Iterative learning control applies to applications in which the same finite-duration task is repeated, with each instance termed a trial. The objective is to track a specified reference trajectory over a finite duration, termed the trial length. In some applications, such as multi-agent systems, tracking at each instant or point over the trial length is not required; only at selected points is it required, known as point-to-point iterative learning control. This article develops a new point-to-point design in which the points requiring tracking vary from trial to trial, and the solution minimizes energy, which is relevant to systems with a limited power budget. Also, an algorithm is developed to improve computational efficiency by sharing the burden among the agents forming the system. A numerical case study highlights the benefits of the new design.

This paper investigates the problem of designing iterative learning control laws based on input and state measurements collected during an open-loop experiment. Disturbances corrupt the measured data, and we have a set of dynamics that could have generated the collected data. The problem considered is control law design to achieve robust convergence of the tracking error in the trial-to-trial direction. It is shown that the design problem can be formulated in a repetitive process setting, as it is required to consider the interaction between the trial-to-trial error and the transient response along the trials. The stability analysis for linear repetitive processes is used to develop conditions for the existence of a control law, and the computation of the required control law matrices is linear matrix inequality-based. Finally, comparative simulation results show the effectiveness of the new design.

This paper develops new results on data-driven iterative learning control for nonlinear batch processes. The dynamic linearization approach is used to obtain linearized local dynamical models utilizing only the collected process input and output data. As a result, no dynamic structure of the nonlinear model is required for the control design. Additionally, the design problem is formulated within the repetitive process framework, which simplifies the design procedure, facilitates the integrated synthesis of feedback and learning controllers, and aids in the adjustment of control parameters. The convergence of the new data-driven control method is demonstrated by the stability of the resulting repetitive process, which ensures that the tracking error decreases along both the time and iteration (batch) axes. Stability properties can be effectively checked using linear matrix inequality techniques. A numerical example is included to highlight the application of the new results.

In iterative learning control, the aim is to exploit the repeated executions, termed trials, of the same task over a finite duration by designing a control input sequence that forces the sequence of errors formed by the difference on each trial between the output and the supplied reference trajectory to converge as the number of trials increases. This paper uses the stability theory for repetitive processes to develop new design algorithms that can enhance trial-to-trial error convergence while simultaneously regulating any trial's dynamics.

This article considers the design of a decentralized iterative learning control (ILC) scheme for spatiotemporal systems modeled by a partial differential equation of advection-diffusion type. In particular, the optimal tracking problem is formulated using a sensor-actuator network operating over an m-dimensional spatial domain. Then, a decentralized ILC design is developed to reduce complexity. The main idea is to decompose the whole system into several smaller interacting subsystems and build the control update rule for each local controller based on the respective subsystem measurements and optimal system response prediction from the other subsystems. This approach simplifies the control system and significantly reduces the learning effort while providing a control quality comparable to a fully centralized control scheme. A nontrivial simulation example on friction welding of multiple aluminum plates illustrates the effectiveness and performance of this design.

In this paper, we present an observer-based output feedback Iterative Learning Control (ILC) scheme for single input, single output discrete-time Luré-type systems with sector-bounded nonlinearities in the state equation. The design is achieved by concatenating trials and casting the trial-by-trial memory of ILC as a delay system. A pair of synthesis Linear Matrix Inequalities is formulated to solve the observer and controller design problems, respectively. The proposed design is tested on an unstable nonlinear system.

This paper develops an iterative learning control (ILC) design for marginally stable systems where control input saturation may occur due to actuator limits. To achieve a good control performance directly after saturation, the control system was equipped with a model recovery anti-windup compensator (MRAWC). A state feedback control system was also used to ensure good tracking properties starting from the first iteration. The applied ILC law includes a finite impulse response learning filter to enable a flexible shaping of the ILC dynamics. To calculate learning filter coefficients and a gain vector of MRAWC, convex optimization problems were formulated using linear matrix inequalities to specify the desired properties of the control system. Since the considered system with input saturation is marginally stable, its stability is guaranteed within a particular region. By defining a range of the actuator input for which the regional sector condition, characterising the actuator nonlinearity, is satisfied, the determination of the reference signal slopes became simpler. The paper also presents results from a comprehensive experimental investigation, including a comparison with a previous design that did not include MRAWC.

The subject of this paper is aerodynamic load control for wind turbines, which has the potential to increase power extraction efficiency, including economic competitiveness when compared to other sources of alternative energy. The general feasibility of this approach is developments in sensor and actuator technology, which enables their embedding into the rotor blades. Minimizing lift fluctuations due to disturbances is feasible when combined with active control to modify the blade section aerodynamics. Previous research has shown that it is possible to combine such an actuator sensor combination with a control law for this application. In general, this approach will require a model-based design, and previously published results have shown that proper orthogonal decompositions can produce finite-dimensional models from the computational fluid dynamics-based representations of the defining partial differential equations and enable control law design.

This study aims to develop a robust computational scheme to address the optimal tracking control problem for repetitive distributed parameter systems, in situations where the controlled quantity is not directly observable. In such a case, the reliability of the model predictions becomes a crucial factor affecting the quality of control design in consecutive process replications. To maximize the accuracy of prediction, the optimal sensor location problem is considered. It consists in selecting gaged sites from among all available sites so that the suitable criterion defined on the Fisher information matrix associated with the model parameters is minimal. To effectively solve it, a relaxed convex optimization problem is formulated, and then suitable optimality conditions are provided. Then the measurement locations that provide the most informative system observations are further incorporated into the predictive control scheme based on the iterative learning control. The proposed approach is verified on the example of repetitive control for a thermophotovoltaic cell.

Iterative learning control (ILC) can significantly reduce the tracking error between the repetitive reference trajectory and the output by refining the ILC input with plenty of trials. However, re-learning is usually necessary in the presence of trajectory switching. To address this issue, this paper develops an experience transfer-based ILC method for nonaffine nonlinear systems by employing the radial basis function (RBF) neural network. First, a data-driven ILC algorithm that integrates feedback control is designed to acquire high-precision control performance of a nominal trajectory, which serves as the offline priors. Then, an RBF network is used to project the known experience information from the finite time-indexed domain into a state-dependent feature space for obtaining an equivalent controller. The developed method can extract the generalized inverse dynamics of the considered system by tracking on the same trajectory repetitively, which can be used for a new trajectory without re-iteration. Theoretical analysis is given, and a numerical case study demonstrates the effectiveness of the ILC design.

Iterative learning control applies to systems that repeat the same finite duration operation. Each execution is termed a trial, and once a trial is complete, all information is available to update the control law for the subsequent trial. Given a reference trajectory representing desired performance for all trials, the error on each trial is the difference between the reference trajectory and the trial output. The problem is to design a control law that converges trial-to-trial errors and regulates the dynamics of each trial. This paper uses stability theory for repetitive processes to develop a new law for applications in which the reference trajectory and dynamics switch on particular trials in presence of the input backlash. The new design offers accelerated trial-to-trial error convergence and compensates for temporary errors generated by the switching dynamics.

This article develops iterative learning control designs to handle actuator nonlinearities that can occur during implementation. Unlike existing designs, the new results can be adapted to several commonly encountered nonlinearities. The application of the new design is highlighted through a detailed case study based on a model for the dynamics of a robot system constructed from measured frequency response data. In particular, this case study shows that the control law developed can accelerate error convergence and compensate for the effects of nonlinear actuator dynamics.

A robust indirect-type iterative learning control scheme is developed for batch processes with state delays, time-varying uncertainties, and disturbances. In contrast to direct-type designs, the new scheme consists of two control loops, each of which can be designed independently. In the inner loop, a control law that is the sum of a generalised extended state observer-based state feedback and proportional plus integral control action acting on an error signal is designed for stability and robustness. The outer loop is designed to update the set-point command for the resulting closed-loop system. Finally, the stability theory for linear repetitive processes ensures robust tracking error convergence for the resulting dynamics in the presence of non-repetitive uncertainties and disturbances. Two numerical examples demonstrate the attributes of the new design.

Iterative learning control (ILC) is typically applied in practice combined with a feedback controller for time-domain stability. In this closed-loop design with actuator constraints, existing constrained ILC designs suffer from determining the exact input constraint on the ILC controller. This issue brings in an important gap between the existing constrained ILC designs and their real-world applications. This paper gives a systematic consideration of the input constraint problem in the closed-loop ILC design with actuator saturation. A constraint-aware ILC is developed to autonomously determine the constraint on the feedforward controller. The convergence of the constrained ILC process is proved under the framework of alternating projection. Finally, the effectiveness of the developed method is verified on a numerical simulation.

Iterative learning control (ILC) applies to systems that repeat the same finite-duration task repeatedly, where each repetition is termed a trial and the finite duration is termed the trial length. The control method involves specifying a reference trajectory, calculating the error at each trial, and designing a control law to drive the error sequence toward convergence as the number of trials increases. This letter considers the ILC design problem for stochastic discrete linear systems with multiple reference trajectory switching and parameter variations, using a combination of optimization and vector Lyapunov functions. The design also includes compensation for the temporary increase in learning error caused by switching the reference trajectory and parameter variations. A numerical example demonstrates the properties of the new design and includes a brief comparison with an alternative design.

For industrial batch processes with unknown dynamics subject to nonrepetitive initial conditions and disturbances, this article develops a novel adaptive data-driven set-point learning control (ADDSPLC) scheme based on only the measured process input and output data, which has two loops, one for the dynamics within a batch and the other for the batch-to-batch dynamics. In the former case, a model-free tuning strategy is first presented for determining the closed-loop proportional-integral controller parameters. For the latter case, a set-point learning control law with adaptive set-point learning gain and gradient estimation is developed for batch run optimization. The robust convergence of the output tracking error is rigorously analyzed together with the boundedness of adaptive learning gain and real-time updated set-point command. Moreover, another iterative extended-state-observer-based ADDSPLC scheme is developed with rigorous convergence and boundedness analysis to enhance the robust tracking performance against nonrepetitive uncertainties. Finally, two illustrative examples from the literature are used to demonstrate the effectiveness and superiority of the new schemes over the recently developed data-driven learning control designs.

This paper considers the class of 2D linear systems where a linear differential equation governs information propagation in one of the two directions, and in the other, the updating is governed by a difference equation; in some of the literature, these systems are referred to as mixed or hybrid. Linear repetitive processes are a particular case of such systems that have been used in several areas, such as iterative learning control. Stability margins for these systems have received attention in the literature. In this paper, new results on these margins for differential linear repetitive processes are derived and applied to iterative learning control law design. Sufficient conditions for computing the required stability margins are formulated using linear matrix inequalities, which can be readily adapted to design the required controllers. Finally, the applications of the developed results to design of ILC scheme for a typical actuator in a tracking servo system is presented to demonstrate the effectiveness of the design and highlight its advantages over existing alternatives.

This paper develops a predictive optimal iterative learning control design for nonlinear systems based on the Koopman operator. Iterative learning control applies to systems that undergo repeated executions, known as trials, over a finite duration, the trial length. Once a trial is complete, all information generated is available to update the control signal for the subsequent trial. The first step in design is to approximately model the nonlinear system as a high-dimensional linear model using the Koopman operator and extended dynamic mode decomposition, which is applied on each trial. Then, an iterative learning control law is designed with predictive action over an infinite duration in the trial-to-trial direction. The robust convergence of the tracking error is analyzed, and a numerical case study demonstrates the effectiveness of the design.

Iterative learning control for lumped-parameter systems is very well developed. Still, comparatively less attention has been directed to applying this method to those whose dynamics evolve in space and time. This paper gives new results in assessing the performance of various iterative learning control designs, focusing on a heat transfer application described by partial differential equations using a network of sensors and actuators.

This paper investigates the problem of designing robust iterative learning control laws for discrete-time batch processes with norm-bounded parameter uncertainties. A law of proportional-differential type is designed to achieve robust convergence of the tracking error in the batch-to-batch direction. It is shown that the design problem can be written as a two-dimensional system. Then, the recently developed non-conservative conditions for (structural) stability analysis for a linear Roesser model are used. The conditions for the existence and computation of the required control law matrices are linear matrix inequality-based. Finally, comparative simulation results show the effectiveness of the new design.