一类不确定非线性系统基于特征模型的复合自适应控制

针对一类不确定非线性系统的跟踪控制问题,提出一种基于特征模型的复合自适应控制方法.该方法的创新性在于基于系统的误差特征模型,构建一种综合跟踪控制误差和模型估计误差的特征参量复合自适应律,该自适应律用于控制器设计和分析,可同时实现跟踪控制误差和模型估计误差的收敛.此外,为便于特征参量自适应律的设计和分析,根据特征参量的慢时变特性,将其视为未知标称常数项和时变误差项之和,并且选用其中常数项的估计量作为自适应控制参数.进一步,为抑制特征参量中时变误差项对系统稳定性和模型估计误差收敛性的影响,在控制器及复合自适应律设计中引入带饱和函数的非线性环节.理论分析证明闭环控制系统稳定,且跟踪控制误差和模型估计误差收敛到原点的一个邻域内.仿真结果表明,与现有仅根据模型估计误差调节的基于特征模型的自适应控制方法相比,所提出的复合自适应控制方法具有更好的控制性能.     

含有非线性不确定参数的电液系统滑模自适应控制

针对含有非线性不确定参数的电液控制系统, 提出了一种滑模自适应控制方法. 该控制方法主要是为了解决由于初始控制容积的不确定性而引起的, 非线性不确定参数自适应律设计的难题. 其主要特点为, 通过定义一个新型的特Lyapunov 函数, 进而构建系统的自适应控制器及参数自适应律, 并结合滑模控制方法及一种简单的鲁棒设计方法, 给出整个电液系统的滑模自适应控制器, 及所有不确定参数的自适应律. 试验结果表明, 采用该控制方法能够取得良好的性能, 尤其可以补偿非线性不确定参数对系统的影响.     

非线性严格反馈系统自适应非反步输出反馈控制

针对传统反步控制器设计方法存在复杂度爆炸、参数收敛难、控制奇异、需全系统状态已知等问题,提出一种新的可保证参数收敛的未知系统动态辨识和非反步输出反馈自适应控制方法.首先,通过定义新的状态变量和系统等价变换,将严格反馈系统状态反馈控制转化为标准系统的输出反馈控制,进而设计包含高阶微分器的自适应单步控制器,避免反步递推设计的问题;然后,采用两个神经网络对系统集总未知动态进行估计,避免传统控制方法在未知控制增益在线估计过零引发的奇异问题;最后,构造一种新的自适应算法在线更新神经网络权值确保其收敛到真实值,进而实现对未知系统动态的精准辨识.基于Lyapunov定理的分析表明,跟踪误差和估计误差均可收敛到零点附近紧集.基于液压伺服系统模型的对比仿真验证了所提出方法的有效性和优越性.     

基于系统浸入和流形不变自适应方法的静止无功补偿器非线性鲁棒自适应控制方法

本文提出一种将系统浸入和流形不变(I&I)自适应控制方法与L2-增益抑制鲁棒控制方法相结合的静止无功补偿器(SVC)的非线性鲁棒自适应控制方法.所提方法首先通过参数估计误差和鲁棒控制律的设计,使得所构造的表示参数估计误差函数的流形不变且吸引,从而使参数估计误差在这一流形上收敛于零.然后,通过所设计的可调参数对参数估计误差的收敛性能进行控制,以此来保证参数估计器对不确定参数的自适应估计能力.最后,采用自适应逆推算法推导鲁棒控制律,并通过使不确定外部扰动满足从输入到输出的耗散性来保证系统对不确定扰动的鲁棒性.仿真结果表明,利用所提方法设计的SVC控制器和参数替换律在参数估计、发电机功角动态响应方面优于传统自适应逆推算法,从而提高了输电系统的稳定水平.     

相对阶n= 3 = 3 的鲁棒直接型模型参考自适应控制

针对相对阶n^*=3具有噪声的一类简单系统，给出了具有未规范化自适应律的鲁棒直接型模型参考自适应控制器的设计，通过引入非线性阻尼项，保证了闭环系统的所有信号都是全局稳定的，而且跟踪误差及参数估计误差均收敛于零。     

含正反馈振动主动控制系统的混合自适应控制

对于存在结构正反馈的振动主动控制系统,传统的基于有限冲击响应的自适应前馈控制器设计方法难以同时保证控制系统稳定与良好的控制性能.本文在分析正反馈对前馈控制系统影响的基础上,基于无限冲击响应控制器设计模式,提出一种结合前馈自适应控制器和反馈自适应控制器的混合自适应振动主动控制方法.其中前馈自适应控制器采用参考传感器采集到的扰动相关信号作为参考信号,反馈自适应控制器通过构建扰动的估计量作为参考信号,控制器参数更新采用Landau参数递推算法.以一典型的具有固有正反馈性质的机械振动系统为控制对象,给出了该混合自适应控制算法的详细推导过程以及稳定性和收敛性分析过程,得到了算法稳定与收敛的严格正实条件以及相应放松严格正实条件的要求.在此基础上,通过构建实时振动主动控制实验平台,针对多种振动扰动开展对比实验分析.相关实验结果验证了本文提出的混合自适应振动主动控制方法的可行性和有效性.     

一种非线性系统自适应控制及其收敛性分析*

本文对基于输入输出随机梯度的非线性系统的控制律进行了收敛性分析，给出了ＳＩＳＯ控制系统收敛的充分条件，并根据该条件给出一种非线性系统自适应控制器的设计方法。     

任意初值非线性不确定系统的迭代学习控制

为解决任意初态下的轨迹跟踪问题, 针对一类含参数和非参数不确定性的非线性系统, 提出基于滤波误差初始修正的自适应迭代学习控制方法. 利用修正滤波误差信号设计学习控制器, 并以Lyapunov方法进行收敛性能分析. 依据类Lipschitz条件处理非参数不确定性, 对于处理过程中出现的未知时变参数向量, 利用自适应迭代学习机制进行估计. 经过足够多次迭代后, 藉由修正滤波误差在整个作业区间收敛于零, 实现滤波误差本身在预设的作业区间也收敛于零. 仿真结果表明了本文所提控制方法的有效性.     

无抖振离散重复控制器的设计与实现

针对周期参考/干扰信号下的不确定离散时间系统,提出一种基于吸引律的重复控制方法,在吸引律中"嵌入"干扰抑制措施,构造理想误差动态,并基于此设计重复控制器.文中推导出单调减区域、绝对吸引层和稳态误差带边界的表达式,用于整定控制器参数和表征闭环系统的跟踪性能,并给出了跟踪误差在无干扰时收敛于原点及在干扰存在时收敛进入稳态误差带内所需最多步数的表达式.设计的重复控制器不仅能够完全抑制周期干扰信号,而且可以消除系统抖振.在电机实验装置上的应用结果表明了所提出控制方法的有效性.     

集成神经网络与自适应算法的分数阶滑模控制

针对被控对象的参数时变和外部扰动问题,本文融合神经网络的万能逼近能力和自适应控制技术,并结合分数阶微积分理论,提出了基于神经网络和自适应控制算法的分数阶滑模控制策略.本文采用等效控制的方法设计滑模控制律,并利用神经网络的万能逼近能力估测控制律的变化,结合自适应控制算法和分数阶微积分理论抑制传统滑模控制系统的抖震,同时根据Lyapunov稳定性理论分析了系统的稳定性,最后给出了实验结果.实验结果表明,本文提出的基于神经网络和自适应控制算法的分数阶滑模控制系统,能保持滑模控制器对系统外部扰动和参数变化鲁棒性的同时,也能有效地抑制抖震,使得系统获得较高的控制性能.     

Improving transient performance of adaptive control via a modified reference model and novel adaptation

This paper presents a new model reference adaptive control (MRAC) framework for a class of nonlinear systems to address the improvement of transient performance. The main idea is to introduce a nonlinear compensator to reshape the closed‐loop system transient, and to suggest a new adaptive law with guaranteed convergence. The compensator captures the unknown system dynamics and modifies the given nominal reference model and the control action. This modified controlled system can approach the response of the ideal reference model. The transient is easily tuned by a new design parameter of this compensator. The nominal adaptive law is augmented by new leakage terms containing the parameter estimation errors. This allows for fast, smooth and exponential convergence of both the tracking error and parameter estimation, which again improves overall reference model following. We also show that the required excitation condition for the estimation convergence is equivalent to the classical persistent excitation (PE) condition. In this respect, this paper provides an intuitive and numerically feasible approach to online validate the PE condition. The salient feature of the suggested methodology is that the rapid suppression of uncertainties in the controlled system can be achieved without using a large, high‐gain induced, learning rate in the adaptive laws. Extensive simulations are given to show the effectiveness and the improved response of the proposed schemes. Copyright © 2016 John Wiley & Sons, Ltd.     

Composite Adaptive Control of Uncertain Euler‐Lagrange Systems with Parameter Convergence without PE Condition

This work proposes a novel composite adaptive controller for uncertain Euler‐Lagrange (EL) systems. The composite adaptive law is strategically designed to be proportional to the parameter estimation error in addition to the tracking error, leading to parameter convergence. Unlike conventional adaptive control laws which require the regressor function to be persistently exciting (PE) for parameter convergence, the proposed method guarantees parameter convergence from a milder initially exciting (IE) condition on the regressor. The IE condition is significantly less restrictive than PE, since it does not rely on the future values of the signal and that it can be verified online. The proposed adaptive controller ensures exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met. Simulation results corroborate the efficacy of the proposed technique and also establishes it's robustness property in the presence of unmodeled bounded disturbance.     

On parameter convergence in least squares identification and adaptive control

Least squares estimation is appealing in performance and robustness improvements of adaptive control. A strict condition termed persistent excitation (PE) needs to be satisfied to achieve parameter convergence in least squares estimation. This paper proposes a least squares identification and adaptive control strategy to achieve parameter convergence without the PE condition. A modified modeling error that utilizes online historical data together with instant data is constructed as additional feedback to update parameter estimates, and an integral transformation is introduced to avoid the time derivation of plant states in the modified modeling error. On the basis of these results, a regressor filtering–free least squares estimation law is proposed to guarantee exponential parameter convergence by an interval excitation condition, which is much weaker than the PE condition. And then, an identification‐based indirect adaptive control law is proposed to establish exponential stability of the closed‐loop system under the interval excitation condition. Illustrative results considering both identification and control problems have verified the effectiveness and superiority of the proposed approach.     

Robust adaptive finite‐time parameter estimation and control for robotic systems

This paper studies adaptive parameter estimation and control for nonlinear robotic systems based on parameter estimation errors. A framework to obtain an expression of the parameter estimation error is proposed first by introducing a set of auxiliary filtered variables. Then three novel adaptive laws driven by the estimation error are presented, where exponential error convergence is proved under the conventional persistent excitation (PE) condition; the direct measurement of the time derivatives of the system states are avoided. The adaptive laws are modified via a sliding mode technique to achieve finite‐time convergence, and an online verification of the alternative PE condition is introduced. Leakage terms, functions of the estimation error, are incorporated into the adaptation laws to avoid windup of the adaptation algorithms. The adaptive algorithm applied to robotic systems permits that tracking control and exact parameter estimation are achieved simultaneously in finite time using a terminal sliding mode (TSM) control law. In this case, the PE condition can be replaced with a sufficient richness requirement of the command signals and thus is verifiable a priori. The potential singularity problem encountered in TSM controls is remedied by introducing a two‐phase control procedure. The robustness of the proposed methods against disturbances is investigated. Simulations based on the ‘Bristol‐Elumotion‐Robotic‐Torso II’ (BERT II) are provided to validate the efficacy of the introduced methods. Copyright © 2014 John Wiley & Sons, Ltd.     

A robust adaptive controller for Hammerstein nonlinear systems

Hammerstein nonlinear systems have appeared useful in modeling nonlinear processes encountered in engineering practice. Control algorithms may lead to unsatisfactory performance if the parametric model does not agree with the plant. To this end, this paper proposes a new robust adaptive control approach for discrete-time Hammerstein nonlinear systems which are more close to some industrial plants. The adaptive control law and recursive parameter estimation are updated by introducing the estimate of the model error as a feedback. Theoretical results show that parameter estimation convergence and closed-loop system stability can be guaranteed under mild conditions. Simulation examples including a continuous stirred tank reactor (CSTR) system are given to show the effectiveness of the obtained results.     

Adaptive parameter identification of linear SISO systems with unknown time-delay

An adaptive online parameter identification is proposed for linear single-input-single-output (SISO) time-delay systems to simultaneously estimate the unknown time-delay and other parameters. After representing the system as a parameterized form, a novel adaptive law is developed, which is driven by appropriate parameter estimation error information. Consequently, the identification error convergence can be proved under the conventional persistent excitation (PE) condition, which can be online tested in this paper. A finite-time (FT) identification scheme is further studied by incorporating the sliding mode scheme into the adaptation to achieve FT error convergence. The previously imposed constraint on the system relative degree is removed and the derivatives of the input and output are not required. Comparative simulation examples are provided to demonstrate the validity and efficacy of the proposed algorithms.     

Globally stabilizing adaptive control design for nonlinearly-parameterized systems

In this note, a new adaptive control design is proposed for nonlinear systems that are possibly nonaffine and contain nonlinearly parameterized unknowns. The proposed control is not based on certainty equivalence principle which forms the foundation of existing and standard adaptive control designs. Instead, a biasing vector function is introduced into parameter estimate; it links the system dynamics to estimation error dynamics, and its choice leads to a new Lyapunov-based design so that affine or nonaffine systems with nonlinearly parameterized unknowns can be controlled by adaptive estimation. Explicit conditions are found for achieving global asymptotic stability of the state, and the convergence condition for parameter estimation is also found. The conditions are illustrated by several examples and classes of systems. Besides global stability and estimation convergence, the proposed adaptive control has the unique feature that it does not contains any robust control part which typically overpowers unknown dynamics, may be conservative, and also interferes with parameter estimation.