An input-output view of robustness in adaptive control

The stability and robustness properties of adaptive control systems are examined using input-output stability theory, i.e. passivity and small-gain theory. A generic adaptive error system is developed based on the concept of a tuned system—an ideal converged (nonadaptive) closed-loop system. Using this error system with passivity theory gives conditions for global stability where only boundedness (in norm) is required on the external inputs, e.g. disturbance, reference and initial conditions. Small gain theory is used to develop local stability results where the magnitudes of the external inputs are restricted. In the global case, a particular system operator (not the plant) is required to be strictly-passive, a condition which is unlikely to hold in actual use due to unmodeled dynamics. The local results, however, are not so restricted and allow for unmodeled dynamics. In this latter case an estimate of the stability margin is given under a persistent excitation condition.     

不确定控制系统概率鲁棒性分析——自适应重要抽样法

将自适应重要抽样(AIS)法应用于不确定控制系统的概率鲁棒性分析问题,克服了标准MonteCarlo仿真(MCS)方法不能有效解决小概率事件的困难.给出了一种新的AIS方案.首先采用了一种递归的估计条件众数算法来产生一组使得系统不稳定或性能不可接受的不确定参数向量样本.然后利用这组样本来估计初始高斯型重要抽样密度函数的参数,并执行随后的迭代仿真过程.仿真结果验证了该方法的有效性.     

一种具有强鲁棒性的模型参考自适应控制系统

提出一种模型参考自适应控制系统．该系统只要求知道对象阶次的上界,不要求对象严格正实和最小相位,并且允许存在建模误差和作用在对象任何部位的大幅值高频干扰．系统的强鲁棒性来源于特殊的系统结构和对信号的良好滤波．Lyapunov稳定性理论证明了系统的渐近稳定性,Matlab仿真验证了系统的强鲁棒性．     

扰动抑制无模型自适应控制的鲁棒性分析

针对一类存在测量扰动的SISO非线性离散时间系统,研究无模型自适应控制算法的扰动作用问题.首先给出了系统输出误差与测量扰动的关系,分析了测量扰动对控制性能的影响.然后提出了一种带有滤波器的改进无模型自适应控制算法,该算法较常规无模型自适应控制算法可有效抑制测量扰动的作用.仿真结果验证了理论分析的正确性.     

基于向量图分析的一种迭代学习控制算法及其鲁棒性

为了增强迭代学习控制的鲁棒性,加快学习过程的收敛速度,而又不过多地依赖于系统内部信息,本文基于向量图分析思路,利用输入空间的向量构造三角形修正结构,得到了一种新的迭代学习控制算法．该算法根据跟踪误差的大小,调节输入控制量在三角形的一条边上滑动,在跟踪误差较大时,算法能找到控制期望的大致位置并加速收敛,在跟踪误差较小时,能将控制量稳定在其期望的很小邻域内,理论上证明了该邻域直径大小为跟踪误差的二阶无穷小．数值仿真结果说明了它的有效性和优越性．     

Transient-performance improvement with a new class of adaptive controllers

Computable performance bounds are derived in addition to global stability and asymptotic tracking, a systematic improvement of transient performance can be achieved. The underlying linear nonadaptive controller is shown to possess a parametric robustness property, but for a large parameter uncertainty it requires high gain. A comparison between the adaptive and the nonadaptive performance bounds demonstrates that adaptation improves the overall performance without the undesirable effects of high gain.     

Sliding mode control of singularly perturbed systems and its application in quad-rotors

This paper presents a sliding mode control scheme for tracking control of nonlinear singularly perturbed systems in the presence of model errors and external disturbances. A dual-loop feedback control is developed to provide accurate tracking capability and sufficient robustness to system uncertainties. A sliding mode controller is proposed in the outer-loop feedback design such that the plant states are stabilised for given reference trajectories, while an additional robust controller is designed in the inner loop to increase the adaptability to uncertainties, and reduce the effect of unmodelled high-frequency dynamics on plant dynamics. An appealing feature of the control scheme is the attenuation of chattering. The effectiveness and merits of the new control scheme developed are shown via a verification example of velocity control of a quad-rotor.     

Stability and robustness analysis of cyclic pseudo-downsampled iterative learning control

Cyclic pseudo-downsampled iterative learning control (ILC) has shown advantages to achieve good learning performance for trajectories containing high-frequency components and has been verified on industrial robot application. This scheme is a multirate ILC in nature and downsamples the fast rate signals (with a sampling period T) to slow rate signals (with a sampling period mT) with a ratio m. Then ILC is carried out on the downsampled signals and interpolates its output to a fast rate signal. For the next iteration, ILC scheme downsamples the signals with the same ratio m but at different sampling points with a time shift T. This process is repeated on the iteration axis so that ILC updates the input of all the sampling points once every m cycles. By experiments [Zhang, B., Wang, D., Ye, Y., Zhou, K. and Wang, Y. (2009) ‘Cyclic Pseudo-downsampled Iterative Learning Control for High Performance Tracking’, Control Engineering Practice, 17, 957–965], this scheme has been shown effective and comparisons with other relevant schemes demonstrate its superior performance. In this article, this cyclic pseudo-downsampled ILC scheme is examined analytically and proved mathematically to be stable and robust. Extensions and insights are also established based on the theoretical developments and simulation verification. pseudo-downsampled ILC scheme.     

Robustness of adaptive control of robots

In this paper we discuss the robustness of adaptive control of rigid robots and methods for improving robustness in the face of unmodeled dynamics and external disturbances. Robustness to unmodeled dynamics is achieved using a so-called composite control strategy based on a singular perturbation formulation of the manipulator dynamics together with -modificiation. Rigorous stability proofs are given using a composite Lyapunov function approach.Research partially supported by the National Science Foundation under Grants INT-8902476 and MSM-9100618 and by the University of Illinois Manufacturing Research Center.     

基于内模结构的GPC 鲁棒性改进与分析

在内模结构下，广义预测控制器和滤波器的定量表达是在优化过程中同时形成的，缺乏对未建模动态的主动抑制能力，对此引入新的失配滤波器以改进系统的鲁棒性，利用Roche定理，给出改进后系统鲁棒稳定的区域，仿真研究表明、引入失配滤波器后系统的鲁棒域得到了有效的改善。     

Direct adaptive control of robotic systems

This paper presents a new approach to adaptive motion control of an important class of robotic systems. The control schemes developed using this approach are very simple and computationally efficient since they do not require knowledge of either the mathematical model or the parameter values of the robotic system dynamics. It is shown that the control strategies are globally stable in the presence of bounded disturbances, and that the size of the tracking errors can be made arbitrarily small. The proposed controllers are very general and are implementable with a wide variety of robotic systems, including both open- and closed-kinematic-chain manipulators. Computer simulation results are given for a seven degree-of-freedom (DOF) Robotics Research Corporation Model K-1607 arm. These results demonstrate that accurate and robust trajectory tracking can be achieved by using the proposed schemes.     

Stability analysis of decentralised robust adaptive control

Recent results on robustness of continuous time adaptive controllers using a relative deadzone are extended to the situation of many interacting adaptive controllers. With a special form for the deadzone function which allows for interactions and an M-matrix stability condition, stability is established in the sense that all signals are bounded for bounded inputs.     

A general analysis and control framework for process systems with inventory recycling

In this work, we generalize our previous results concerning the impact of material recycling and energy recovery on plant dynamics and control. We define a generic class of integrated process systems, in which an extensive quantity that obeys conservation laws is recovered from the process output and recycled to the process feed; the operation of the system is assumed to be subject to time‐varying, measurable disturbances. We establish, in this general case, that integration is conducive to the emergence of a two‐time‐scale dynamic behavior and derive reduced‐order models for the dynamics in each time scale. Subsequently, we postulate a hierarchical control framework that exploits these dynamics results in the design of coordinated fast and slow feedback/feedforward controllers and formulate a stability result for the closed‐loop system. We demonstrate these concepts on a case study concerning an energy‐integrated process. Copyright © 2013 John Wiley & Sons, Ltd.     

Design and stability analysis of a variable structure adaptive backstepping controller

This paper presents the design and stability analysis of a Variable Structure Adaptive Backstepping Controller (VS‐ABC) for linear plants with relative degree one, using only input/output measurements. Instead of traditional integral adaptive laws for estimating the plant parameters, switching laws are proposed to increase robustness to parametric uncertainties and disturbances, as well as to improve transient response. Moreover, the controller design is more intuitive when compared with the original adaptive backstepping controller, since the relay amplitudes are related to the plant nominal parameters and their respective uncertainties. Simplified algorithm versions are also presented, named Compact and Relay VS‐ABC, which reduce the practical implementation complexity, and encourage applications in industrial environments. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Passivity-based adaptive inventory control

A new adaptive inventory control strategy is developed by applying online adaptation in the framework of passivity-based control. By using the system model and definition of the inventory, a feedback-feedforward control structure is derived from the passivity theorem. The stability analysis and the extension of the controller to a non-passive system are also given in this paper. This control strategy is demonstrated in a transfer function example and an application to a pressure tank unit in a chemical plant.     

Stability of discrete model reference adaptive control — revisited

We demonstrate that the model reference adaptive controller is robust with respect to small model/plant mismatch. The sign and a lower bound on the high frequency gain are known and the control parameters are constrained to belong to a compact set which contains the parameters of a stabilizing controller. Data normalization and deadzones do not play a role in the analysis. A constructive proof is used to develop bounds for the allowable gain of the model mismatch. When the algorithm state is far from equilibrium the signals are measured by a decaying exponential. The rate of convergence is estimated. An expression which can be used to calculate the size of an overbounding set is developed. Its size scales uniformly with respect to the external disturbances, the inverse of the adaptive gain and the reference. The ideal case is obtained as these tend to zero. This result holds true even when there is a model mismatch.     

An alternate stability analysis framework for adaptive control

A proof is given for the uniform asymptotic stability of a class of pointwise-in-time stable systems of time-varying ordinary differential equations. The sufficient conditions for stability are shown to be naturally testable in a general adaptive control context. A weak form of robust identification is found to imply robust stability of the overall closed-loop adaptive control system.     

两能级量子系统的固定时间控制及鲁棒性

本文考虑刘维尔方程描述的两能级量子系统对于目标平衡态的固定时间控制问题.首先通过相干矢量和复数的指数形式对系统模型及控制目标进行等价变换,并借助合适的Lyapunov函数设计一个含分数幂的连续非光滑控制律,然后利用固定时间稳定性定理给出了系统实现固定时间收敛的条件.针对某些分数幂取值导致控制性能较差的情况,提出了两种非...     

Design and stability analysis of an indirect variable structure model reference adaptive control

This paper presents the stability and robustness analysis of an indirect adaptive control based variable structure algorithm for uncertain plants with relative degree one. The indirect approach has been proposed as a way to get an easier design of the switching laws, compared to the direct relationship between the plant transfer function parameters and the physical parameters of the system. Here, a singular perturbation approach is used to establish the robustness of the controller in the presence of unmodelled dynamics and disturbances. It is shown that, for sufficiently small parasitics, the system remains stable with respect to some small residual set.