Iterative Learning Control Algorithm Research Articles

Nonlinear Iterative Learning Control: A Frequency-Domain Approach for Fast Convergence and High Accuracy

Iterative learning control (ILC) involves a trade-off between perfect, fast attenuation of iteration-invariant disturbances and amplification of iteration-varying ones. The aim of this paper is to develop a nonlinear ILC framework that achieves fast convergence, robustness, and low converged error values in ILC. To this end, the method includes a deadzone nonlinearity in the learning update, which uses the difference in amplitude characteristics of repeating and varying disturbances to modify the learning gain for each error sample. A criterion for monotonic convergence of the nonlinear ILC algorithm is provided, which is used in combination with system measurements to select suitable design parameters. The proposed algorithm is validated using simulations, in which fast convergence to low error values is demonstrated.

Data-driven Norm Optimal Iterative Learning Control for Point-to-Point Tasks

Iterative learning control (ILC) is suitable for high-performance repetitive tasks since it learns from past trials to improve the tracking performance. Existing ILC designs often require a model, which can be difficult or expensive to obtain in practice. To address this problem, we recently developed a data-driven norm optimal ILC using the latest developments from data-driven control, namely, the Willems’ fundamental lemma. In this paper, we show that the idea can also be extended to point-to-point ILC tasks that focus on tracking some intermediate points of the whole trial. We propose a novel data-driven point-to-point norm optimal ILC algorithm that can achieve the same performance as the model-based algorithm but without using an analytical model. The design requires the available data to be persistently exciting of a sufficiently high order. To relax this requirement, a receding horizon based algorithm and a trial partition based algorithm are further developed with well-defined, but different convergence properties. Numerical examples are given to illustrate the proposed algorithms’ effectiveness.

Iterative learning control based on dynamic time warping for a class of discrete‐time nonlinear systems with varying trial lengths and terminus constraint

AbstractThis article proposes a dynamic time warping (DTW)‐based iterative learning control (ILC) scheme for discrete‐time nonlinear systems to tackle the path learning problem with varying trial lengths and terminus constraint. By incorporating the improved DTW algorithm, the varying trial lengths are aligned as a desired length. Meanwhile, this algorithm can find the most similar waypoints between the output and the desired paths, which can be used to design an updating law and facilitate the convergence of path learning. Different from the existing ILC methods based on the probability distribution function for learning trajectory in the time domain, the method in this article can be applied to learn the spatial path corresponding to the desired trajectory. Furthermore, the learning property in the presence of variable initial states is discussed under the proposed method. Several illustrative examples manifest the validity of the proposed DTW‐based ILC algorithm.

Design of data-driven mode-free iterative learning controller based higher order parameter estimation for multi-agent systems consistency tracking

In this study, an adaptive data-driven control protocol design scheme based on higher order parameter (HOP) estimation and iterative learning is proposed for a class of nonaffine multi-agent systems (MAS) with unknown nonlinearity to solve the consistency tracking problem of MAS with fixed and switching topology communications. The control protocol mainly comprises HOP estimation and an iterative learning controller. The iterative learning control (ILC) algorithm is mainly used for system synergy, and the adaptive control algorithm based on HOP estimation mainly completes the system stabilization. The main advantage of the control protocol is that it uses only the input/output (I/O) data of the agents to complete the consensus tracking task and does not require specifying the dynamical system of each agent. The control protocol has a modular design, in which the iterative learning and HOP estimation algorithms complement each other without affecting the structure of the controller. The effectiveness of the control protocol is demonstrated using two simulation experiments.

Decentralized iterative learning control for constrained collaborative tracking

ABSTRACTHigh performance collaborative tracking where multiple subsystems work together repetitively to track a reference has found applications in various areas. To meet the high accuracy requirements, iterative learning control (ILC) has recently been used. However, most existing designs ignore the system constraints that are often encountered in practice. Furthermore, they usually have a centralized structure (or controller parameter) that needs to be redesigned or re‐tuned when the system changes which may cause difficulties for handling large scale systems. In this article, we consider the constrained collaborative tracking problem and propose a novel constrained ILC design. The resulting ILC algorithm guarantees not only the satisfaction of the system constraints, but also the monotonic convergence of the collaborative tracking error norm to a minimum (possible) value. We further develop a decentralized implementation of the proposed algorithm using the alternating direction method of multipliers, allowing the design to scale up to large scale and varying system dynamics. Finally, we provide numerical examples to verify the algorithms' effectiveness.

Iterative learning contouring control: Theory and application to biaxial systems

This paper is concerned with the iterative learning control (ILC) for the contouring control of multi-axis motion system. A novel ILC algorithm, which is called iterative learning contouring control (ILCC), is proposed and verified with biaxial motion systems. In motion control, conventional ILC requires that the number of control objectives is the same as the number of command inputs, which is called square property. This allows for the formulation of transfer function or matrix inversion. The unique feature of contouring control is its non-square property. For contouring control, conventional ILC circumvents the non-square property by adopting the configuration of cross-coupled control (CCC). In other words, the estimated contour error is decomposed into components of individual axis for compensation by ILC and thus the contour error is reduced indirectly. The proposed ILCC can deal with the non-square property and can directly reduce the contour error by adopting the equivalent contour error as the control objective of the ILC. The equivalent contour error represents an accurate contour error model and hence better contouring accuracy can be achieved. The ILCC algorithm is implemented on two platforms, an XY table and a commercial CNC machine tool. Experiments on the contouring control of a circular path with different speeds and a B-spline path are conducted. It is found that the contour error can be reduced about 88% after several learning iterations. The experimental results confirm the effectiveness of the proposed method and show the excellent contouring performance.

Data-Driven Iterative Learning Control of Nonlinear Systems by Adaptive Model Matching

Iterative learning control (ILC) has proven successful in the industry for enhancing tracking performance of repetitive tasks. The high accuracy and fast convergence of ILC algorithms hinge on: 1) the knowledge of the system model and 2) an effective learning algorithm. For general industrial systems with nonlinear dynamics, this raises technical challenges because acquiring a nonlinear dynamical model or several linearized models at different operating points may be difficult and costly. It is also nontrivial to determine the learning algorithm for the complex model obtained. To address these challenges, this article proposes a novel data-driven ILC algorithm for single-input-single-output nonlinear systems. Without explicit nonlinear models, our algorithm treats the nonlinear system as an unknown linear time-varying system linearized on a specified input–output (I/O) trajectory in each ILC iteration. A linearly parameterized time-varying adaptive filter is constructed in each ILC iteration so that, when cascading with the nonlinear plant, the I/O dynamics around the specified trajectory follow a linear time-invariant reference model. The ILC error trajectory is then filtered by the adaptive time-varying filter, which represents the inverse dynamics with a bandwidth specified by the reference model, to render fast convergence. The benefits of the proposed data-driven algorithm is demonstrated by comparing to a gradient and Hessian-based data-driven ILC algorithm on a prototypical two-degree-of-freedom nonlinear pendulum.

Research on iterative learning control of lower limb exoskeleton of rehabilitation robot

It is difficult to establish an accurate mathematical model for the lower limb exoskeleton system of a rehabilitation robot, and there are unknown external disturbances. In this paper, an accurate model-independent closed-loop PD-type iterative learning control algorithm is adopted, which enables the system to track a given desired trajectory with uncertain dynamic models and parameters. The simulation results show that the algorithm can effectively improve the control accuracy of the trajectory tracking of the lower limb exoskeleton.

Iterative Learning Control for Robotic Path Following With Trial-Varying Motion Profiles

Iterative learning control (ILC) aims to maximize the performance of systems performing repeated tracking tasks. However, in most existing applications, the motion profile is inherently specified <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> , which has restricted both its application range and scope of performance improvement. For example, the typical repeated path-following task in robotics only requires a spatial path profile rather than a temporal trajectory profile, for which most existing ILC designs are unsuitable. To handle this requirement, this article extends the ILC task description by relaxing this postulate to enable a trial-varying motion profile and formulate an ILC path-following problem with system constraints. Under this extended problem setup, a spatial ILC algorithm is proposed with efficient implementation and robust convergence analysis, which updates the input signal and motion profile at the end of each trial to reduce the tracking error. This algorithm is implemented experimentally on a gantry robot test platform to verify performance, practical feasibility, and reliability. Comparisons with other control methods are also made to clarify its advantages, such as error reduction, control effort reduction, and constraint handling.

Iterative learning control of complex Ginzburg–Landau system

Different from the existing research on iterative learning control (ILC) real-valued systems, complex-valued partial differential system is studied in this paper. All variables and parameters of the system are complex, and distributed control is imposed on the system. First, the original complex system is transformed into two coupled real systems, which represent the real and imaginary parts of the original complex system, respectively. Second, a complex [Formula: see text]-type ILC algorithm is designed that the real and imaginary parts of the learning law are coupled to each other. Then, the contraction mapping principle and analytical techniques are used to ensure that the tracking error converges to zero in the sense of [Formula: see text]-norm. Finally, a numerical simulation is presented to show the effectiveness of the proposed algorithm.

Model‐free adaptive and iterative learning composite control for subway train under actuator faults

AbstractIn this article, the model‐free adaptive and iterative learning composite control (CMFAC‐ILC) is proposed to ensure the speed and position tracking for the subway train system subjected to the iteration‐time‐varying actuator faults. First, a nonlinear subway train system is transformed into a faults‐related full‐form dynamic linearization data model (FFDLDM), which relies on the input, output, and faults data of the subway train system. The actuator faults and unknown nonlinear terms of the subway train system are estimated by the projection algorithm. Then, in the time domain, the model‐free adaptive control (MFAC) algorithm is utilized and unknown controller parameters are estimated by the RBFNN algorithm. In the iteration domain, a feedforward D‐type iterative learning control (ILC) algorithm is added to the outer loop of the MFAC algorithm. Finally, the theoretical analysis proves that the speed and position tracking errors of the subway train are bounded, the simulations demonstrate the effectiveness of the proposed composite control scheme of the subway train.

Internal pressure control for high-speed trains based on condition matching and performance iteration

When a high-speed train passes through tunnels, tunnel pressure waves will cause pressure fluctuation inside carriage. Traditional control strategy of shutting down air ducts for a fixed period may fail to consider both riding comfort and air quality. The similarity of tunnel pressure waves when the same train passes through the same tunnel provides a possibility to solve the problem by iterative learning control (ILC) algorithm. However, the varying amplitude and scale limit the application of conventional ILC. Thus in each iteration, the control inputs of the nearest condition in the historical database will be matched and applied to the control process, after which the control error will be gained and then the control inputs will be updated by the error. Next, the performance will be evaluated to refresh the database to make the control inputs in the database to be optimal. Feasibility analysis and simulations show the feasibility of controlling the fluctuation inside the carriage by matching the database records.

Adaptive Fuzzy Iterative Learning Control for Systems with Saturated Inputs and Unknown Control Directions

An adaptive fuzzy iterative learning control (ILC) algorithm is designed for the iterative variable reference trajectory problem of nonlinear discrete-time systems with input saturations and unknown control directions. Firstly, an adaptive fuzzy iterative learning controller is constructed by combining with the fuzzy logic system (FLS), which can compensate the loss caused by input saturation. Then, the discrete Nussbaum gain technique is adopted along the iteration axis, which can be embedded to the learning control method to identify the control direction of the system. Finally, based on the nonincreasing Lyapunov-like function, it is proven that the adaptive iterative learning controller can converge asymptotically when the number of iterations tends to infinity, and the system signals always remain bounded in the learning process. A simulation example verifies the feasibility and effectiveness of the learning control method.

Implementation of Iterative Learning Control on a Pneumatic Actuator

Pneumatic actuators demonstrate various nonlinear and uncertain behavior, and as a result, precise control of such actuators with model-based control schemes is challenging. The Iterative Learning Control (ILC) algorithm is a model-free control method usually used for repetitive processes. The ILC uses information from previous repetitions to learn about a system’s dynamics for generating a more suitable control signal. In this paper, an ILC method to overcome the nonlinearities and uncertainties in a pneumatic cylinder-piston actuator is suggested. The actuator is modeled using MATLAB SimScape blocks, and the ILC scheme has been expanded for controlling nonlinear, non-repetitive systems so that it can be used to control the considered pneumatic system. The simulation results show that the designed ILC controller is capable of tracking a non-repetitive reference signal and can overcome the internal and payload uncertainties with the precision of 0.002 m. Therefore, the ILC can be considered as an approach for controlling the pneumatic actuators, which is challenging to obtain their mathematical modeling.

Iterative learning control for integrated system of robot and machine tool

AbstractThis study is concerned with the integrated system of a robot and a machine tool. The major task of robot is loading the workpiece to the machine tool for contour cutting. An iterative learning control (ILC) algorithm is proposed to improve the accuracy of the finished product. The proposed ILC is to modify the input command of the next machining cycle for both robot and machine tool to iteratively enhance the output accuracy of the robot and machine tool. The modified command is computed based on the current tracking/contour error. For the ILC of the robot, tracking error is considered as the control objective to reduce the tracking error of motion path, in particular, the error at the endpoint. Meanwhile, for the ILC of the machine tool, contour error is considered as the control objective to improve the contouring accuracy, which determines the quality of machining. In view of the complicated contour error model, the equivalent contour error instead of the actual contour error is taken as the control objective in this study. One challenge for the integrated system is that there exists an initial state error for the machine tool dynamics, violating the basic assumption of ILC. It will be shown in this study that the effects of initial state error can be significantly reduced by the ILC of the robot. The proposed ILC algorithm is verified experimentally on an integrated system of commercial robot and machine tool. The experimental results show that the proposed ILC can achieve more than 90% of reduction on both the RMS tracking error of the robot and the RMS contour error of the machine tool within six learning iterations. The results clearly validate the effectiveness of the proposed ILC for the integrated system.

A unified adaptive control approach of nonlinear continuous non‐parameterized systems with asymmetric control gains for trajectory tracking in different domains

AbstractIn this article, for nonlinear continuous non‐parameterized (NCNP) systems, an adaptive iterative learning control (ILC) algorithm, which can adjust the adaptive parameters in both iteration‐domain and time‐domain, is first proposed to track different reference trajectories repetitively over a finite time interval. As the NCNP system is required to asymptotically track reference trajectory in infinite time‐domain, by virtue of partitioning the reference trajectory and system signals with a fixed time interval, the proposed adaptive ILC controller is then extended to handle the asymptotic tracking issue in infinite time‐domain. Therefore, a unified adaptive control approach is practically presented for NCNP systems to track reference trajectories in different domains (the infinite iteration‐domain and the infinite time‐domain). A prominent feature of the unified adaptive control approach is that the unknown control gain matrices in the NCNP systems are assumed to be invertible only. As a result, the general requirement in conventional adaptive control and adaptive ILC that the control gain matrices of plants are real symmetric and positive‐definite (or negative‐definite) is greatly relaxed. In addition, only three adaptive variables are designed for adjusting or updating in the proposed unified adaptive control approach such that the structure of controller is very simple and the memory space for computing is saved.

Resilient iterative learning control for a class of discrete‐time nonlinear systems under hybrid attacks

AbstractThe security control problem for a class of unknown nonlinear systems is considered in this paper. For the nonlinear system running in the network environment, the measurement channel is subjected to hybrid attacks. Intermittent denial of service attacks and false data injection attacks are modeled as the hybrid attacks. According to the characteristics of the repetitive system, a resilient iterative learning control (ILC) algorithm under hybrid attacks is devised. Subsequently, the stability of the system is proved by mathematical derivation and theoretical analysis in the sense of mathematical expectation. The theoretical analysis results indicate that the resilient ILC algorithm can ensure the stability of the system, and the tracking error converges with the increased number of iterations. Finally, the validity of the algorithm is illustrated by numerical simulation and mobile robot simulation.

Machine learning based iterative learning control for non‐repetitive time‐varying systems

AbstractThe repetitive tracking task for time‐varying systems (TVSs) with non‐repetitive time‐varying parameters at each trial, which is also called non‐repetitive TVSs, is realized in this article using iterative learning control (ILC). A machine learning (ML) based nominal model update mechanism, which utilizes the linear regression technique to update the nominal model at each ILC trial using only the current trial information, is proposed for non‐repetitive TVSs in order to enhance the ILC performance. Given that the ML mechanism forces the model uncertainties to remain within the ILC robust tolerance, an ILC update law is proposed to deal with non‐repetitive TVSs. How to tune parameters inside ML and ILC algorithms to achieve the desired aggregate performance is also provided. The robustness and reliability of the proposed method are verified by real experiments. Real data comparison with current state‐of‐the‐art methods demonstrates its superior control performance in terms of controlling precision. This article broadens ILC applications from time‐invariant systems to non‐repetitive TVSs, adopts ML regression technique to estimate non‐repetitive time‐varying parameters between two ILC trials and proposes a detailed parameter tuning mechanism to achieve desired performance, which are the main contributions.

Robust Iterative Learning Control Algorithm for Lower Limb Rehabilitation Proactive Human-robot Collaboration

At present, the motion control algorithms of lower limb exoskeleton robots have errors in tracking the desired trajectory of human hip and knee joints, which leads to poor follow-up performance of the human-machine system. Therefore, an iterative learning control algorithm is proposed to track the desired trajectory of human hip and knee joints. In this paper, the experimental platform of lower limb exoskeleton rehabilitation robot is built, and the control system software and hardware design and robot prototype function test are carried out. On this basis, a series of experiments are carried out to verify the rationality of the robot structure and the feasibility of the control method. Firstly, the dynamic model of the lower limb exoskeleton robot is established based on the structure analysis of the human lower limb; secondly, the servo control model of the lower limb exoskeleton robot is established based on the iterative learning control algorithm; finally, the exponential gain closed-loop system is designed by using MATLAB software. The relationship between convergence speed and spectral radius is analyzed, and the expected trajectory of hip joint and knee joint is obtained. The simulation results show that the algorithm can effectively improve the gait tracking accuracy of the lower limb exoskeleton robot and improve the follow-up performance of the human-machine system.

Iterative learning control for hyperbolic distributed parameter systems based on sensor–actuator networks

AbstractThis paper proposes two kinds of iterative learning control (ILC) schemes for a class of the distributed parameter systems based on sensor–actuator networks which can be described by hyperbolic partial differential equations. A D‐type ILC algorithm is first considered and the convergent condition of the output error is obtained via the contraction mapping methodology. Then, the PD‐type ILC algorithm is considered in this hyperbolic distributed parameter systems based on sensor–actuator networks. Finally, a cable equation with air and structural damping is given to illustrate the effectiveness of the proposed methods.