Iterative Learning Control Design Research Articles

Conic Input Mapping Design of Constrained Optimal Iterative Learning Controller for Uncertain Systems.

In this article, we study the optimal iterative learning control (ILC) for constrained systems with bounded uncertainties via a novel conic input mapping (CIM) design methodology. Due to the limited understanding of the process of interest, modeling uncertainties are generally inevitable, significantly reducing the convergence rate of the control systems. However, huge amounts of measured process data interacting with model uncertainties can easily be collected. Incorporating these data into the optimal controller design could unlock new opportunities to reduce the error of the current trail optimization. Based on several existing optimal ILC methods, we incorporate the online process data into the optimal and robust optimal ILC design, respectively. Our methodology, called CIM, utilizes the process data for the first time by applying the convex cone theory and maps the data into the design of control inputs. CIM-based optimal ILC and robust optimal ILC methods are developed for uncertain systems to achieve better control performance and a faster convergence rate. Next, rigorous theoretical analyses for the two methods have been presented, respectively. Finally, two illustrative numerical examples are provided to validate our methods with improved performance.

Emerging robust and data‐driven control methods for uncertain learning systems

Emerging robust and data‐driven control methods for uncertain learning systems

Optimal iterative learning control design for continuous-time systems with nonidentical trial lengths using alternating projections between multiple sets

Iterative learning control (ILC) applies to systems that repeat the same finite duration task repeatedly. Each repetition is usually termed as a trial, and the associated duration is called the trial length. Once a trial is completed, all information is available for use in updating the control input for the subsequent trial. The vast majority of the currently available designs demand a strictly identical trial length. This paper gives a new result on the design and analysis for continuous-time linear dynamics based on a modified alternating projection method, where the trial lengths may be nonidentical. This result employs multiple sets to represent the actual varying trial length dynamics and is developed by reformulating the problem to one that minimizes the defined distance in a Hilbert space setting. Compared to the standard alternating projections using two sets, the theory of alternating projections between multiple sets is employed to obtain deterministic convergence result for the nonidentical trial length problem. A numerical case study is also given to illustrate the application of the new design.

Feedback-aided PD-type iterative learning control for time-varying systems with non-uniform trial lengths

In most implementations of iterative learning control (ILC) for trajectory tracking, it is usually required that the trial lengths of different iterations are uniform. However, this requirement may not always be ensured in practical applications. In this paper, a feedback-aided PD-type ILC design for time-varying systems with non-uniform trial lengths is proposed. Although the actual trial lengths are non-uniform, the designed update sequences provide uniform full-length signals for the update process. Meanwhile, information from the most recent valid iterations can be better used than the mechanisms that compensate with hypothesized data, such as zero. Their recursive generation also reduces the storage burden compared to search strategies. The feedback error signal can be additionally used as part of the correction term to improve the system performance compared to the traditional open-loop approaches. Under a deterministic model, the main convergence results are obtained by combining the [Formula: see text]-norm technique with the inductive analysis approach. At last, a linear numerical simulation and a nonlinear single-joint robot simulation are performed, respectively, to show that the proposed design can achieve the asymptotic tracking of the desired trajectories for time-varying systems with non-uniform trial lengths.

Design of robust fuzzy iterative learning control for nonlinear batch processes.

In this paper, a two-dimensional (2D) composite fuzzy iterative learning control (ILC) scheme for nonlinear batch processes is proposed. By employing the local-sector nonlinearity method, the nonlinear batch process is represented by a 2D uncertain T-S fuzzy model with non-repetitive disturbances. Then, the feedback control is integrated with the ILC scheme to be investigated under the constructed model. Sufficient conditions for robust asymptotic stability and 2D $ H_\infty $ performance requirements of the resulting closed-loop fuzzy system are established based on Lyapunov functions and some matrix transformation techniques. Furthermore, the corresponding controller gains can be derived from a set of linear matrix inequalities (LMIs). Finally, simulations on the three-tank system and the highly nonlinear continuous stirred tank reactor (CSTR) are carried out to prove the feasibility and efficiency of the proposed approach.

Distributed Data-driven Iterative Learning Control for Consensus Tracking

High performance consensus tracking of networked dynamical systems working repetitively has found applications in a range of areas. Existing iterative learning control (ILC) designs for this problem either require a system model that can be difficult or expensive to obtain in practice, and/or cannot guarantee the monotonic convergence of the tracking error norm. They often have difficulties handling varying networks too. This paper proposes a data-driven norm optimal ILC (DD-NOILC) framework to address these limitations using the recent development in data-driven control, in particular, the so called Willems’ fundamental lemma. The novel design guarantees that even without using any model information, the proposed DD-NOILC framework can achieve the same convergence performance as the model-based NOILC framework, i.e., monotonic convergence of the tracking error norm to zero. Furthermore, using the alternating direction method of multipliers (ADMM), a distributed implementation of the framework is developed such that each subsystem's input can be updated locally, making the proposed distributed DD-NOILC algorithm suitable for large-scale and varying networks. Convergence properties of the proposed algorithms are analysed rigorously, and numerical examples are provided to verify the effectiveness of the distributed DD-NOILC algorithm.

Networked Iterative Learning Control Under Changing Operating Mode of Agents and Configuration of Information Network

The paper considers the iterative learning control (ILC) design problem of a network system under changing operating mode of subsystems (agents) and configuration of information network. The network system consists of identical agents, which are discrete linear dynamic plants operating in a repetitive mode. The operating modes of agents depend on their parameters and the reference trajectory, which must be tracked with required accuracy at output of system. The configurations of information network define the group of functioning agents and the type of information exchange between them. The mode and the configuration change takes place in accordance with certain external rules. The control design is based on the divergent method of the vector Lyapunov function. For reducing the transient error caused by the mode change and the connection of new agents, a special rule for switching the ILC law is proposed. The results of modeling the obtained control law for a group of manipulators with flexible link are presented.

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.

Data-Based Control for Learning Systems With Nonlinear Dynamics: A Case Study

This paper focuses on exploiting a data-based control design framework for a class of iterative learning control (ILC) systems with nonlinear dynamics. A test method is first presented for nonlinear ILC systems to generate some helpful output data under some specific test inputs. Then, a data-based P-type ILC updating law is developed by resorting to these input and output data, for which a simple data-based selection condition on the gain matrix is provided to accomplish the perfect tracking objective of ILC systems having the globally Lipschitz nonlinear dynamics. The proposed data-based P-type ILC updating law is applicable for nonlinear ILC systems without the common full rank requirement, where none of the specific model information is utilized. A simulation example is given to illustrate the validity of the data-based ILC design framework for nonlinear ILC systems.

Frequency‐domain‐based iterative learning control utilizing n‐best adaptive Fourier decomposition for nonrepetitive unknown iteration‐independent and iteration‐varying discrete time‐delay systems

AbstractThe bulk of well‐known control techniques for time‐delay systems are sensitive to the system's uncertainty. For unknown nonrepetitive iteration‐independent and iteration‐varying linear discrete time‐delay (LDTD) systems, an iterative learning control (ILC) design with a frequency domain identification technique is devised. The proposed ILC method is based on a novel n‐best adaptive Fourier decomposition (n‐BAFD) approach for approximating the unknown time‐delay transfer function. An extended anticipatory ILC law is developed that uses anticipatory time to compensate for both iteration‐independent and iteration‐varying time delays in the frequency domain for unknown nonrepetitive LDTD systems. Three examples are used to validate the proposed frequency‐domain‐based ILC method.

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 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.

Predictive compensation based quantization iterative learning control for nonlinear nonaffine discrete‐time systems

AbstractIn this work, the problems of predictive compensation, unknown nonlinearity, and nonaffine structure are considered simultaneously for a quantized iterative learning control (QILC) design and analysis under a data‐driven framework. The compensation strategy can avoid deteriorated data transmission quality owing to limited channel capacities. First, a dynamic linearization methodology is employed to transform the nonlinear plant into a virtual iterative linear data model (iLDM) which includes all the input signals over a time‐window from the initial time instant to the current one. The iLDM is also used as a predictive model to estimate the unavailable information caused by the encoding–decoding mechanism. Then, a predictive compensation‐based QILC is proposed by optimizing quadratic functions, which includes an output prediction mechanism, a quantized iterative learning updating law, a quantized iterative parameter estimation law, and a resetting algorithm. The result is also extended to a class of MIMO nonlinear nonaffine discrete‐time systems. The developed control laws are data‐driven and independent of any system information. The theoretical results are proved by the use of contraction mapping principle and induction method. Examples are provided to verify the effectiveness of the proposed methods.

Robust convergence conditions of iterative learning control for time‐delay systems under random non‐repetitive uncertainties

Some of the most fundamental assumptions in the design of iterative learning control (ILC) for uncertain systems are the strict repetitiveness (i.e. iteration-independence) of uncertainties in all factors of plant dynamic, external disturbances, initial conditions, and reference trajectory, which may not always hold in practical applications. The simultaneous relaxation of all these assumptions is a challenging problem that has been addressed only for delay-free systems. This problem is still open for time-delay systems, especially when the time-delay factor also has non-repetitive (i.e. iteration-dependent/varying) uncertainty. Hence, this study extends the problem of robust ILC for a class of time-delay systems under nonrepetitive uncertainties in not only plant dynamic, external disturbances, initial conditions, and reference trajectory but also time-delay. By using the ILC scheme introduced in this work, and based on the frequency domain analysis, it is shown that both monotonic convergence and boundedness of the expected tracking error can be achieved (in the sense of L2-norm) when the non-repetitiveness (i.e. iteration-dependence) of all existing uncertainties from a random viewpoint are taken into account. The effectiveness of the proposed strategy is verified by two simulation examples.

Control Design for Iterative Methods in Solving Linear Algebraic Equations

In the interaction between control and mathematics, mathematical tools are fundamental for all the control methods, but it is unclear how control impacts mathematics. This is the first part of our paper that attempts to give an answer with focus on solving linear algebraic equations (LAEs) from the perspective of systems and control, where it mainly introduces the controllability-based design results. By proposing an iterative method that integrates a learning control mechanism, a class of tracking problems for iterative learning control (ILC) is explored for the problem solving of LAEs. A trackability property of ILC is newly developed, by which analysis and synthesis results are established to disclose the equivalence between the solvability of LAEs and the controllability of discrete control systems. Hence, LAEs can be solved by equivalently achieving the perfect tracking tasks of resulting ILC systems via the classic state feedback-based design and analysis methods. It is shown that the solutions for any solvable LAE can all be calculated with different selections of the initial input. Moreover, the presented ILC method is applicable to determining all the least squares solutions of any unsolvable LAE. In particular, a deadbeat design is incorporated to ILC such that the solving of LAEs can be completed within finite iteration steps. The trackability property is also generalized to conventional two-dimensional ILC systems, which creates feedback-based methods, instead of the common used contraction mapping-based methods, for the design and convergence analysis of ILC.

Stability of Sliding Mode ILC Design for a Class of Nonlinear Systems With Unknown Control Input Delay.

This article studied the stability and convergence of a robust iterative learning control (ILC) design for a class of nonlinear systems with unknown control input delay. First, the iterative integral sliding mode (IISM) design was proposed, which comprised iterative actions. The iterative action made the convergence of the tracking error under the ideal sliding mode. Then, a suitable iterative update law was provided for the IISM-based robust ILC controller. The controller had the capability of both minimizing the steady tracking error and suppressing the unrepeatable disturbance. Using the controller, the closed-loop system stability was analyzed, and the stability conditions were given. Consequently, the sliding mode convergence in the iteration domain was proved by a composite energy function (CEF). In addition, by analyzing the influence of affection on the tracking error, several measures were taken to solve the chattering problem of the sliding mode control. Finally, a one-link robotic manipulator and a vertical three-tank system were used to verify the control design. The application simulations validated the performance of the proposed sliding mode iterative learning control (SMILC) design, which achieved the stability of the nonlinear system and overcame the control input time delay.

Constrained Iterative Learning Control for Linear Time-Varying Systems With Experimental Validation on a High-Speed Rack Feeder

Iterative learning control (ILC) applies to systems required to track the desired trajectory of finite duration repeatedly. This article considers constrained ILC design for linear time-varying systems, a problem with limited, in relative terms, results in the literature but not uncommon in practical applications. Different design algorithms are developed, and their convergence properties are established. An extension of these designs to point-to-point tracking tasks is given. A high-speed rack feeder typically used in automated warehouses is considered to verify the designs. It represents a flexible beam structure subject to kinematic constraints, such as a maximum velocity and a maximum acceleration with a vertically moving mass causing the time-varying characteristics. Experimental results demonstrate the effectiveness of the designs.

Conic Iterative Learning Control Using Distinct Data for Constrained Systems With State-Dependent Uncertainty

In batch processes, the ability to learn from previous process data results in high-value and batch-improved products. For batch processes with constraints and state-dependent uncertainty, this article presents a conic iterative learning control (ILC) approach, which uses cone theory to incorporate historical process data into optimization-based ILC design. The proposed conic ILC approach uses rank conditioning to select distinct data samples and conic mapping to map the data to the to-be-optimized control input variables, since adding all historical process data would be computationally intensive. Our method yields a tradeoff between learning ability from historical experience and computational efficiency from solving the optimization problem. Provable constraint satisfaction and robust stability are considered separately. To demonstrate the proven properties and effectiveness of the approach, we present a case study of the injection molding process.

Data-driven ILC algorithms using AFD in frequency domain for unknown linear discrete-time systems

In conventional PID-type iterative learning control (ILC) designs, to determine the learning control gains involved, relevant model knowledge on the controlled systems is often dependent. In this paper, two completely data-driven ILC laws, the extended PD-type ILC law and the extended P-type ILC law, are designed in frequency domain for linear discrete-time (LDT) single-input single-output (SISO) systems. The designs of the proposed ILC laws are based on the approximation/identification to unknown transfer function with a novel adaptive Fourier decomposition (AFD) technique. As a result, the strictly monotonic convergence of ILC tracking error is guaranteed in a deterministic way. A numerical example on a four-axis robot arm is performed to illustrate the effectiveness of the proposed data-driven ILC algorithms