Approximate adjoint-based iterative learning control

This paper characterises stochastic convergence properties of adjoint-based (gradient-based) iterative learning control (ILC) applied to systems with load disturbances, when provided only with approximate gradient information and noisy measurements. Specifically, conditions are discussed under which the approximations will result in a scheme which converges to an optimal control input. Both the cases of time-invariant step sizes and cases of decreasing step sizes (as in stochastic approximation) are discussed. These theoretical results are supplemented with an application on a sequencing batch reactor for wastewater treatment plants, where approximate gradient information is available. It is found that for such case adjoint-based ILC outperforms inverse-based ILC and model-free P-type ILC, both in terms of convergence rate and measurement noise tolerance.     

Estimation-based norm-optimal iterative learning control

The norm-optimal iterative learning control (ilc) algorithm for linear systems is extended to an estimation-based norm-optimal ilc  algorithm where the controlled variables are not directly available as measurements. A separation lemma is presented, stating that if a stationary Kalman filter is used for linear time-invariant systems then the ilc  design is independent of the dynamics in the Kalman filter. Furthermore, the objective function in the optimisation problem is modified to incorporate the full probability density function of the error. Utilising the Kullback–Leibler divergence leads to an automatic and intuitive way of tuning the ilc  algorithm. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ilc  algorithm. Stability and convergence properties for the proposed scheme are also derived.     

A pseudoinverse-based iterative learning control

Learning control is a very effective approach for tracking control in processes occurring repetitively over a fixed interval of time. In this paper, an iterative learning control (ILC) algorithm is proposed to accommodate a general class of nonlinear, nonminimum-phase plants with disturbances and initialization errors. The algorithm requires the computation of an approximate inverse of the linearized plant rather than the exact inverse. An advantage of this approach is that the output of the plant need not be differentiated. A bound on the asymptotic trajectory error is exhibited via a concise proof and is shown to grow continuously with a bound on the disturbances. The structure of the controller is such that the low frequency components of the trajectory converge faster than the high frequency components     

Constrained data-driven optimal iterative learning control

A constrained optimal ILC for a class of nonlinear and non-affine systems, without requiring any explicit model information except for the input and output data, is proposed in this work. In order to address the nonlinearities, an iterative dynamic linearization method without omitting any information of the original plant is introduced in the iteration direction. The derived linearized data model is equivalent to the original nonlinear system and reflects the real-time dynamics of the controlled plant, rather than a static approximate model. By transferring all the constraints on the system output, control input, and the change rate of input signals into a linear matrix inequality, a novel constrained data-driven optimal ILC is developed by minimizing a predesigned objective function. The optimal learning gain is unfixed and updated iteratively according to the input and output measurements, which enhances the flexibility regarding modifications and expansions of the controlled plant. The results are further extended to the point-to-point control tasks where the exact tracking performance is required only at certain points and a constrained data-driven optimal point-to-point ILC is proposed by only utilizing the error measurements at the specified points only.     

Data-driven optimal terminal iterative learning control

This paper presents a data-driven optimal terminal iterative learning control (TILC) approach for linear and nonlinear discrete-time systems. The iterative learning control law is updated from only terminal output tracking error instead of entire output trajectory tracking error. The only required knowledge of a controlled system is that the Markov matrices of linear systems or the partial derivatives of nonlinear systems with respect to control inputs are bounded. Rigorous analysis and convergence proof are developed with sufficient conditions for the terminal ILC design and the results are developed for both linear and nonlinear discrete-time systems. Simulation results illustrate the applicability and effectiveness of the proposed approach.     

Parameter optimization in iterative learning control

In this paper parameter optimization through a quadratic performance index is introduced as a method to establish a new iterative learning control law. With this new algorithm, monotonic convergence of the error to zero is guaranteed if the original system is a discrete-time LTI system and it satisfies a positivity condition. If the original system is not positive, two methods are derived to make the system positive. The effect of the choice of weighting parameters in the performance index on convergence rate is analysed. As a result adaptive weights are introduced as a method to improve the convergence properties of the algorithm. A high-order version of the algorithm is also derived and its convergence analysed. The theoretical findings in this paper are highlighted with simulations.     

All-pass filtering in iterative learning control

In iterative learning control (ILC), it is highly desirable to have a learning compensator with a unit-gain for all frequencies, in order to avoid noise amplification and learning speed degradation during the learning process. In this paper, we show that the realization of a unit-gain compensator is straightforward in ILC, using both forward and backward filtering. As an illustrative example, a unit-gain derivative is proposed to overcome the drawbacks of the conventional derivative. The proposed scheme is equivalent to an all-pass unit-gain phase shifter; the forward filtering uses a 0.5-order derivative and the backward filtering employs a 0.5-order integral. The all-pass phase shifter is deployed in a unit-gain D-type ILC. The advantages of the unit-gain feature are demonstrated by some experimental results on a robot manipulator.     

迭代学习在网络控制中的应用*

针对网络拥塞控制中网络拥塞本身无法建立精确的数学模型的问题,基于迭代学习控制具有结构简单及对系统精确模型不依赖等优点,首次提出了用迭代学习控制算法来解决网络拥塞,其主要目的是提高网络资源的利用率并提供给信源公平的资源分配份额。在提出算法前,首先通过分析网络模型建立了网络拥塞被控系统;然后提出了针对该被控系统的开闭环PID型迭代学习控制算法并证明了其收敛性;最后运用此算法建立了网络拥塞控制模型。通过实验和仿真表明,该算法对解决网络拥塞问题有很好的效果。     

分数线性相位超前迭代学习控制

线性相位超前迭代学习控制的超前拍数需要取整,不利于控制系统的性能达到最优.对此提出分数线性相位超前迭代学习控制.对系统的收敛条件进行频域分析,得到超前拍数,学习增益和可学习带宽的范围.通过调节超前拍数来提高系统的可学习带宽,以达到更高的跟踪精度.给出了分数线性相位超前的具体实现方法,并在此基础上对整数与分数相位超前的补偿效果进行比较.以机械臂为被控对象的仿真结果表明了分数线性相位超前更能提高系统的可学习带宽及跟踪精度.     

高阶参数优化迭代学习控制算法

针对线性时不变离散系统的跟踪问题提出一种高阶参数优化迭代学习控制算法.该算法通过建立考虑了多次迭代误差影响的参数优化目标函数,求解得出优化后的时变学习增益参数.从理论上证明了:对于线性离散时不变系统,该算法在被控对象不满足正定性的松弛条件下仍可保证跟踪误差单调收敛于零.同时,采用之前多次迭代信息的高阶算法具有更好的收敛性和鲁棒性.最后利用一个仿真实例验证了算法的有效性.     

高阶无模型自适应迭代学习控制

针对一类非线性非仿射离散时间系统,提出了高阶无模型自适应迭代学习控制方案.控制器的设计和分析仅依赖于系统的输入/输出(I/O)数据,不需要已知任何其他知识.该方法采用了高阶学习律,可利用更多以前重复过程中的控制信息提高系统收敛性,且学习增益可通过"拟伪偏导数"更新律迭代调节.仿真结果验证了所提出算法的有效性.     

分数阶迭代学习控制的收敛性分析

本文将传统的迭代学习控制时域和频域分析方法扩展到一类针对分数阶非线性系统的分数阶迭代学习控制时域分析方法.提出了一类新的分数阶迭代学习控制框架并简化了收敛条件,且证明了常增益情况下两类分数阶迭代学习控制收敛条件的等价性问题.该讨论进一步引出了如下两个结果:分数阶不确定系统的分数阶自适应迭代学习控制的可学习区域以及理想带阻型分数阶迭代学习控制的框架.上述结果均得到了仿真验证.     

Adaptive iterative learning control for robot manipulators

In this paper, we propose some adaptive iterative learning control (ILC) schemes for trajectory tracking of rigid robot manipulators, with unknown parameters, performing repetitive tasks. The proposed control schemes are based upon the use of a proportional-derivative (PD) feedback structure, for which an iterative term is added to cope with the unknown parameters and disturbances. The control design is very simple in the sense that the only requirement on the PD and learning gains is the positive definiteness condition and the bounds of the robot parameters are not needed. In contrast to classical ILC schemes where the number of iterative variables is generally equal to the number of control inputs, the second controller proposed in this paper uses just two iterative variables, which is an interesting fact from a practical point of view since it contributes considerably to memory space saving in real-time implementations. We also show that it is possible to use a single iterative variable in the control scheme if some bounds of the system parameters are known. Furthermore, the resetting condition is relaxed to a certain extent for a certain class of reference trajectories. Finally, simulation results are provided to illustrate the effectiveness of the proposed controllers.     

On initial conditions in iterative learning control

Initial conditions, or initial resetting conditions, play a fundamental role in all kinds of iterative learning control methods. In this note, we study five different initial conditions, disclose the inherent relationship between each initial condition and corresponding learning convergence (or boundedness) property. The iterative learning control method under consideration is based on Lyapunov theory, which is suitable for plants with time-varying parametric uncertainties and local Lipschitz nonlinearities.     

An extended PID type iterative learning control

This paper presents a new iterative learning control (ILC) for discrete-time single-input single-output (SISO) linear time-invariant (LTI) systems. To establish this ILC, the input of the controlled system is modified by using a novel four-parametric algorithm. This algorithm is called the extended proportional plus integral and derivative (EPID) type, since by eliminating the fourth parameter of it one would get to the PID type ILC, therefore PID type ILC is a special case of it. The convergence of the proposed ILC is analyzed and an optimal method is presented to determine its parameters. It is shown that the given ILC has a better performance than the PID-type one. Three illustrative examples are included to demonstrate the effectiveness and the preference of the presented ILC.     

Suppressing intersample behavior in iterative learning control

Iterative Learning Control (ILC) is a control strategy to improve the performance of digital batch repetitive processes. Due to its digital implementation, discrete time ILC approaches do not guarantee good intersample behavior. In fact, common discrete time ILC approaches may deteriorate the intersample behavior, thereby reducing the performance of the sampled-data system. In this paper, a generally applicable multirate ILC approach is presented that enables to balance the at-sample performance and the intersample behavior. Furthermore, key theoretical issues regarding multirate systems are addressed, including the time-varying nature of the multirate ILC setup. The proposed multirate ILC approach is shown to outperform discrete time ILC in realistic simulation examples.     

Predictive iterative learning control with experimental validation

This paper develops an iterative learning control law that exploits recent results in the area of predictive repetitive control where a priori information about the characteristics of the reference signal is embedded in the control law using the internal model principle. The control law is based on receding horizon control and Laguerre functions can be used to parameterize the future control trajectory if required. Error convergence of the resulting controlled system is analyzed. To evaluate the performance of the design, including comparative aspects, simulation results from a chemical process control problem and supporting experimental results from application to a robot with two inputs and two outputs are given.     

网络控制系统中一种新形式的开闭环迭代学习控制

本文研究了网络控制系统中迭代学习控制方法, 借鉴网络控制系统的分层结构形式, 提出了一种远程开环本地闭环的迭代学习控制形式. 这种形式的学习律中, 只有开环学习律的离散数据通过网络传输, 对控制系统进行前馈补偿同时降低了网络丢包对系统的实时影响. 针对线性系统, 利用2–D系统的分析方法, 给出了网络控制中开闭环迭代学习控制的收敛性判别条件. 仿真和实验结果证实了所提方法的可行性和有效性.     

A guaranteed monotonically convergent iterative learning control

This paper presents a new iterative learning control (ILC) scheme for linear discrete time systems. In this scheme, the input of the controlled system is modified by applying a semi‐sliding window algorithm, with a maximum length of n + 1, on the tracking errors obtained from the previous iteration (n is the order of the controlled system). The convergence of the presented ILC is analyzed. It is shown that, if its learning gains are chosen proportional to the denominator coefficients of the system transfer function, then its monotonic convergence condition is independent of the time duration of the iterations and depends only on the numerator coefficients of the system transfer function. The application of the presented ILC to control second‐order systems is described in detail. Numerical examples are added to illustrate the results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society