Robust Backstepping Control of Robotic Systems Using Neural Networks

Neural network (NN) controllers for the robust back stepping control of robotic systems in both continuous and discrete-time are presented. Control action is employed to achieve tracking performance for unknown nonlinear system. Tuning methods are derived for the NN based on delta rule. Novel weight tuning algorithms for the NN are obtained that are similar to -modification in the case of continuous-time adaptive control. Uniform ultimate boundedness of the tracking error and the weight estimates are presented without using the persistency of excitation (PE) condition. Certainty equivalence is not used and regression matrix is not computed. No learning phase is needed for the NN and initialization of the network weights is straightforward. Simulation results justify the theoretical conclusions.     

A direct NN‐approximation control for uncertain nonaffine systems with unknown control direction

In this paper, we present an adaptive neural network (NN) controller for uncertain nonaffine systems with unknown control direction. Most of the previous NN‐based controllers included a damping term in the adaptive law of NN weights to ensure the closed‐loop stability. The estimated error of the NN weights as well as the tracking error were therefore increased, relying not only on the size of the NN approximation error but also on the ideal NN weights. Compared with those, the proposed controller evades using the damping term through combining a novel adaptive algorithm and a switching mechanism to update the weights. The NN thus can directly approach a target controller with satisfactory accuracy even if the control direction is unknown. Stability analysis shows that the tracking error and the estimated error of NN weights both converge to small neighbors of 0 which solely depend on the NN approximation error. At last, simulations on a Duffing‐Holmes chaotic model show the effectiveness of the proposed controller in comparison to another NN‐based method.     

基于参数估计误差的辊道窑温度场优化控制方法

辊道窑烧结过程的温度是决定锂离子电池正极材料产品质量的关键. 然而, 根据炉内有限个测温点的温度 建立起描述整个温度场的模型往往非常困难, 导致无法优化控制烧结过程的温度分布; 而控制方法的设计一般需要 进行参数估计, 已有参数估计方法大多依赖于观测器/预测器的状态误差信息, 无法直接反映待估计参数的变化特 征且方法的准确性取决于观测器/预测器的性能. 为此, 本文提出一种基于参数估计误差的温度场自适应动态规划 (adaptive dynamic programming, ADP)优化控制方法. 首先, 基于传热机理建立二维多孔介质能量守恒方程, 构建包 含角系数的边界条件以反映热辐射作用; 考虑到竖直方向温度变化较大, 通过转换边界条件建立起辊道窑一维温 度场模型, 并根据正极材料的特性获得模型参数. 然后, 采用ADP中的策略迭代(policy iteration, PI) 优化设计温度场 控制器, 神经网络(neural network, NN)用于PI中的评价网络以逼近代价函数; 基于权值参数的估计值与真实值之差 构建参数估计误差, 通过将估计误差的信息融入到评价NN参数更新过程, 提出基于参数估计误差的NN权值更新算 法, 以提高参数估计误差的收敛性, 实现有限时间内NN权值的快速收敛. 最后, 通过仿真验证所提建模和控制方法 的有效性.     

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.     

Projection-Based Adaptive Neurocontrol With Switching Logic Deadzone Tuning

In this brief, an adaptive neural network (NN) controller is proposed for multiple-input-multiple-output (MIMO) nonlinear systems with triangular control structure and unknown control directions. Deadzones are employed in the projection-based NN weight learning laws and the Nussbaum parameter update laws with levels tuned by an innovative switching logic tuning mechanism. Detailed analysis using a family of Lyapunov-like integral functions and the function approximation capability of NNs proves that all the tracking errors are semiglobal uniform ultimate bounded in small neighborhoods of the origin while the closed-loop system variables (state vector, NN weights, Nussbaum parameters) and the control law remain bounded. A simulation study confirms the theoretical results and verifies the effectiveness of the proposed design.     

An online fault tolerant actor-critic neuro-control for a class of nonlinear systems using neural network HJB approach

In this paper, we propose an actor-critic neuro-control for a class of continuous-time nonlinear systems under nonlinear abrupt faults, which is combined with an adaptive fault diagnosis observer (AFDO). Together with its estimation laws, an AFDO scheme, which estimates the faults in real time, is designed based on Lyapunov analysis. Then, based on the designed AFDO, a fault tolerant actor- critic control scheme is proposed where the critic neural network (NN) is used to approximate the value function and the actor NN updates the fault tolerant policy based on the approximated value function in the critic NN. The weight update laws for critic NN and actor NN are designed using the gradient descent method. By Lyapunov analysis, we prove the uniform ultimately boundedness (UUB) of all the states, their estimation errors, and NN weights of the fault tolerant system under the unpredictable faults. Finally, we verify the effectiveness of the proposed method through numerical simulations.     

Multilayer neural-net robot controller with guaranteed trackingperformance

A multilayer neural-net (NN) controller for a general serial-link rigid robot arm is developed. The structure of the NN controller is derived using a filtered error/passivity approach. No off-line learning phase is needed for the proposed NN controller and the weights are easily initialized. The nonlinear nature of the NN, plus NN functional reconstruction inaccuracies and robot disturbances, mean that the standard delta rule using backpropagation tuning does not suffice for closed-loop dynamic control. Novel online weight tuning algorithms, including correction terms to the delta rule plus an added robust signal, guarantee bounded tracking errors as well as bounded NN weights. Specific bounds are determined, and the tracking error bound can be made arbitrarily small by increasing a certain feedback gain. The correction terms involve a second-order forward-propagated wave in the backpropagation network. New NN properties including the notions of a passive NN, a dissipative NN, and a robust NN are introduced.     

未知饱和控制系统有穷域最优控制

针对带有饱和执行器且局部未知的非线性连续系统的有穷域最优控制问题,设计了一种基于自适应动态规划(ADP)的在线积分增强学习算法,并给出算法的收敛性证明.首先,引入非二次型函数处理控制饱和问题.其次,设计一种由常量权重和时变激活函数构成的单一网络,来逼近未知连续的值函数,与传统双网络相比减少了计算量.同时,综合考虑神经网络产生的残差和终端误差,应用最小二乘法更新神经网络权重,并且给出基于神经网络的迭代值函数收敛到最优值的收敛性证明.最后,通过两个仿真例子验证了算法的有效性.     

Cooperative learning neural network output feedback control of uncertain nonlinear multi-agent systems under directed topologies

Without assuming that the communication topologies among the neural network (NN) weights are to be undirected and the states of each agent are measurable, the cooperative learning NN output feedback control is addressed for uncertain nonlinear multi-agent systems with identical structures in strict-feedback form. By establishing directed communication topologies among NN weights to share their learned knowledge, NNs with cooperative learning laws are employed to identify the uncertainties. By designing NN-based κ-filter observers to estimate the unmeasurable states, a new cooperative learning output feedback control scheme is proposed to guarantee that the system outputs can track nonidentical reference signals with bounded tracking errors. A simulation example is given to demonstrate the effectiveness of the theoretical results.     

Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.     

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.     

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.     

动态规划最优控制在非线性系统中的应用

应用一种新的自适应动态最优化方法(ADP),在线实现对非线性连续系统的最优控制。首先应用汉密尔顿函数（Hamilton-Jacobi-Bellman, HJB）求解系统的最优控制,并应用神经网络BP算法对汉密尔顿函数中的性能指标进行估计,进而得到非线性连续系统的最优控制。同时引进一种新的自适应算法,基于参数误差,在线实现对系统进行动态最优求解,而且通过李亚普诺夫方法对参数收敛情况也进行详细的分析。最后,用仿真结果来验证所提出的方法的可行性。     

An Iterative Learning Control of Nonlinear Systems Using Neural Network Design

In this paper, a feedforward neural network with sigmoid hidden units is used to design a neural network based iterative learning controller for nonlinear systems with state dependent input gains. No prior offline training phase is necessary, and only a single neural network is employed. All the weights of the neurons are tuned during the iteration process in order to achieve the desired learning performance. The adaptive laws for the weights of neurons and the analysis of learning performance are determined via Lyapunov‐like analysis. A projection learning algorithm is used to prevent drifting of weights. It is shown that the tracking error vector will asymptotically converges to zero as the iteration goes to infinity, and the all adjustable parameters as well as internal signals remain bounded.     

Adaptive backstepping control for a class of semistrict feedback nonlinear systems using neural networks

This paper addresses a neural adaptive backstepping control with dynamic surface control technique for a class of semistrict feedback nonlinear systems with bounded external disturbances.Neural networks (NNs) are introduced as approximators for uncertain nonlinearities and the dynamic surface control (DSC) technique is involved to solve the so-called "explosion of terms" problem.In addition,the NN is used to approximate the transformed unknown functions but not the original nonlinear functions to overcome the possible singularity problem.The stability of closed-loop system is proven by using Lyapunov function method,and adaptation laws of NN weights are derived from the stability analysis.Finally,a numeric simulation validates the results of theoretical analysis.     

Neural net robot controller: Structure and stability proofs

A multilayer neural net (NN) controller for a general serial-link robot arm is developed. The structure of the NN controller is derived using a filtered error approach. It is argued that standard backpropagation tuning, when used for real-time closed-loop control, can yield unbounded NN weights if: (1) the net can not exactly reconstruct a certain required control function, (2) there are bounded unknown disturbances in the robot dynamics, or (3) the robot arm has more than one link (i.e. nonlinear case). On-line weight tuning algorithms including correction terms to backpropagation, plus an added robustifying signal, guarantee tracking as well as bounded weights. The correction terms involve a second-orderforward-propagated wave in the backprop network.     

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.     

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.      

Discrete-time neural net controller for a class of nonlineardynamical systems

A family of two-layer discrete-time neural net (NN) controllers is presented for the control of a class of mnth-order MIMO dynamical system. No initial learning phase is needed so that the control action is immediate; in other words, the neural network (NN) controller exhibits a learning-while-functioning-feature instead of a learning-then-control feature. A two-layer NN is used which is linear in the tunable weights. The structure of the neural net controller is derived using a filtered error approach. It is indicated that delta-rule-based tuning, when employed for closed-loop control, can yield unbounded NN weights if: 1) the net cannot exactly reconstruct a certain required function, or 2) there are bounded unknown disturbances acting on the dynamical system. Certainty equivalence is not used, overcoming a major problem in discrete-time adaptive control. In this paper, new online tuning algorithms for discrete-time systems are derived which are similar to ϵ-modification for the case of continuous-time systems that include a modification to the learning rate parameter and a correction term to the standard delta rule     

Intelligent adaptive observer-based optimal control of overhead transmission line de-icing robot manipulator

In cold season, wet snow ice accretion on overhead transmission lines increases wind load effects which in turn increases line tension. This increased line tension causes undesirable effects in power systems. This paper discusses the design of an observer-based boundary sliding mode control (BSMC) for 3 DOF overhead transmission line de-icing robot manipulator (OTDIRM). A robust radial basis functional neural network (RBFNN) observer-based neural network (NN) controller is developed for the motion control of OTDIRM, which is a combination of BSMC, NN approximation and adaptation law. The RBFNN-based adaptive observer is designed to estimate the positions and velocities. The weights of both NN observer and NN approximator are tuned off-line using particle swarm optimization. Using Lyapunov analysis the closed loop tracking error was verified for a 3 DOF OTDIRM. Finally, the robustness of the proposed neural network-based adaptive observer boundary sliding mode control (NNAOBSMC) was verified against the input disturbances and uncertainties.