分域设计迭代学习控制器抑制非重复性扰动

为了抑制迭代方向上已知重复样式的非重复性输出扰动,提出了迭代学习控制(Iterative Learning Control,ILC)的分域算法。时间域内设计传统PID型迭代学习控制器,并且优化其参数;迭代域内利用内模原理抑制非重复性输出扰动,跟踪期望轨迹;利用加权思想将两者相结合,得到迭代学习控制器的分域设计算法。相对于已有算法,建立了针对一般扰动的设计框架,并且合理配置了算法的参数,使收敛速度及精度有所提高。仿真结果说明了该算法的有效性。     

基于强化迭代学习的四旋翼无人机轨迹控制

为进一步提升在未知环境下四旋翼无人机轨迹的跟踪精度,提出了一种在传统反馈控制架构上增加迭代学习前馈控制器的控制方法。针对迭代学习控制（ILC）中存在的学习参数整定困难的问题,提出了一种利用强化学习（RL）对迭代学习控制器的学习参数进行整定优化的方法。首先,利用RL对迭代学习控制器的学习参数进行优化,筛选出当前环境及任务下最优的学习参数以保证迭代学习控制器的控制效果最优;其次,利用迭代学习控制器的学习能力不断迭代优化前馈输入,直至实现完美跟踪;最后,在有随机噪声存在的仿真环境中把所提出的强化迭代学习控制（RL-ILC）算法与未经参数优化的ILC方法、滑模变结构控制（SMC）方法以及比例-积分-微分（PID）控制方法进行对比实验。实验结果表明,所提算法在经过2次迭代后,总误差缩减为初始误差的0.2%,实现了快速收敛;并且与SMC控制方法及PID控制方法相比,RL-ILC算法在算法收敛后不会受噪声影响产生轨迹波动。由此可见,所提算法能够有效提高无人机轨迹跟踪的准确性和鲁棒性。     

Consensus seeking via iterative learning for multi‐agent systems with switching topologies and communication time‐delays

This paper deals with the high‐precision consensus seeking problem of multi‐agent systems when they are subject to switching topologies and varying communication time‐delays. By combining the iterative learning control (ILC) approach, a distributed consensus seeking algorithm is presented based on only the relative information between every agent and its local (or nearest) neighbors. All agents can be enabled to achieve consensus exactly on a common output trajectory over a finite time interval. Furthermore, conditions are proposed to guarantee both exponential convergence and monotonic convergence for the resulting ILC processes of multi‐agent consensus systems. In particular, the linear matrix inequality technique is employed to formulate the established convergence conditions, which can directly give formulas for the gain matrix design. An illustrative example is included to validate the effectiveness of the proposed ILC‐motivated consensus seeking algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimal <Emphasis Type="Italic">N</Emphasis>-Parametric Type Iterative Learning Control

One of the most important problems in the field of the iterative learning control (ILC) is to design algorithms, in order to achieve a desired convergence rate. In this paper a new type of the ILC algorithm is introduced, which is called N-parametric type ILC with optimal gains. The convergence of the proposed algorithm is analyzed and an optimal design method is presented to determine its gains. The effect of the number of the parameters on the convergence rate of the presented ILC is investigated. It is shown that N parametric type of this ILC has a better performance than the N-1 one. Illustrative simulation examples are given to verify the theoretical analysis.     

Sampled‐data iterative learning control for continuous‐time nonlinear systems with iteration‐varying lengths

In this work, sampled‐data iterative learning control (ILC) method is extended to a class of continuous‐time nonlinear systems with iteration‐varying trial lengths. In order to propose a unified ILC algorithm, the tracking errors will be redefined when the trial length is shorter or longer than the desired one. Based on the modified tracking errors, 2 sampled‐data ILC schemes are proposed to handle the randomly varying trial lengths. Sufficient conditions are derived rigorously to guarantee the convergence of the nonlinear system at each sampling instant. To verify the effectiveness of the proposed ILC laws, simulations for a nonlinear system are performed. The simulation results show that if the sampling period is set to be small enough, the convergence of the learning algorithms can be achieved as the iteration number increases.     

ILC for non-minimum phase system

In this paper we propose a design method of an iterative learning controller (ILC) for a non-minimum phase (NMP) system by model-matching theory. The ILC consists of two learning filters acting on both the previous input signal and the previous error signal. To design the learning filters, we convert the convergence condition of the ILC into the model-matching problem and get the stable and proper learning filter by solving the Nevanlinna's algorithm. To show the usefulness of the proposed algorithm, some design examples are included.     

A Study On Iterative Learning Control With Adjustment Of Learning Interval For Monotone Convergence In The Sense Of Sup‐Norm

It has been found that some huge overshoot in the sense of sup‐norm may be observed when typical iterative learning control (ILC) algorithms are applied to LTI systems, even though monotone convergence in the sense of λ‐norm is guaranteed. In this paper, a new ILC algorithm with adjustment of learning interval is proposed to resolve such an undesirable phenomenon, and it is shown that the output error can be monotonically converged to zero in the sense of sup‐norm when the proposed ILC algorithm is applied. A numerical example is given to show the effectiveness of the proposed algorithm.     

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．     

Performance Enhancement for Rigid Tapping by Iterative Learning Control

In this study, an iterative learning control (ILC) algorithm is proposed to improve synchronous errors in rigid tapping. In rigid tapping, the displacements of the z‐axis and spindle must be kept synchronous to prevent damage. Using learning control provides better commands for both the z‐axis and spindle dynamics, improving the synchronicity of the output responses of the z‐axis and spindle. The proposed ILC makes use of synchronous errors in the previous cycle of tapping to modify the current position commands of both the z‐axis and spindle. A systematic algorithm is proposed for the computation of learning gains that guarantee the monotonic convergence of synchronous errors. A systematic procedure of applying ILC to rigid tapping is also proposed, where the ideas of effective learning gains and stop learning criteria are discussed. Experimental results on a tapping machine verify the effectiveness of the proposed ILC algorithm.     

基于Jacobi方法的线性离散时间系统的迭代学习控制

提出线性离散时间系统基于Jacobi方法的迭代学习控制问题.通过构建线性迭代学习控制问题与线性方程组之间的联系,将Jacobi方法引入到迭代学习控制中,并由此构建得到迭代学习控制律.借助于矩阵运算,证明这种学习律能使得系统的输出跟踪误差经有限次迭代后为零.数值例子说明了算法的可适用性.     

A numerical method for determining monotonicity and convergence rate in iterative learning control

In iterative learning control (ILC), a lifted system representation is often used for design and analysis to determine the convergence rate of the learning algorithm. Computation of the convergence rate in the lifted setting requires construction of large N×N matrices, where N is the number of data points in an iteration. The convergence rate computation is O(N²) and is typically limited to short iteration lengths because of computational memory constraints. As an alternative approach, the implicitly restarted Arnoldi/Lanczos method (IRLM) can be used to calculate the ILC convergence rate with calculations of O(N). In this article, we show that the convergence rate calculation using IRLM can be performed using dynamic simulations rather than matrices, thereby eliminating the need for large matrix construction. In addition to faster computation, IRLM enables the calculation of the ILC convergence rate for long iteration lengths. To illustrate generality, this method is presented for multi-input multi-output, linear time-varying discrete-time systems.     

New quasi-Newton iterative learning control scheme based on rank-one update for nonlinear systems

This paper develops an algorithm for iterative learning control on the basis of the quasi-Newton method for nonlinear systems. The new quasi-Newton iterative learning control scheme using the rank-one update to derive the recurrent formula has numerous benefits, which include the approximate treatment for the inverse of the system’s Jacobian matrix. The rank-one update-based ILC also has the advantage of extension for convergence domain and hence guaranteeing the choice of initial value. The algorithm is expressed as a very general norm optimization problem in a Banach space and, in principle, can be used for both continuous and discrete time systems. Furthermore, a detailed convergence analysis is given, and it guarantees theoretically that the proposed algorithm converges at a superlinear rate. Initial conditions which the algorithm requires are also established. The simulations illustrate the theoretical results.     

Robust monotone gradient‐based discrete‐time iterative learning control

This paper considers the use of matrix models and the robustness of a gradient‐based iterative learning control (ILC) algorithm using both fixed learning gains and nonlinear data‐dependent gains derived from parameter optimization. The philosophy of the paper is to ensure monotonic convergence with respect to the mean‐square value of the error time series. The paper provides a complete and rigorous analysis for the systematic use of the well‐known matrix models in ILC. Matrix models provide necessary and sufficient conditions for robust monotonic convergence. They also permit the construction of accurate sufficient frequency domain conditions for robust monotonic convergence on finite time intervals for both causal and non‐causal controller dynamics. The results are compared with recently published results for robust inverse‐model‐based ILC algorithms and it is seen that the algorithm has the potential to improve the robustness to high‐frequency modelling errors, provided that resonances within the plant bandwidth have been suppressed by feedback or series compensation. Copyright © 2008 John Wiley & Sons, Ltd.     

内模强化学习型模型预测控制及其在人工胰脏上的应用

在学习型模型预测控制的框架里,迭代学习控制器被用来更新模型预测控制器的设定点.在已经发表的研究成果里,学习型模型预测控制用到的是比例型的学习率,这种学习率的学习能力有限,而且怎样设计学习增益仍然是一个开放性问题.在本文中,基于内模控制理论提出的PID型的迭代学习控制器被用来更新模型预测控制器的设定点.为了方便起见,本文提出的结合算法可称为内模强化学习型模型预测控制.本文提出的算法应用在(1)型糖尿病人的人工胰脏闭环控制上.仿真结果显示,本算法对比于比例学习型模型预测控制可以达到更好的收敛性能,而且对非重复干扰有很好的鲁棒性.     

A two-stage iterative learning control technique combined with real-time feedback for independent disturbance rejection

A novel control framework for batch and repetitive processes is proposed. The currently practiced methods to combine real-time feedback control (RFC) with iterative learning control (ILC) share a problem that RFC causes ILC to digress from its convergence track along the run index when there occur real-time disturbances. The proposed framework provides a pertinent means to incorporate RFC into ILC so that the performance of ILC is virtually separated from the effects of real-time disturbances. As a prototypical algorithm, a two-stage algorithm has been devised by modifying and combining the existing QILC and BMPC techniques.     

Variable-gain PD-type iterative learning control for a class of nonlinear time-varying systems

This paper investigates variable-gain PD-type iterative learning control (ILC) for a class of nonlinear time-varying systems to well balance high-gain convergence rate and low-gain noise transmission. Different from the classic PD-type ILC, the control gains of the proposed method are variable. Each variable-gain consists of an amplitude-dependent term and an iteration-varying term. The amplitude-dependent terms vary with the amplitudes of tracking error and derivative of tracking error, and the iteration-varying terms are increasing along the iteration axis. The proposed ILC achieves a faster convergence rate than low-gain ILC and higher tracking accuracy with limited noise amplification than high-gain ILC. Moreover, the convergence condition of the proposed method in the presence of external noise is provided. Simulation and experimental results demonstrate the effectiveness of the proposed method.     

数据丢失对迭代学习控制的影响分析

针对一类线性系统,分析数据丢失对迭代学习控制算法的影响.首先基于lifting方法给出跟踪误差渐近收敛和单调收敛的条件,并分析收敛速度与数据丢失率的关系,结果表明收敛速度随着数据丢失程度的增加而变慢.其次,为抑制迭代变化扰动的影响,给出一种存在数据丢失时的鲁棒迭代学习控制器设计方法,并将控制器设计问题转化为求取线性矩阵不等式的可行解.仿真示例验证了理论分析的结果以及鲁棒迭代学习控制算法的有效性.

     

A generalized iterative learning controller against initial state error

In this paper, the previous results that the performance of iterative learning control (ILC) algorithm can be improved by adding a proportional term and/or an integral term of error in D-type ILC algorithm are generalized using an operator. Then, a sufficient condition for convergence and robustness of the generalized ILC algorithm are investigated against initial state error. As a special case of the operator, a non-linear ILC algorithm is also proposed and it is shown that the effect of initial state error can be reached to zero in a given finite time. It is shown that the bound of error reduction can be effectively controlled by tuning gains of the proposed non-linear ILC algorithm. In order to confirm validity of the proposed algorithms, two examples are presented.     

Novel iterative learning controls for linear discrete-time systems based on a performance index over iterations

An optimal iterative learning control (ILC) is proposed to optimize an accumulative quadratic performance index in the iteration domain for the nominal dynamics of linear discrete-time systems. Properties of stability, convergence, robustness, and optimality are investigated and demonstrated. In the case that the system under consideration contains uncertain dynamics, the proposed ILC design can be applied to yield a guaranteed-cost ILC whose solution can be found using the linear matrix inequality (LMI) technique. Simulation examples are included to demonstrate feasibility and effectiveness of the proposed learning controls.     

Integrated predictive iterative learning control based on updating reference trajectory for point-to-point tracking

A novel control technique is proposed by combining iterative learning control (ILC) and model predictive control (MPC) with updating-reference trajectory for point-to-point tracking problem of batch process. In this paper, a batch-to-batch updating-reference trajectory, which passes through the desired points, is firstly designed as the tracking trajectory within a batch. The updating control law consists of P-type ILC part and MPC part, in which P-type ILC part can improve the performance by learning from previous executions and MPC part is used to suppress the model perturbations and external disturbances. Convergence properties of the integrated predictive iterative learning control (IPILC) are analyzed theoretically, and the sufficient convergence conditions of output tracking error are also derived for a class of linear systems. Comparing with other point-to-point tracking control algorithms, the proposed algorithm can perform better in robustness. Furthermore, updating-reference relaxes the constraints for system outputs, and it may lead to faster convergence and more extensive range of application than those of fixed-reference control algorithms. Simulation results on typical systems show the effectiveness of the proposed algorithm.