局部对称积分型迭代学习控制

提出了一个新的迭代学习控制（ＩＬＣ）更新律用于连续线性系统的有限时间区间跟踪控制,迭代学习控制作为一个前馈控制,迭代学习控制作为一个前馈控制器加在已有的反馈控制器之上,对于上倥 的反馈控制信号作局部对称积分,所提出的迭代学习控制更新律具备较简单的形式且仅含有两个设计参数,即：学习增益和局部积分的区间长度,给出了收敛性分析以及设计步骤。     

A Practical Iterative Learning Path‐Following Control Of An Omni‐Directional Vehicle

A new practical iterative learning control (ILC) updating law is proposed to improve the path following accuracy for an omni‐directional autonomous mobile robot. The ILC scheme is applied as a feedforward controller to the existing feedback controller. By using the local symmetrical double‐integral of the feedback control signal of the previous iteration, the ILC updating law takes a simple form with only two design parameters: the learning gain and the range of local integration. Convergence analysis is presented together with a design procedure. Simulation results on a difficult maneuver are presented to illustrate the effectiveness of the proposed simple and yet practical scheme. The simulation is based on the model of a novel robotic platform, the Utah State University (USU) Omni‐Directional Vehicle (ODV), which uses multiple “smart wheels,” whose speed and direction can be independently controlled through dedicated processors for each wheel.     

Iterative learning feedback control of human limbs via functional electrical stimulation

A high-order iterative learning controller (ILC) is proposed for the tracking control of an electrically stimulated human limb that is repeatedly required to perform a given task. The limb is actuated by the muscles, which are out of the control of the central nerve systems (CNS), through functional electrical stimulation (FES) or functional neuromuscular stimulation (FNS). By using the proposed discrete-time high-order P-type ILC updating law and the PD-type feedback controller, it is shown that the proposed control strategy, which learns from repetitions, provides strong robustness in tracking control of the uncertain time-varying FES systems, which is essential for the adaptation and customization of FES applications. The effectiveness of the proposed control scheme is demonstrated by simulation results on a one-segment planar system. Some experimental results are also presented to validate the proposed control method.     

A design method for indirect iterative learning control based on two-dimensional generalized predictive control algorithm

Indirect iterative learning control (ILC) facilitates the application of learning-type control strategies to the repetitive/batch/periodic processes with local feedback control already. Based on the two-dimensional generalized predictive control (2D-GPC) algorithm, a new design method is proposed in this paper for an indirect ILC system which consists of a model predictive control (MPC) in the inner loop and a simple ILC in the outer loop. The major advantage of the proposed design method is realizing an integrated optimization for the parameters of existing feedback controller and design of a simple iterative learning controller, and then ensuring the optimal control performance of the whole system in sense of 2D-GPC. From the analysis of the control law, it is found that the proposed indirect ILC law can be directly obtained from a standard GPC law and the stability and convergence of the closed-loop control system can be analyzed by a simple criterion. It is an applicable and effective solution for the application of ILC scheme to the industry processes, which can be seen clearly from the numerical simulations as well as the comparisons with the other solutions.     

Robust design of feedback feed-forward iterative learning control based on 2D system theory for linear uncertain systems

For a class of linear discrete-time uncertain systems, a feedback feed-forward iterative learning control (ILC) scheme is proposed, which is comprised of an iterative learning controller and two current iteration feedback controllers. The iterative learning controller is used to improve the performance along the iteration direction and the feedback controllers are used to improve the performance along the time direction. First of all, the uncertain feedback feed-forward ILC system is presented by an uncertain two-dimensional Roesser model system. Then, two robust control schemes are proposed. One can ensure that the feedback feed-forward ILC system is bounded-input bounded-output stable along time direction, and the other can ensure that the feedback feed-forward ILC system is asymptotically stable along time direction. Both schemes can guarantee the system is robust monotonically convergent along the iteration direction. Third, the robust convergent sufficient conditions are given, which contains a linear matrix inequality (LMI). Moreover, the LMI can be used to determine the gain matrix of the feedback feed-forward iterative learning controller. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed schemes.     

Iterative learning control for position tracking of a pneumatic actuated X–Y table

The iterative learning control (ILC) obtains the unknown information from repeated control operations. Meanwhile, the tracking error from previous stages is used as the correction factor for the next control action. Therefore, the ILC controller can make the system tracking error converge to a small region within a limited number of iterations. This study builds a proportional-valve-controlled pneumatic X–Y table system for performing position tracking control experiments. The experiments involve implementing the ILC controllers and comparing the results. The P-type updating law with delay parameters is used for both the x- and y-axes in the repetitive trajectory tracking control. Experimental results demonstrate that the ILC controller can effectively control the system and track the desired circular trajectory at different speeds. The control parameters are varied to investigate their effects on the ILC convergence.     

An open-closed-loop iterative learning control approach for nonlinear switched systems with application to freeway traffic control

For nonlinear switched discrete-time systems with input constraints, this paper presents an open-closed-loop iterative learning control (ILC) approach, which includes a feedforward ILC part and a feedback control part. Under a given switching rule, the mathematical induction is used to prove the convergence of ILC tracking error in each subsystem. It is demonstrated that the convergence of ILC tracking error is dependent on the feedforward control gain, but the feedback control can speed up the convergence process of ILC by a suitable selection of feedback control gain. A switched freeway traffic system is used to illustrate the effectiveness of the proposed ILC law.     

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.     

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.     

Iterative learning control with input sharing for multi-agent consensus tracking

In this paper, a novel iterative learning control (ILC) scheme with input sharing is presented for multi-agent consensus tracking. In many ILC works for multi-agent coordination problem, each agent maintains its own input learning, and the input signal is corrected by local measurements over iteration domain. If the agents are allowed to share their learned inputs among them, the strategy can improve the learning process as more learning resources are available. In this work, we develop a new type of learning controller by considering the input sharing among agents, which includes the traditional ILC strategy as a special case. The convergence condition is rigorously derived and analyzed as well. Furthermore, the proposed controller is extended to multi-agent systems under iteration-varying graph. It turns out that the developed controller is very robust to communication variations. In the numerical study, three illustrative examples are presented to show the effectiveness of the proposed controller. The learning controller with input sharing demonstrates not only faster convergence but also smooth transient performance.     

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.     

Indirect iterative learning control for a discrete visual servo without a camera-robot model.

This paper presents a discrete learning controller for vision-guided robot trajectory imitation with no prior knowledge of the camera-robot model. A teacher demonstrates a desired movement in front of a camera, and then, the robot is tasked to replay it by repetitive tracking. The imitation procedure is considered as a discrete tracking control problem in the image plane, with an unknown and time-varying image Jacobian matrix. Instead of updating the control signal directly, as is usually done in iterative learning control (ILC), a series of neural networks are used to approximate the unknown Jacobian matrix around every sample point in the demonstrated trajectory, and the time-varying weights of local neural networks are identified through repetitive tracking, i.e., indirect ILC. This makes repetitive segmented training possible, and a segmented training strategy is presented to retain the training trajectories solely within the effective region for neural network approximation. However, a singularity problem may occur if an unmodified neural-network-based Jacobian estimation is used to calculate the robot end-effector velocity. A new weight modification algorithm is proposed which ensures invertibility of the estimation, thus circumventing the problem. Stability is further discussed, and the relationship between the approximation capability of the neural network and the tracking accuracy is obtained. Simulations and experiments are carried out to illustrate the validity of the proposed controller for trajectory imitation of robot manipulators with unknown time-varying Jacobian matrices.     

Iterative Learning Control for Nonlinear Systems with Data Dropouts at Both Measurement and Actuator Sides

This paper discusses the iterative learning control (ILC) for nonlinear systems under a general networked control structure, in which random data dropouts occur independently at both measurement and actuator sides. Both updating algorithms are proposed for the computed input signal at the learning controller and the real input signal at the plant, respectively. The system output is strictly proved to converge to the desired reference with probability one as the iteration number goes to infinity. A numerical simulation is provided to verify the effectiveness of the proposed mechanism and algorithms.     

Compensation of hysteresis in piezoelectric actuator with iterative learning control

This paper presents the application of iterative learning control (ILC) to compensate hysteresis in a piezoelectric actuator. The proposed controller is a hybrid of proportional-integral-differential (PID) control, whose main function is for trajectory tracking, and a chatter-based ILC, whose main function is for hysteresis compensation. Stability analysis of the proposed ILC is presented, with the PID included in the dynamic of the piezoelectric actuator. The performance of the proposed controller is analysed through simulation and verified with experiment with a piezoelectric actuator.     

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.     

A P‐type Iterative Learning Controller for Uncertain Robotic Systems with Exponentially Decaying Error Bounds

This paper presents a P‐type iterative learning control (ILC) scheme for uncertain robotic systems that perform the same tasks repetitively. The proposed ILC scheme comprises a linear feedback controller consisting of position error and exponentially weighted velocity error with respect to the number of iterations, and a feedforward learning controller updated by the exponentially weighted velocity error from previous trial. As the learning iteration proceeds, the position and velocity errors converge uniformly to zero within error bounds that decay exponentially through the sequence of iterations with arbitrarily selected convergence rate. Consequently, the proposed ILC scheme enables analysis and tuning of the exponential convergence rate in the iteration domain in contrast to other existing P‐type ILC schemes. © 2003 Wiley Periodicals, Inc.     

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control (AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance. To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control (ILC), a new boundary layer function is proposed by employing Mittag-Leffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function (CEF) containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.      

An iterative learning control design approach for networked control systems with data dropouts

In network‐based iterative learning control (ILC) systems, data dropout often occurs during data packet transfers from the remote plant to the ILC controller. This paper considers the problem of controller design for such ILC processes. Packet missing is modeled by stochastic variables satisfying the Bernoulli random binary distribution, which renders such an ILC system to be a stochastic one. Then, the design of ILC law is transformed into the stabilization of a 2‐D stochastic system described by the Roesser model. A sufficient condition for mean‐square asymptotic stability is established by means of a linear matrix inequality technique, and formulas can be given for the control law design simultaneously. This result is further extended to more general cases where the system matrices also contain uncertain parameters. The effectiveness and merits of the proposed method are illustrated by a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.     

Higher Relative Degree Nonlinear Systems With ilc Using Lower‐order Differentiations

This paper addresses the problem of iterative learning control (ILC) for a class of nonlinear continuous‐time systems with higher relative degree. The proposed ILC solution is a family of updating laws using differentiations of tracking error with the order less than the system relative degree. A unified convergence condition for this family of ILC updating laws is provided and proved to be independent of the highest order of differentiation. The application to path tracking of a robotic manipulator is presented to illustrate the effectiveness of the proposed method.