基于Backstepping的非一致轨迹迭代学习控制研究

针对一类在有限时间区间上可重复运行的高阶混合参数化非线性系统,利用改进Backstepping方法,将参数重组技巧和分段积分机制相结合,提出了一种混合自适应迭代学习控制算法。该算法由参数的微分-差分型自适应律和学习控制律组成,可以处理目标轨线迭代可变的跟踪问题。通过构造Lyapunov-like泛函使得跟踪误差的平方在一个有限时间区间上的积分收敛于零,同时保证所有信号均在有限时间区间内有界。仿真结果说明了所提算法的有效性。     

含有参数化和非参数化不确定性系统重复学习控制

针对含有参数化和非参数化的高阶非线性系统,设计了一种重复学习控制方案.假设未知时变参数和参考信号的共同周期是已知的,通过参数重组技巧,将所有未知时变项合并为一个周期时变向量.将改进Backstepping方法与分段积分机制相结合,构造了微分-差分参数自适应律和重复学习控制律,使跟踪误差在误差平方范数意义下渐近收敛于零.利用Lyapunov泛函,给出了闭环系统收敛的充分条件.仿真结果验证了该方法的有效性.     

非一致目标跟踪的混合自适应迭代学习控制

针对一类含有时变和时不变参数的高阶非线性系统,结合Backstepping方法,提出了一种新的自适应迭代学习控制方法,该方法由微分-差分型自适应率和学习控制率组成,保证对非一致目标的跟踪误差平方在一个有限区间上的积分渐近收敛于零,克服了传统的迭代学习控制(ILC)对目标轨线限制,可以跟踪非一致目标轨线.通过构造复合能量函数,给出了闭环系统收敛的一个充分条件,仿真结果说明了该方法的有效性和可行性.     

未知时变时滞非线性参数化系统自适应迭代学习控制

针对含有未知时变参数和时变时滞的非线性参数化系统,提出了一种新的自适应迭代学习控制方法.该方法将参数分离技术与信号置换思想相结合,可以处理含有时变参数和时滞相关不确定性的非线性系统.设计了一种自适应控制策略,使跟踪误差的平方在一个有限区间上的积分渐近收敛于零.通过构造Lyapunov-Krasovskii型复合能量函数,给出了闭环系统收敛的一个充分条件.给出两个仿真例子验证了控制方法的有效性.     

严格反馈随机非线性系统的鲁棒自适应逆最优跟踪

针对具有未知定常参数和标准Wiener噪声扰动的严格反馈非线性系统,结合参考信号,构造了误差系统,使用Backstepping算法设计了误差系统的自适应逆最优控制律和参数自适应律,进而解决了原系统的鲁棒自适应逆最优跟踪.     

具有非线性不确定参数的电液伺服系统自适应backstepping控制

针对电液伺服系统中存在非线性不确定参数的问题,提出了一种采用积分型Lyapunov函数的自适应backstepping控制方法.首先定义积分型Lyapunov函数,将电液伺服系统中的非线性不确定参数转化为线性表示;然后逐步递推设计backstepping控制器,同时在控制律中加入阻尼项,从而补偿外界干扰对控制性能的影响;基于Lyapunov稳定性方法,设计了参数自适应律,并且在自适应律中引入充分光滑投影算子,实现对电液伺服系统中不确定参数漂移的抑制作用.搭建了AMESim与MATLAB的联合仿真平台,对所设计的自适应backstepping控制器进行仿真,作为对比,设计了不带有非线性参数估计的自适应backstepping控制器和PID算法.仿真表明,本文所设计的控制器具有良好的跟踪性能和补偿非线性不确定参数变化的能力.     

非线性时滞大系统自适应神经网络分散控制

针对一类未知非线性时滞关联大系统,提出一种自适应神经网络分散跟踪控制方案．采用神经网络逼近各子系统内部的非线性函数和关联项中的时滞非线性函数;利用占有方法处理时滞项,采用Backstepping技术设计分散控制律和参数自适应律．基于Lyapunov-Krasoviskii泛函证明了闭环大系统所有信号半全局一致最终有界．通过调节设计参数和增加神经元个数,可以实现任意输出跟踪精度．实例仿真说明了该方案的可行性。     

一类非线性时滞输出反馈系统的自适应控制

针对一类参数化非线性时滞输出反馈系统,提出了一种无记忆自适应跟踪控制器的设计方案.采用时滞滤波器估计系统状态,用Domination处理非线性时滞项,应用Backstepping技术设计控制器和参数自适应律.放宽了对时滞项的要求.通过构建一个Lyapunov＿Krasoviskii泛函,证明了闭环系统的稳定性,实现了对目标轨线的渐近跟踪,保证了所有信号一致有界.实例仿真说明了该方案的可行性.     

非线性参数化系统自适应迭代学习控制

研究一类含有未知时变参数的非线性参数化系统的学习控制问题.利用参数分离技术和信号置换思想,通过置换系统方程,合并所有时变参数为一个未知时变参数,用迭代自适应方法估计该未知参数,设计了一种自适应迭代学习控制方法,使得跟踪误差的平方在一个有限区间上的积分渐近收敛于零.通过构造一个类Lyapunov函数,给出了跟踪误差收敛和所有闭环系统信号有界的一个充分条件.仿真结果验证了该方法的有效性.     

一类非线性参数化系统自适应重复学习控制

针对一类高阶非线性参数化系统, 利用分段积分机制, 提出了一种新的自适应重复学习控制方法. 该方法结合反馈线性化, 可以处理参数在一个未知紧集内周期性快时变的非线性系统, 通过引进微分-差分混合型参数自适应律, 设计了一种自适应控制策略, 使广义跟踪误差在误差平方范数意义下渐近收敛于零, 通过构造Lyapunov泛函, 给出闭环系统收敛的一个充分条件. 实例仿真结果说明了该方法的可行性.     

任意初态下不确定时滞系统的PD型迭代学习控制*

针对不确定时滞系统讨论带有初始修正的ＰＤ型迭代学习控制算法，给出这类系统的输出极限轨迹，以及迭代输出收敛于该极限轨迹的较弱的充分条件，其中将初始条件放宽为某任意可达初始状态函数的可重复性。仿真结果表明这种算法中的初始修正项可以有效地抑制初始偏移的影响。     

不确定受扰电液伺服系统智能自学习PID控制

针对具有参数不确定和外负载扰动的不确定受扰电液伺服系统,提出一种智能自学习PID控制策略.该方法不依赖于系统的精确模型,是一种数据驱动的控制方法.首先,通过改进的动态线性化方法将非线性非仿射的电液伺服系统等效为含有时变参数项和非线性不确定项的线性仿射形式;然后,采用梯度估计算法和时间差分算法分别对时变参数项和非线性不确定项进行估计;接着,利用iPID控制引入附加误差信息对过度线性化丢失的信息进行补偿;最后,根据最优准则,设计不确定受扰电液伺服系统的参数更新律和学习控制律.通过理论分析和仿真实验验证所提出控制策略的收敛性,并通过对比实验,验证该控制方案应用于电液伺服系统的优越性和精确性.实验结果表明,所提出方法能够抑制非线性扰动对系统造成的不良影响,实现理想轨迹的精确跟踪.     

非完整移动机器人的连续时变鲁棒K指数镇定

针对带有参数不确定性动态非完整移动机器人的镇定问题,提出一个全局连续的时变鲁棒控制律.首先,使用全局可逆变换将系统的动力学模型转换成一个不确定性线性子系统和一个不确定性非线性子系统;然后,引入一个与初值有关的指数衰减项,将非线性子系统转换成带扰动项的线性系统;最后,设计鲁棒控制律将整个系统镇定到原点.与已有的控制器相比,所提出的控制器能同时获得连续性、渐近性和指数收敛速度,仿真结果也验证了这一点.     

Robust model reference adaptive control for transient performance enhancement

To circumvent the potentially poor transient response induced by nonlinear uncertain dynamics in the adaptive control system, this article proposes a new model reference adaptive control design scheme to improve its transient control response. We first construct a compensator to online extract the undesired dynamics in the online learning, which is incorporated into the reference model and control simultaneously. Then, an error feedback term is incorporated into the reference model to speed up the convergence of both the compensator and tracking error. Moreover, a new leakage term containing the estimation error is constructed and then added in the adaptive law to guarantee the convergence of both the estimation error and tracking error. To further reveal the mechanisms behind these proposed methods, a new methodology to analyze the transient error bounds based on L₂‐norm and Cauchy‐Schwartz inequality is also developed. Based on the analysis results, we find that the proposed methods can effectively reduce the bound of the tracking error and thus achieve an improved transient control performance without violating the system stability even with high‐gain adaptation. In addition, the frequency‐domain analysis is resorted to show the comparative responses of different adaptive laws, which indicate that the proposed adaptive law can maintain the stability margin even with a high‐gain learning rate. A numerical example is given to demonstrate improved control responses of these proposed schemes.     

Parameterizing robust manipulator controllers under approximate inverse dynamics: A double‐Youla approach

We consider the goal of ensuring robust stability when a given manipulator feedback control law is modified online, for example, to safely improve the performance by a learning module. To this end, the factorization approach is applied to both the plant and controller models to characterize robustly stabilizing controllers for rigid‐body manipulators under approximate inverse dynamics control. Outer‐loop controllers to stabilize the nonlinear uncertain loop that results from approximate inverse dynamics are often derived by lumping uncertainty in a single term and subsequent analysis of the error system. Here, by contrast, the well‐known norm bounds of these uncertain dynamics are first recast into a generalized plant configuration that preserves the characteristic uncertainty structure. Then, the overall loop uncertainty is expressed with respect to the nominal outer‐loop feedback controller by means of an uncertain dual‐Youla operator. Therefore, using the dual‐Youla parameterization, we provide a novel way to rigorously quantify permissible perturbations of robot manipulator feedforward/feedback controllers. The method proposed in this paper does not constitute another robust control law for rigid‐body manipulators, but rather a characterization of a set of robustly stabilizing controllers. The resulting double‐Youla parameterization for the control of robot manipulators is amenable to numerous advanced design methods. The result is thoroughly discussed by a planar elbow manipulator and exemplified with a six‐degree‐of‐freedom robot scenario with varying payload.     

Authors' reply [to comments on "Variable structure control of discretized continuous-time systems"]

In their comments (IEEE Trans. Autom. Control, vol. 50, no. 4, pp. 538-540, Apr. 2004), Paranjpe and Phadke show that the control law inside the sector we proposed (Corradini and Orlando, "Variable structure control of discretized continuous-time systems", IEEE Trans. Autom. Control, vol. 43,no.9,pp.1329-1334,Sep.1998) works even in the case when the control input vector has a not negligible uncertain term b. Though this result is of course welcome since it widens the validity range of the controller, it is still our opinion that the control law (17b) is not completely insensitive to the amplitude of the uncertain term b. This issue is explained in the reply.     

未知相对度非线性系统的一阶D型迭代学习控制

The classical D-type iterative learning control law depends crucially on the relative degree of the controlled system, high order differential iterative learning law must be taken for systems with high order relative degree. It is very difficult to ascertain the relative degree of the controlled system for uncertain nonlinear systems. A first-order D-type iterative learning control design method is presented for a class of nonlinear systems with unknown relative degree based on dummy model in this paper. A dummy model with relative degree 1 is constructed for a class of nonlinear systems with unknown relative degree. A first-order D-type iterative learning control law is designed based on the dummy model, so that the dummy model can track the desired trajectory perfectly, and the controlled system can track the desired trajectory within a certain error. The simulation example demonstrates the feasibility and effectiveness of the presented method.     

具有自适应调节律的非线性系统执行器故障检测和隔离方法

针对受到外部干扰的非线性系统,讨论了基于观测器的执行器故障检测和隔离方法.首先,通过引入一个对Lipschitz非线性项Lipschitz常数自适应调节的微分调节项,使得观测器具有自适应性,从而使观测器设计具有无须知道Lipschitz常数大小的优点;然后,通过一滑模控制项来抑制干扰,使观测器具有鲁棒性,并在此基础上,结合多观测器故障隔离的思想,提出了执行器故障检测和隔离方法;最后,通过对一个七阶飞行器实际模型的仿真,表明了该方法的实用性.     

一类高阶非线性参数化系统自适应重复学习控制

针对一类高阶非线性参数化系统,利用参数重组技巧,提出了一种自适应重复学习控制方法.该方法结合反馈线性化,可以处理参数在一个未知紧集内周期性、快时变的非线性系统.通过引进微分-差分参数自适应律,设计了一种自适应控制策略,使广义跟踪误差在误差平方范数意义下渐近收敛于零.通过构造Lyapunov泛函,给出了闭环系统收敛的一个充分条件.实例仿真结果说明了该方法的可行性和有效性.