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.     

不确定性系统的非因果鲁棒学习控制

针对不确定性系统提出一种非因果鲁棒学习控制方法。该学习控制律的非因果学习部分通过标称系统的优化指标得到,鲁棒部分通过设计鲁棒加权来实现。首先,不考虑鲁棒部分的具体形式,推导出标称系统描述的学习控制律的鲁棒收敛性条件;然后,设计与系统不确定性相关的鲁棒加权,由鲁棒收敛性条件得到鲁棒加权的设计原则;最后,通过仿真实验验证了所提出方法的有效性,并分析了不同形式不确定性系统鲁棒设计的保守性。     

On functional approximation of the equivalent control usinglearning variable structure control

A learning variable structure control (LVSC) approach is originated to obtain the equivalent control of a general class of multiple-input-multiple-output (MIMO) variable structure systems under repeatable control tasks. LVSC synthesizes variable structure control (VSC) as the robust part which stabilizes the system, and learning control (LC) as the "plug-in" intelligent part which completely nullifies the effects of the matched uncertainties on tracking error. Rigorous proof based on energy function and functional analysis shows. that the tracking error sequence converges uniformly to zero, and that the bounded LC sequence converges to the equivalent control almost everywhere     

非参数不确定系统约束迭代学习控制

讨论一类非参数不确定系统的约束迭代学习控制问题.构造二次分式型障碍李雅普诺夫函数(Barrier Lyapunov functions),用于学习控制器设计.控制方案采用鲁棒方法与学习机制相结合的手段处理非参数不确定性,鲁棒方法对处理后的不确定性的界予以补偿,学习机制对处理后的不确定性进行估计.可实现系统状态在整个作业区间上完全跟踪参考轨迹,并使得系统误差的二次型在迭代过程中囿于预设的界内,进而在运行过程中实现状态约束.提出的迭代学习算法包括部分限幅与完全限幅学习算法.采用这种BLF约束控制系统有利于提高控制系统中设备安全性.仿真结果用于验证所提出控制方法的有效性.     

Intelligent control of DC motor driven mechanical systems: a robust learning control approach

A robust learning controller is presented for DC motor driven mechanical systems with friction. The proposed controller takes advantage of both robust and learning control approaches to learn and compensate periodic and non‐periodic uncertain dynamics. In the learning controller, a set of learning rules is implemented in which three types of learnings occur: one is direct learning of desired inverse dynamics input and the other two learning of unknown linear parameters and nonlinear bounding functions in the models of system dynamics and friction. The global asymptotic stability of learning control system is shown by using the Lyapunov stability theory. Experimental data demonstrate the effectiveness of developed learning approach to tracking of DC motor driven mechanical systems. Copyright © 2002 John Wiley & Sons, Ltd.     

Model reference robust control of a class of SISO systems

A new control design technique, model reference robust control (MRRC), is introduced for a class of SISO systems which contain unknown parameters, possible nonlinear uncertainties, and additive bounded disturbances. The design methodology is a natural, nontrivial extension of model reference adaptive control (MRAC) which is essential to achieving robust stability and performance for linear time-invariant systems. The methodology also represents an important step toward achieving robust stability for time-varying and nonlinear systems. MRRC requires only input and output measurements of the system, rather than the full state feedback and structural conditions on uncertainties required by existing robust control results. MRRC is developed from existing model reference control (MRC) in a manner similar to MRAC. An intermediate result gives conditions under which MRRC yields exponentially asymptotic stability. The general result yielding uniformly ultimately bounded stability is then developed. A scalar example provides intuition into why the control works against a wide class of uncertainties and reveals the implicit learning capability of MRRC     

Robust learning control for robotic manipulators with an extension to a class of non-linear systems

A robust learning control (RLC) scheme is developed for robotic manipulators by a synthesis of learning control and robust control methods. The non-linear learning control strategy is applied directly to the structured system uncertainties that can be separated and expressed as products of unknown but repeatable (over iterations) state-independent time functions and known state-dependent functions. The non-linear uncertain terms in robotic dynamics such as centrifugal, Coriolis and gravitational forces belong to this category. For unstructured uncertainties which may have non-repeatable factors but are limited by a set of known bounding functions as the only a priori knowledge, e.g the frictions of a robotic manipulator, robust control strategies such as variable structure control strategy can be applied to ensure global asymptotic stability. By virtue of the learning and robust properties, the new control system can easily fulfil control objectives that are difficult for either learning control or variable structure control alone to achieve satisfactorily. The proposed RLC scheme is further shown to be applicable to certain classes of non-linear uncertain systems which include robotic dynamics as asubset. Various important properties concerning learning control, such as the need for a resetting condition and derivative signals, whether using iterative control mode or repetitive control mode, are also made clear in relation to different control objectives and plant dynamics.     

An input-output based robust stabilization criterion forneural-network control of nonlinear systems

A stabilization method based on the input-output conicity criterion is presented. Conventional learning algorithms are applied to adjust the controller dynamics, and robust stability of the closed-loop system is guaranteed by modifying the training patterns which yield unstable behavior. The methodology developed expands the class of nonlinear systems to be controlled using neural control schemes, so that the stabilization of a broad class of neural-network-based control systems, even with unknown dynamics, is assured. Straightforwardness in the application of this method is evident in contrast to the Lyapunov function approach.     

非线性时滞系统的高阶迭代学习控制

针对非线性时滞系统,讨论了输出跟踪控制的高阶迭代学习算法,并给出了算法的收敛性 证明.当由于重复定位等原因造成初态偏差时,提出一种反复学习方案,完成初态和轨迹跟 踪,它对初态偏差有较强的鲁棒性.仿真结果表明了该算法的有效性.     

自适应模糊逻辑系统的鲁棒学习算法

通过对常规最小方差型目标函数局限性的分析，根据鲁棒统计学理论和目标函数在参数学习中的导向作用，对目标函数进行修正，在此基地之上，提出一种模糊逻辑系统的鲁棒学习算法，在噪声环境中，通过对该算法的仿真验证以及与常规算法性能的比较，表明该鲁棒学习算法在逼近精度和鲁棒性等方面优于传统方法，在实际工程中具有较高的应用价值。     

A robust Markov game controller for nonlinear systems

This paper proposes a reinforcement learning (RL)-based game-theoretic formulation for designing robust controllers for nonlinear systems affected by bounded external disturbances and parametric uncertainties. Based on the theory of Markov games, we consider a differential game in which a ‘disturbing’ agent tries to make worst possible disturbance while a ‘control’ agent tries to make best control input. The problem is formulated as finding a min–max solution of a value function. We propose an online procedure for learning optimal value function and for calculating a robust control policy. Proposed game-theoretic paradigm has been tested on the control task of a highly nonlinear two-link robot system. We compare the performance of proposed Markov game controller with a standard RL-based robust controller, and an H_∞ theory-based robust game controller. For the robot control task, the proposed controller achieved superior robustness to changes in payload mass and external disturbances, over other control schemes. Results also validate the effectiveness of neural networks in extending the Markov game framework to problems with continuous state–action spaces.     

非参数不确定系统状态受限误差跟踪学习控制方法

针对一类非参数不确定系统,提出误差跟踪学习控制方法,同时解决学习控制系统的初值问题和状态约束问题.利用障碍Lyapunov函数设计控制器,采用鲁棒方法与学习方法相结合的策略处理非参数不确定性,将滤波误差约束于预设的界内,并由此实现对系统状态在各次迭代运行过程中的约束.文中构造了一种期望误差轨迹,经过足够多次迭代后,所提控制方法使得系统误差在整个作业区间以预设精度跟踪期望误差轨迹,系统状态在部分作业区间精确跟踪参考信号.仿真结果表明了该控制方案的有效性.     

Neural critic learning toward robust dynamic stabilization

In this article, we focus on developing a neural‐network‐based critic learning strategy toward robust dynamic stabilization for a class of uncertain nonlinear systems. A type of general uncertainties involved both in the internal dynamics and in the input matrix is considered. An auxiliary system with actual action and auxiliary signal is constructed after dynamics decomposition and combination for the original plant. The reasonability of the control problem transformation from robust stabilization to optimal feedback design is also provided theoretically. After that, the adaptive critic learning method based on a neural network is established to derive the approximate optimal solution of the transformed control problem. The critic weight can be initialized to a zero vector, which apparently facilitates the learning process. Numerical simulation is finally presented to illustrate the effectiveness of the critic learning approach for neural robust stabilization.     

基于混合灵敏度设计的鲁棒迭代学习控制

提出一种鲁棒迭代学习控制的设计方法．利用混合灵敏度设计方法,控制器满足一定鲁棒性条件时就可以直接获得收敛更新规则．此外,只要学习滤波函数满足一定条件,系统跟踪误差将显著降低．仿真结果表明该方法有效性较高．     

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.      

Robust adaptive repetitive learning control for a class of time-varying nonlinear systems with unknown control direction

A robust adaptive repetitive learning control method is proposed for a class of time-varying nonlinear systems. Nussbaum-gain method is incorporated into the control design to counteract the lack of a priori knowledge of the control direction which determines the motion direction of the system under any input. It is shown that the system state could converge to the desired trajectory asymptotically along the iteration axis through repetitive learning. Simulation is carried out to show the validity of the proposed control method.     

基于量化依赖Lyapunov函数的有界丢包网络控制系统的保成本控制

研究了一类具有有界丢包的网络控制系统（Networked control systems，NCSs）的保成本控制问题，提出了一种包含量化反馈的网络控制系统数学模型，该模型将系统的镇定问题转化为镇定一系列子系统的鲁棒控制问题.在对网络控制系统的分析中，区别于常用的二次型Lyapunov函数，本文采用了一种新的且能够降低保守性的量化依赖Lyapunov函数方法.基于本文的Lyapunov函数，得到了充分考虑丢包过程的保成本控制器的设计方法.仿真算例验证了所给出方法的有效性.     

迭代学习控制系统的鲁棒收敛性分析(英)

本文提出一种开闭环配合的滤波器型选代学习控制算法，并将这种算法应用于一般非线性动态系统的轨迹跟踪．对于渐近重复初始条件和渐近周期干扰的情形，通过控制误差估计和输出误差估计，文中分别证明了学习过程的一致收敛性．证明中未采用线性化手段．     

Model reference adaptive robust fuzzy control for ship steering autopilot with uncertain nonlinear systems

A novel model reference adaptive robust fuzzy control algorithm is presented for ship steering autopilot, which is an uncertain nonlinear system. In the proposed algorithm, fuzzy logic systems have been used to approximate lumped unknown function in the ship steering systems and the adaptive mechanism with minimal learning parameter, i.e. only one parameter, has been achieved by use of Lyapunov approach. The proposed methodology is verified using the simulation mode of the Dalian Maritime University's ocean-going training ship named Yulong. It is shown that the proposed algorithm guarantees that the ship steering autopilot system is asymptotically stable and its tracking error can approach to zero.