High-order Iterative Learning Control Research Articles

Higher-order iterative learning control for nonlinear continuous systems with variable input trail lengths and input saturation

Higher-order iterative learning control for nonlinear continuous systems with variable input trail lengths and input saturation

Feedback higher-order iterative learning control for nonlinear systems with non-uniform iteration lengths and random initial state shifts

For nonlinear discrete-time systems with non-uniform iteration lengths and random initial state shifts, this paper developed a feedback higher-order iterative learning control (ILC) approach. To compensate the absent information of last iteration caused by non-uniform iteration lengths, the tracking information in both iteration domain and time domain is included in ILC design with the help of higher-order control and feedback control, respectively, while the general ILC schemes just adopt the information in iteration domain. A sufficient condition based on the higher-order ILC gains is derived. It is guaranteed that as the iteration number goes to infinity, the asymptotic bound of tracking error is proportional to random initial state shifts in mathematical expectation sense. Specifically, as the expectation of initial state shifts is zero, the ILC tracking error can be controlled to zero along the iteration direction. Two examples with different initial conditions are provided to validate the proposed ILC approach.

High‐order iterative learning model predictive control for batch chemical processes

AbstractIn order to address two‐dimensional (2D) control issue for a class of batch chemical processes, we propose a novel high‐order iterative learning model predictive control (HILMPC) method in this paper. A set of local state‐space models are first constructed to represent the batch chemical processes by adopting the just‐in‐time learning (JITL) technique. Meanwhile, a pre‐clustered strategy is used to lessen the computational burden of the modelling process and improve the modelling efficiency. Then, a two‐stage 2D controller is designed to achieve integrated control by combining high‐order iterative learning control (HILC) on the batch domain with model predictive control (MPC) on the time domain. The resulting HILMPC controller can not only guarantee the convergence of the system on the batch domain, but also guarantee the closed‐loop stability of the system on the time domain. The convergence of the HILMPC method is ensured by rigorous analysis. Two examples are presented in the end to demonstrate that the developed method provides better control performance than its previous counterpart.

A Data-Driven ILC Framework for a Class of Nonlinear Discrete-Time Systems.

In this article, we propose a data-driven iterative learning control (ILC) framework for unknown nonlinear nonaffine repetitive discrete-time single-input-single-output systems by applying the dynamic linearization (DL) technique. The ILC law is constructed based on the equivalent DL expression of an unknown ideal learning controller in the iteration and time domains. The learning control gain vector is adaptively updated by using a Newton-type optimization method. The monotonic convergence on the tracking errors of the controlled plant is theoretically guaranteed with respect to the 2-norm under some conditions. In the proposed ILC framework, existing proportional, integral, and derivative type ILC, and high-order ILC can be considered as special cases. The proposed ILC framework is a pure data-driven ILC, that is, the ILC law is independent of the physical dynamics of the controlled plant, and the learning control gain updating algorithm is formulated using only the measured input-output data of the nonlinear system. The proposed ILC framework is effectively verified by two illustrative examples on a complicated unknown nonlinear system and on a linear time-varying system.

Robust Iterative Learning Control for 2-D Linear Nonrepetitive Discrete Systems With Iteration-Dependent Trajectory

In the existing robust iterative learning control (ILC) for 2-D discrete systems, they typicallly require to satisfy a core hypothesis that the strict repetitiveness of tracking reference trajectory and system model should be satisfied. This paper first investigates the robustness and convergence of a P-type ILC law and a high-order ILC law for 2-D linear nonrepetitive discrete systems (LNDS) with arbitrarily bounded reference trajectory and iteration-dependent reference trajectory described by a high order internal model (HOIM) operator in iteration domain, respectively. It is theoretically proved by using the 2-D linear nonrepetitive inequalities that the ILC tracking error and the control input robustly converge to a bounded range, the bound of which depends continuously on the bounds of all the nonrepetitive uncertainties. If these uncertainties are progressively convergent along the iteration domain, a precise tracking on the 2-D reference trajectory can be achieved. Two illustrative examples are provided to demonstrate the validity of the presented ILC law. Additionally, some comparative result on the practical dynamical processes is given.

Robust high-order iterative learning control approach for two-dimensional linear discrete time-varying Fornasini–Marchesini systems with iteration-dependent reference trajectory

This paper first investigates robust tracking problem of a high-order iterative learning control (HOILC) algorithm for two classes of two-dimensional linear discrete time-varying Fornasini–Marchesini systems (2-D LDTVFMS) and 2-D LDTVFMS with input delays with iteration-dependent reference trajectory described by a high-order internal model (HOIM) operator, boundary states and disturbances. An extended high-order linear discrete inequality is proposed to guarantee the ILC tracking error of 2-D LDTVFMS converge robustly to a bounded range, the bound of which is relied on iteration-dependent uncertainties from reference trajectory, boundary states and disturbances. A simulation example on a practical thermal process is used to validate the effectiveness and feasibility of the proposed HOILC law. Additionally, it is verified by theory analysis and simulation that no matter how the ILC controller gain is selected, the convergence condition in Theorem 2 of Wan and Li [(2021). High-order internal model based iterative learning control for 2-D linear FMMI systems with iteration-varying trajectory tracking. IEEE Transactions on Systems Man and Cybernetics: Systems, 51, 1462–1472] is not satisfied. Using the proposed HOILC law, perfect tracking result in Theorem 2 of Wan and Li (2021) can be obtained.

Higher‐Order Iterative Learning Control with Optimal Control Gains Based on Evolutionary Algorithm for Nonlinear System

For the nonlinear discrete‐time system, higher‐order iterative learning control (HOILC) with optimal control gains based on evolutionary algorithm (EA) is developed in this paper. Since the updating actions are constituted by the tracking information from several previous iterations, the suitably designed HOILC schemes with appropriate control gains usually achieve fast convergence speed. To optimize the control gains in HOILC approach, EA is introduced. The encoding strategy, population initialization, and fitness function in EA are designed according to the HOILC characteristics. With the global optimization of EA, the optimal control gains of HOILC are selected adaptively so that the number of convergence iteration is reduced in ILC process. It is shown in simulation that the sum absolute error, total square error, and maximum absolute error of tracking in the proposed HOILC based on EA are convergent faster than those in conventional HOILC.

Adaptive Iterative Learning Control of an Industrial Robot during Neuromuscular Training

To prevent the reduction of muscle mass and loss of strength coming along with the human aging process, regular training with e.g. a leg press is suitable. However, the risk of training-induced injuries requires the continuous monitoring and controlling of the forces applied to the musculoskeletal system as well as the velocity along the motion trajectory and the range of motion. In this paper, an adaptive norm-optimal iterative learning control algorithm to minimize the knee joint loadings during the leg extension training with an industrial robot is proposed. The response of the algorithm is tested in simulation for patients with varus, normal and valgus alignment of the knee and compared to the results of a higher-order iterative learning control algorithm, a robust iterative learning control and a recently proposed conventional norm-optimal iterative learning control algorithm. Although significant improvements in performance are made compared to the conventional norm-optimal iterative learning control algorithm with a small learning factor, for the developed approach as well as the robust iterative learning control algorithm small steady state errors occur.

Consensus Learning Control for Leader-Following Nonlinear Multiagent Systems with Control Delay

In this paper, the consensus tracking problem of leader-following nonlinear control time-delay multiagent systems with directed communication topology is addressed. An improved high-order iterative learning control scheme with time-delay is proposed, where the local information between agents is considered. The uniformly global Lipschitz condition is applied to deal with the nonlinear dynamics. Then, a sufficient condition is driven, which guarantees that all the following agents track the trajectory of leader. Also, the convergence of proposed control protocol is analyzed by the norm theory. Finally, two cases are provided to illustrate the validity of theoretical results.

Optimized Iterative Learning Control for Linear Discrete-Time-Invariant Systems

In this paper, an optimized first-order iterative learning control (OILC) scheme is explored for a class of linear discrete-time-invariant systems with Markov parameters available and the system relative degree being unity. For the OILC scheme, the iteration-time-variable derivative learning-gain vector is argued by sequentially minimizing the sum of the tracking error energy and the learning effort intensity amplified by an iteration-wise tuning factor. In virtue of the optimization criterion, the existence and the uniqueness of the iteration-time-variable learning-gain vector is achieved. Then, by making use of the elementary transformations which exchange the rows and columns of a matrix and by taking advantage of the positivity relationship of the eigenvalues with the matrix-weighing quadratic function, the strictly monotone convergence of the OILC scheme is derived, which conveys that the strict monotonicity is guaranteed without any requirement to the system Markov parameters and the convergence rate is adjustable by scaling the tuning factor. Furthermore, an optimized higher-order iterative learning control mechanism is developed for the system relative degree is larger than unity, for which the existence and the uniqueness of the optimized higher-order iteration-time-variable learning-gain vector are discussed and the strictly non-conditional monotone convergence is analyzed. The numerical simulations demonstrate the validity and effectiveness.

Consensus Control of Time-Varying Delayed Multiagent Systems with High-Order Iterative Learning Control

We address the consensus control problem of time-varying delayed multiagent systems with directed communication topology. The model of each agent includes time-varying nonlinear dynamic and external disturbance, where the time-varying nonlinear term satisfies the global Lipschitz condition and the disturbance term satisfies norm-bounded condition. An improved control protocol, that is, a high-order iterative learning control scheme, is applied to cope with consensus tracking problem, where the desired trajectory is generated by a virtual leader agent. Through theoretical analysis, the improved control protocol guarantees that the tracking errors converge asymptotically to a sufficiently small interval under the given convergence conditions. Furthermore, the bounds of initial state difference and disturbances tend to zero; the bound of tracking errors also tends to zero. In the end, some cases are provided to illustrate the effectiveness of the theoretical analysis.

High order iterative learning control to solve the trajectory tracking problem for robot manipulators using Lyapunov theory

This paper deals with Iterative Learning Control (ILC) design to solve the trajectory tracking problem for rigid robot manipulators subject to external disturbances, and performing repetitive tasks. A high order ILC scheme is synthetized; this controller contains the information (errors) of several iterations and not only of one iteration. It has been shown that the closed loop system (robot plus controller) is asymptotically stable, over the whole finite time interval, when the iteration number tends to infinity. This proof is based upon the use of a Lyapunov-like positive definite sequence, which is shown to be monotonically decreasing under the proposed controller scheme. Finally, simulation results on two-link manipulator are provided to illustrate the effectiveness of the proposed controller.

Robust higher‐order ILC for non‐linear discrete‐time systems with varying trail lengths and random initial state shifts

This study addresses a robust iterative learning control (ILC) scheme for non-linear discrete-time systems in which both the trail lengths and the initial state shifts could be randomly variant in iteration domain. The proposed higher-order ILC law guarantees that as the iteration number goes to infinity, the ILC tracking errors at the desired output trail period are bounded in mathematical expectation, and the bound of tracking errors is proportional to the random initial state shifts. Specifically, the ILC tracking errors in mathematical expectation can be driven to zero as the expectation of initial state shifts is zero. Two numerical examples are carried out to demonstrate the effectiveness of the proposed higher-order ILC law.

Design of arbitrary-order robust iterative learning control based on robust control theory

Iterative learning control (ILC) is an effective technique that improves the tracking performance of systems by adjusting the feedforward control signal based on the memory data. The key in ILC is to design learning filters with guaranteed convergence and robustness, which usually involves lots of tuning effort especially in high-order ILC. To facilitate this procedure, this paper proposes a systematics approach to design learning filters for arbitrary-order ILC with guaranteed convergence, robustness and ease of tuning. The filter design problem is transformed into an H∞ optimal control problem for a constructed feedback system. This approach is based on an infinite impulse response (IIR) system and conducted directly in iteration-frequency domain. The proposed algorithm is further advanced to the one that explicitly considers system variations based on μ synthesis. Important characteristics of the proposed approach such as convergence and robustness are explored and demonstrated through both simulations and experiments on a wafer scanning system.

Higher-order Iterative Learning Control Law Design using Linear Repetitive Process Theory: Convergence and Robustness

Iterative learning control has been developed for processes or systems that complete the same finite duration task over and over again. The mode of operation is that after each execution is complete the system resets to the starting location, the next execution is completed and so on. Each execution is known as a trial and its duration is termed the trial length. Once each trial is complete the information generated is available for use in computing the control input for the next trial. This paper uses the repetitive process setting to develop new results on the design of higher-order ILC control laws for discrete dynamics. The new results include conditions that guarantee error convergence and design in the presence of model uncertainty.

Forgetting Factor Nonlinear Functional Analysis for Iterative Learning System with Time-Varying Disturbances and Unknown Uncertain

This paper focuses on the iterative learning tracking control problem for a class of nonlinear system with time-varying disturbances. First, because of the mismatches in time-varying disturbances functions, a high-order feed-forward iterative learning control (ILC) is employed to change the original system into an iterative system. Secondly, a variable forgetting factor is developed to stabilize the system. Based on the feed-forward iterative learning controller, a memory controller is constructed for the nonlinear system. By choosing a new variable forgetting factor, we show that the designed continuous adaptive controller makes the solutions of the closed-loop system convergent to a ball exponentially. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed method.

Iterative learning control design for linear discrete-time systems with multiple high-order internal models

This work is focused on the iterative learning control (ILC) design for linear discrete-time systems with iteration-varying factors, including reference, initial state, and exogenous disturbances. First, multiple high-order internal models (HOIMs) are given for various iteration-varying factors. The reference is generated by an HOIM, and the initial state and the exogenous disturbances ultimately satisfy HOIMs but do not strictly follow HOIMs in finite iteration interval. Then, a new ILC scheme, a special high-order ILC (HO-ILC), is constructed according to an augmented HOIM that is the aggregation of all HOIMs. For simplicity, the case with only iteration-varying reference is first considered, where the asymptotic stability and monotone convergence based ILC design methods are both presented by using the 2-D analysis approach. Next, more iteration-varying factors are further considered. In this situation, the HOIM-based ILC is transformed into a controller design problem of a 2-D Roesser model with non-zero boundary states and disturbances, where the 2-D H∞ performance is studied. In consequence, an ILC design criterion is presented to achieve perfect tracking and 2-D H∞ performance. For comparison, the monotone convergence based ILC design method is extended to the situation with more iteration-varying factors. Utilizing information provided by the multiple HOIMs, it is verified that HO-ILC outperforms low-order ILC (LO-ILC) in presence of iteration-varying factors. Meanwhile, the 2-D H∞ based ILC is shown to be superior to the monotone convergence based ILC. Finally, a microscale robotic deposition system with iteration-varying factors is given to illustrate the advantage of the proposed 2-D H∞ based ILC.

High-Order Feedback Iterative Learning Control Algorithm with Forgetting Factor

A novel iterative learning control (ILC) algorithm is proposed to produce output curves that pass close to the desired trajectory. The key advantage of the proposed algorithm is introducing forgetting factor, which is a function of the number of iterations. Due to the forgetting factor characteristic of ILC, the proposed scheme not only stabilizes the nonlinear system with uncertainties but also weakens interference on the tracking desired trajectory. Simulation examples are included to demonstrate feasibility and effectiveness of the proposed algorithm.

Physical layer privacy scheme for networked control systems

Control systems in general and networked controls systems in particular are vulnerable to harmful noise effect and malicious cyber-attacks that may have devastated outcomes on sensitive applications. One approach to address these threats is to introduce a stringent security and privacy schemes that able to protect the attacked systems. This paper addresses this issue by proposing a privacy scheme, for feedback signals, stemmed from the well-known spread spectrum principle and the information system theory. In order to confirm the efficiency of the proposed scheme in offering a good level of control system privacy, a theoretical analysis is provided and supported by a simulation example introduced to one of the relatively weak control systems to noise and malicious attacks namely Higher Order Iterative Learning Control (HOILC).

Stability Analysis of High-Order Iterative Learning Control for a Class of Nonlinear Switched Systems

This paper considers the stability of high-order PID-type iterative learning control law for a class of nonlinear switched systems with state delays and arbitrary switched rules, which perform a given task repeatedly. The stability condition for the proposed high-order learning control law is first established, and then the stability is analyzed based on contraction mapping approach in the sense ofλnorm. It is shown that the proposed iterative learning control law can guarantee the asymptotic convergence of the tracking error for the entire time interval through the iterative learning process. Two examples are given to illustrate the effectiveness of the proposed approach.