humans but also can utilize experience to achieve superior control performance.     

Neural networks stabilization and disturbance attenuation for nonlinear switched impulsive systems

In this paper, we address the problem of neural networks (NNs) stabilization and disturbance rejection for a class of nonlinear switched impulsive systems. An adaptive NN feedback control scheme and an impulsive controller for output tracking error disturbance attenuation of nonlinear switched impulsive systems are given under all admissible switched strategy based on NN. The NN is used to compensate for the nonlinear uncertainties of switched impulsive systems, and the approximation error of NN is introduced to the adaptive law in order to improve the tracking attenuation quality of the switched impulsive systems. Impulsive controller is designed to attenuate effect of switching impulse. Under all admissible switching law, impulsive controller and adaptive NN feedback controller can guarantee asymptotic stability of tracking error and improve disturbance attenuation level of tracking error for the overall nonlinear switched impulsive system. Finally, a numerical example is given to demonstrate the effectiveness of the proposed control and stabilization methods.     

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.     

Adaptive output feedback tracking control of robot manipulators using position measurements only

In this paper, a new adaptive neuro controller for trajectory tracking is developed for robot manipulators without velocity measurements, taking into account the actuator constraints. The controller is based on structural knowledge of the dynamics of the robot and measurements of joint positions only. The system uncertainty, which may include payload variation, unknown nonlinearities and torque disturbances is estimated by a Chebyshev neural network (CNN). The adaptive controller represents an amalgamation of a filtering technique to generate pseudo filtered tracking error signals (for the elimination of velocity measurements) and the theory of function approximation using CNN. The proposed controller ensures the local asymptotic stability and the convergence of the position error to zero. The proposed controller is robust not only to structured uncertainty such as payload variation but also to unstructured one such as disturbances. Moreover the computational complexity of the proposed controller is reduced as compared to the multilayered neural network controller. The validity of the control scheme is shown by simulation results of a two-link robot manipulator. Simulation results are also provided to compare the proposed controller with a controller where velocity is estimated by finite difference methods using position measurements only.     

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.     

Real-time torque control using discrete-time recurrent high-order neural networks

This paper presents a discrete-time direct current (DC) motor torque tracking controller, based on a recurrent high-order neural network to identify the plant model. In order to train the neural identifier, the extended Kalman filter (EKF) based training algorithm is used. The neural identifier is in series-parallel configuration that constitutes a well approximation method of the real plant by the neural identifier. Using the neural identifier structure that is in the nonlinear controllable form, the block control (BC) combined with sliding modes (SM) control techniques in discrete-time are applied. The BC technique is used to design a nonlinear sliding manifold such that the resulting sliding mode dynamics are described by a desired linear system. For the SM control technique, the equivalent control law is used in order to the plant output tracks a reference signal. For reducing the effect of unknown terms, it is proposed a specific desired dynamics for the sliding variables. The control problem is solved by the indirect approach, where an appropriate neural network (NN) identification model is selected; the NN parameters (synaptic weights) are adjusted according to a specific adaptive law (EKF), such that the response of the NN identifier approximates the response of the real plant for the same input. Then, based on the designed NN identifier a stabilizing or reference tracking controller is proposed (BC combined with SM). The proposed neural identifier and control applicability are illustrated by torque trajectory tracking for a DC motor with separate winding excitation via real-time implementation.     

Robust Adaptive Control of Robots Using Neural Network: Global Stability

A desired compensation adaptive law‐based neural network (DCAL‐NN) controller is proposed for the robust position control of rigid‐link robots. The NN is used to approximate a highly nonlinear function. The controller can guarantee the global asymptotic stability of tracking errors and boundedness of NN weights. In addition, the NN weights here are tuned on‐line, with no offline learning phase required. When compared with standard adaptive robot controllers, we do not require linearity in the parameters, or lengthy and tedious preliminary analysis to determine a regression matrix. The controller can be regarded as a universal reusable controller because the same controller can be applied to any type of rigid robots without any modifications. A comparative simulation study with different robust and adaptive controllers is included.     

一类非线性系统的积分变结构模糊自适应跟踪控制

针对一类具有未知常数控制增益的不确定非线性系统,基于变结构控制原理,并利用具有非线性可调参数的模糊系统逼近等价控制,提出一种具有监督控制器的积分变结构模糊自适应跟踪控制策略.该策略通过监督控制器保证闭环系统所有信号有界.进一步,通过引入最优逼近误差的自适应补偿项来消除建模误差的影响.理论分析证明了跟踪误差能够收敛到零.仿真结果表明了该方法的有效性.     

Direct adaptive neural network controller for a class of nonlinear systems based on fuzzy estimator of the control error

A new approach of direct adaptive control of single input single output nonlinear systems in affine form using single-hidden layer neural network (NN) is introduced. In contrast to the algorithms in the literature, the weights adaptation laws are based on the control error and not on the tracking error or its filtered version. Since the control error is being expressed in terms of the NN controller, hence its weights updating laws are obtained via back-propagation concept. A fuzzy inference system (FIS) with heuristically defined rules is introduced to provide an estimate of this error based on the past history of the system behaviour. The stability of the closed loop is studied using Lyapunov theory. A fixed structure is then proposed for the FIS and the design parameters reduce to the parameters of the NN. The method is reproducible and does not require any pre-training of the network weights.     

Neural net robot controller with guaranteed tracking performance

A neural net (NN) controller for a general serial-link robot arm is developed. The NN has two layers so that linearity in the parameters holds, but the "net functional reconstruction error" and robot disturbance input are taken as nonzero. The structure of the NN controller is derived using a filtered error/passivity approach, leading to new NN passivity properties. Online weight tuning algorithms including a correction term to backpropagation, plus an added robustifying signal, guarantee tracking as well as bounded NN weights. The NN controller structure has an outer tracking loop so that the NN weights are conveniently initialized at zero, with learning occurring online in real-time. It is shown that standard backpropagation, when used for real-time closed-loop control, can yield unbounded NN weights if (1) the net cannot exactly reconstruct a certain required control function or (2) there are bounded unknown disturbances in the robot dynamics. The role of persistency of excitation is explored.     

Novel adaptive neural control design for nonlinear MIMO time-delay systems

In this paper, we address the problem of adaptive neural control for a class of multi-input multi-output (MIMO) nonlinear time-delay systems in block-triangular form. Based on a neural network (NN) online approximation model, a novel adaptive neural controller is obtained by constructing a novel quadratic-type Lyapunov-Krasovskii functional, which not only efficiently avoids the controller singularity, but also relaxes the restriction on unknown virtual control coefficients. The merit of the suggested controller design scheme is that the number of online adapted parameters is independent of the number of nodes of the neural networks, which reduces the number of the online adaptive learning laws considerably. The proposed controller guarantees that all closed-loop signals remain bounded, while the output tracking error dynamics converges to a neighborhood of the origin. A simulation example is given to illustrate the design procedure and performance of the proposed method.