Adaptive iterative learning control for switched nonlinear continuous-time systems

In this paper, an adaptive iterative learning control (ILC) method is proposed for switched nonlinear continuous-time systems with time-varying parametric uncertainties. First, an iterative learning controller is constructed with a state feedback term in the time domain and an adaptive learning term in the iteration domain. Then a switched nonlinear continuous-discrete two-dimensional (2D) system is built to describe the adaptive ILC system. Multiple 2D Lyapunov functions-based analysis ensures that the 2D system is exponentially stable, and the tracking error will converge to zero in the iteration domain. The design method of the iterative learning controller is obtained by solving a linear matrix inequality. Finally, the efficacy of the proposed controller is demonstrated by the simulation results.     

高相对阶连续时间系统的间接迭代学习控制

本文提出了一类高相对阶线性连续时间系统的间接迭代学习控制算法,该算法相对独立于系统局部控制器,因此可以应用于已有局部反馈控制器的系统.采用具有极点配置的H_∞鲁棒控制器作为系统的内环控制,而在外环通过迭代学习控制调整内环系统的指令信号.通过引入拉氏变化,构建了迭代学习系统的2-D Roesser模型,推导了系统渐近收敛条件,并研究了存在有界初始条件偏移和迭代变化外部干扰时算法的鲁棒性能.最后,利用空中加油对接控制的算例进一步验证了算法的有效性.     

Noise tolerant iterative learning control for a class of continuous-time systems

The paper proposes a noise tolerant iterative learning control (ILC) for a class of linear continuous-time systems, which achieves high-precision tracking for uncertain plants by iteration of trials in the presence of heavy measurement noise. The robustness against measurement noise is achieved through (i) projection of continuous-time I/O signals onto a finite-dimensional parameter space, (ii) using error data of all past iterations via an integral operation in the learning law and (iii) noise reduction by H² optimization subject to a specified convergence speed of the ILC.     

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.     

On-line identification and optimal control of continuous-time systems

In this paper, a moving algorithm for on-line identification of continuous-time systems is developed. With the proposed algorithm, the observed input–output data can be directly used to estimate the system parameters without any numerical pre-processing, and by means of a recursive formula the estimates can be updated step by step without repeatedly computing the matrix inversion. In this way, the use of both computer memory and computing time can be reduced. Besides, the computations are simple and straightforward. From the moving identification algorithm, a linear moving model can be obtained to represent the control systems. The on-line optimal control algorithm is also developed via the linear moving model. A slider-crank motion control system is used to illustrate that the proposed on-line identification and optimal control algorithms can give satisfactory results.     

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 reinforced learning control using iterative error compensation for uncertain dynamical systems

This paper investigates a learning control using iterative error compensation for uncertain systems to enhance the precision of a high speed, computer-controlled machining process. It is specially useful in mass-produced parts produced by a high-speed machine tool system. This method uses an iterative learning technique which adopts machine commands and cutting errors experienced from previous manoeuvres as references for compensation actions in the current manoeuvre. Non-repetitive disturbances and nonlinear dynamics of the cutting processes and servo systems of the machine which greatly affect the convergence of the learning control systems were studied in this research. State feedback and output feedback methods were used for controller design. Stability and performance of learning control systems designed via the proposed method were verified by simulations on a single degree of freedom servo positioning system.     

2D systems based robust iterative learning control using noncausal finite-time interval data

This paper uses a 2D system setting in the form of repetitive process stability theory to design an iterative learning control law that is robust against model uncertainty. In iterative learning control the same finite duration operation, known as a trial over the trial length, is performed over and over again with resetting to the starting location once each is complete, or a stoppage at the end of the current trial before the next one begins. The basic idea of this form of control is to use information from the previous trial, or a finite number thereof, to compute the control input for the next trial. At any instant on the current trial, data from the complete previous trial is available and hence noncausal information in the trial length indeterminate can be used. This paper also shows how the new 2D system based design algorithms provide a setting for the effective deployment of such information.     

一类线性连续切换系统的迭代学习控制

针对有限时间区间内执行重复控制任务的线性连续切换系统,考虑基于迭代学习的跟踪控制问题.假设线性切换系统的切换率在时间域内是任意的,提出该类系统的D型迭代学习控制算法.理论分析表明,当学习增益矩阵满足一定的条件时,D型迭代学习控制算法可以保证切换系统的实际输出在整个运行区间上一致收敛于期望输出,实现完全跟踪控制.数值仿真进一步验证了方法的有效性.     

Use of neural networks in iterative learning control systems

This paper presents an approach to the use of neural networks to improve iterative learning control performance. The neural networks are used to estimate the learning gain of an iterative learning law and to store the learned control input profiles for different reference trajectories. A neural network of piecewise linear approximation is presented to identify effectively the system dynamics, and the approximation property and persistently exciting condition are discussed. In addition, training of a feedforward neural controller is presented to accumulate control information learned by an iterative update law for various reference trajectories. Then, an iterative learning law with a feedforward neural controller is suggested and its convergence property is stated with the convergence condition. The effectiveness of the present methods has been demonstrated through simulations by applying them to a two-link robot manipulator.     

Recursive identification of continuous-time Wiener systems

Recursive algorithms to identify both subsystems of a continuous-time Wiener system are presented. The system is driven and disturbed by Gaussian white random signals. The impulse response of the linear dynamic subsystem is recovered with a correlation method. It is shown that the inverse of the non-linear characteristic of the other subsystem is a regression function. Then, to recover the inverse, two estimates are presented. The algorithms converge to the unknown impulse response, and the inverse of the characteristic, respectively. Convergence rates are presented. Moreover, results of simulation examples are given.     

Recursive identification of continuous-time Hammerstein systems

A continuous-time Hammerstein system is identified. The characteristic of its nonlinear subsystem and the impulse response of the dynamic parts are estimated from observations taken at input and output of the whole system. All algorithms are of the on-line type. Their convergence is shown. Results of simulation examples are also presented.     

Robust iterative learning controller design using the performance weighting function of feedback control systems

Iterative learning controllers combined with existing feedback controllers have prominent capability of improving tracking performance in repeated tasks. However, the iterative learning controller has been designed without utilizing effective information such as the performance weighting function to design a feedback controller. In this paper, we deal with a robust iterative learning controller design problem for an uncertain feedback control system using its explicit performance information. We first propose a robust convergence condition in the ?₂-norm sense for an iterative learning control (ILC) scheme. We present a method to design an iterative learning controller using the information on the performance of the existing feedback control system such as performance weighting functions and frequency ranges of desired trajectories. From the obtained results, several design criteria for iterative learning controller are provided. Through analysis on the remaining error, the loop properties before and after learning are compared. We also show that, in the ?₂-norm sense, the remaining error can be less than the initial error under certain conditions. Finally, to show the validity of the proposed method, simulation studies are performed.     

Direct adaptive iterative learning control of nonlinear systems using an output-recurrent fuzzy neural network

In this paper, a direct adaptive iterative learning control (DAILC) based on a new output-recurrent fuzzy neural network (ORFNN) is presented for a class of repeatable nonlinear systems with unknown nonlinearities and variable initial resetting errors. In order to overcome the design difficulty due to initial state errors at the beginning of each iteration, a concept of time-varying boundary layer is employed to construct an error equation. The learning controller is then designed by using the given ORFNN to approximate an optimal equivalent controller. Some auxiliary control components are applied to eliminate approximation error and ensure learning convergence. Since the optimal ORFNN parameters for a best approximation are generally unavailable, an adaptive algorithm with projection mechanism is derived to update all the consequent, premise, and recurrent parameters during iteration processes. Only one network is required to design the ORFNN-based DAILC and the plant nonlinearities, especially the nonlinear input gain, are allowed to be totally unknown. Based on a Lyapunov-like analysis, we show that all adjustable parameters and internal signals remain bounded for all iterations. Furthermore, the norm of state tracking error vector will asymptotically converge to a tunable residual set as iteration goes to infinity. Finally, iterative learning control of two nonlinear systems, inverted pendulum system and Chua's chaotic circuit, are performed to verify the tracking performance of the proposed learning scheme.     

改进的时不变系统PD型迭代学习控制算法

针对时不变线性系统的迭代学习控制问题,提出了一种改进的时不变系统的PD型迭代学习控制算法,理论证明了系统满足收敛条件时的改进算法是收敛的。仿真实例分析表明,改进的算法利用最新算出的控制分量代替旧的控制分量,使系统的实际输出以更快的收敛速度逼近系统的理想输出。     

不确定性机器人系统自适应鲁棒迭代学习控制

利用Lyapunov方法, 提出了一种不确定性机器人系统的自适应鲁棒迭代学习控制策略, 整个系统在迭代域里是全局渐近稳定的. 所考虑的机器人系统同时包含了结构和非结构不确定性. 在设计时, 系统的不确定性被分解成可重复性和非重复性两部分, 并考虑了系统的标称模型. 在所提出的控制策略中, 自适应策略用来估算做法确定性的界, 界的修正与迭代学习控制量一样的迭代域得以实现的. 计算机仿真表明本文提出的控制策略是有效的.     

Set-point-related indirect iterative learning control for multi-input multi-output systems

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.     

输出重定义下的非线性非最小相位系统迭代学习控制

讨论非线性非最小相位系统实现完全跟踪的迭代学习控制方法, 适于在有限作业区间上重复运行的受控系统. 在控制器设计时, 通过输出重定义以使非最小相位系统的零动态变成渐近稳定特性. 分别采用部分限幅和完全限幅两种学习算法设计控制器, 理论分析表明两种算法能够保证学习系统中所有变量的有界性和跟踪误差在整个作业区间上渐近收敛于零. 数值仿真验证了两种迭代学习控制系统的跟踪性能.     

Monotonically convergent iterative learning control for linear discrete-time systems

In iterative learning control schemes for linear discrete time systems, conditions to guarantee the monotonic convergence of the tracking error norms are derived. By using the Markov parameters, it is shown in the time-domain that there exists a non-increasing function such that when the properly chosen constant learning gain is multiplied by this function, the convergence of the tracking error norms is monotonic, without resort to high-gain feedback.