Traditional Iterative Learning Control Research Articles

Towards Transparent Control Systems: The Role of Explainable AI in Iterative Learning Control

This paper presents a novel approach to improving the performance and interpretability of Iterative Learning Control (ILC) systems through the integration of Explainable Artificial Intelligence (XAI) techniques. ILC is a powerful method used across various domains, including robotics, process control, and traffic management, where it iteratively refines control inputs based on past performance to minimize errors in system output. However, traditional ILC methods often operate as "black boxes," making it difficult for users to understand the decision-making process. To address this challenge, we incorporate XAI, specifically SHapley Additive exPlanations (SHAP), into the ILC framework to provide transparent and interpretable insights into the algorithm's behavior. The study begins by detailing the evolution of ILC, highlighting key advancements such as predictive optimal control and adaptive schemes, and then transitions into the methodology for integrating XAI into ILC. The integrated system was evaluated through extensive simulations, focusing on robotic arm trajectory tracking and traffic flow management scenarios. Results indicate that the XAI-enhanced ILC not only achieved rapid convergence and high control accuracy but also maintained robustness in the face of external disturbances. SHAP analyses revealed that parameters such as the proportional gain (Kp) and derivative gain (Kd) were critical in driving system performance, with detailed visualizations providing actionable insights for system refinement. A crucial metric for control precision was the root mean square error (RMSE), which was reduced to as low as 0.02 radians in the robotic arm case, indicating extremely precise tracking of the intended route. Similarly, the ILC algorithm effectively maintained the ideal traffic density within the predetermined bounds in the traffic management scenario, resulting in a 40% reduction in congestion compared to baseline control measures. The resilience of the ILC algorithm was also examined by introducing changes to the system model, external disturbances, and sensor noise. The algorithm demonstrated a high degree of stability and accuracy in the face of these disruptions. For instance, in the robotic arm case, adding noise to the sensor readings had a negligible effect on the algorithm's performance, increasing the RMSE by less than 5%. This integration of XAI into ILC addresses a significant gap in control system design by offering both high performance and transparency, particularly in safety critical applications. The findings suggest that future research could further enhance this approach by exploring additional XAI techniques and applying the integrated system to more complex, real-world scenarios.

Experimental validation and analysis of hybrid adaptive iterative learning sliding mode control for PMSM seeker coordinator

High-order nonlinearity, strong coupling, and external disturbances constrain the high-precision servo tracking control of the missile seeker coordinator, which compromises the guidance accuracy of guided weapons. The individual differences in the seekers cause model parameter perturbations, leading to uncertainty and time-varying disturbances, which reduces the tracking performance of the seeker servo system. To cope with these uncertainties various traditional Iterative learning control (ILC) strategies have been designed to suppress high-order nonlinear disturbances. However, these are very sensitive to system uncertainties, external disturbances and model parametric perturbations. In response to this challenge, this paper proposes a hybrid adaptive iterative learning sliding mode control (AILS) methodology. The iterative learning sliding mode control (ILSMC) strategy is used to reduce the impact of periodic disturbances in the system, ensuring a rapid system response. The enhanced adaptive learning law (EAL) strategy offers an estimation of the lumped disturbances of the system, encapsulating both parameter shifts and residual disturbances. Through this appropriate adaptive control, both disturbances compensation and the chattering effect due to sliding mode control are simultaneously minimized. Simulation and experimental results show that compared with the traditional open-loop iterative learning control, the learning convergence speed and convergence accuracy of the proposed hybrid AILS are highly significant. Experimental results also show that the control algorithm designed in this paper can also perform adaptively, has fast learning capability and ensures convergence while guaranteeing the tracking accuracy of the seeker coordinator servo system.

An Adaptive Learning Control for MIMO Nonlinear System with Nonuniform Trial Lengths and Invertible Control Gain Matrix

In the traditional iterative learning control (ILC) method, the operational time interval is conventionally fixed to facilitate a seamless learning process along the iteration axis. However, this condition may frequently be contravened in real-time applications owing to unknown uncertainties and unpredictable factors. In essence, replicating a control system at a consistent time interval proves challenging in practical scenarios. This paper proposes an adaptive iterative learning control (AILC) method for the multi-input–multi-output (MIMO) nonlinear system with nonuniform trial lengths and an invertible control gain matrix. Compared to the existing AILC research that features nonuniform trial lengths, the control gain matrix of the system in this paper is assumed to be invertible. Hence, the general requirement in the conventional AILC method that the control gain matrix of the system is positive-definite (or negative-definite) or even known is relaxed. Moreover, the tracking reference allows it to be iteration-varying. Finally, to prove the convergence of the system, the composite energy function is introduced and to verify the validity of the AILC method, a robot movement imitation with an uncalibrated camera system is used. The simulation results show that the actual output can track the desired reference trajectory well, and the tracking error converges to zero after 30 iterations.

Multivariable Iterative Learning Control Design for Precision Control of Flexible Feed Drives.

Advancements in machining technology demand higher speeds and precision, necessitating improved control systems in equipment like CNC machine tools. Due to lead errors, structural vibrations, and thermal deformation, commercial CNC controllers commonly use rotary encoders in the motor side to close the position loop, aiming to prevent insufficient stability and premature wear and damage of components. This paper introduces a multivariable iterative learning control (MILC) method tailored for flexible feed drive systems, focusing on enhancing dynamic positioning accuracy. The MILC employs error data from both the motor and table sides, enhancing precision by injecting compensation commands into both the reference trajectory and control command through a norm-optimization process. This method effectively mitigates conflicts between feedback control (FBC) and traditional iterative learning control (ILC) in flexible structures, achieving smaller tracking errors in the table side. The performance and efficacy of the MILC system are experimentally validated on an industrial biaxial CNC machine tool, demonstrating its potential for precision control in modern machining equipment.

Adaptive neural network iterative learning control of long-stroke hybrid robots with initial errors and full state constraints

Research on initial errors and constraint restrictions is one of the main research directions in the field of control of uncertain robotic systems. An adaptive iterative learning control (AILC) method based on radial basis function (RBF) neural network is proposed to address the trajectory tracking problem of the long-stroke hybrid robot system with random initial errors and full state constraints. The RBF neural network is used to approximate the unknown nonlinear terms, and the network weights are updated using an iterative learning law that incorporates a projection mechanism. Additionally, a robust learning strategy is used to compensate for both the approximation error of the neural network and the external disturbances that vary with each iteration. To relax the requirement of traditional iterative learning control (ILC) for identical initial condition, an equivalent error function is constructed based on the time-varying boundary layer. The tangent-type barrier Lyapunov function (BLF) is designed to ensure that the joint position and speed of the robot system are bounded within a predetermined range. Through stability analysis based on barrier composite energy function (BCEF), it can be proved that the boundedness of all signals in the closed-loop system and the tracking error of the robot system will converge to an adjustable residual set asymptotically. Finally, through simulation experiments conducted on the MATLAB platform, the results demonstrate that the method overcomes the random initial errors of the system effectively, ensures that the system satisfies the full-state constraints, and realizes high-precision trajectory tracking.

Integrated adaptive iterative learning control based on inter-trial iteration and real-time correction for nonlinear systems with external morphologically-similar disturbances

This paper proposes an adaptive iterative learning control (ILC) scheme for nonlinear systems with iteration-varying trial lengths under external morphologically-similar disturbances, utilising inter-trial iteration and real-time correction. To attenuate external quasi-periodic disturbances and non-repetitive uncertainties, and further achieve better tracking performance along iteration and time axes, the proposed scheme combines the iteration-to-iteration proportional-type (P-type) ILC with the within-iteration P-type scheme. The tracking error with dead zone property and zero filling treatment is constructed. In addition, as opposed to the existing two-dimensional (2D) ILC works, the integrated framework is formed through the connection of adaptive weights, which are calculated by the adaptive weight determination method based on the ideology of the Kalman filter. The convergence of the algorithm is proved based on the contraction mapping principle. Compared with the traditional ILC schemes, illustrative and applicational simulations are provided to demonstrate the effectiveness and the superiority of the proposed framework.

Neural network-based iterative learning control for trajectory tracking of unknown SISO nonlinear systems

This paper proposes a neural network-based (NN-based) data-driven iterative learning control (ILC) algorithm for the tracking problem of nonlinear single-input single-output (SISO) discrete-time systems with unknown models and repetitive tasks. The control objective is to make the output of the system track the reference trajectory in each iteration process. Therefore, at each relative time during every iteration process, a generalized regression neural network (GRNN) is used as the estimator to solve the key parameters of the system, and a radial basis function neural network (RBFNN) is used as the controller to solve the control input. Compared with the traditional ILC algorithm, the two complex solving processes, i.e., dynamic linearization and criterion function minimization, are replaced and simplified into the iterative training of GRNNs and RBFNNs. The proposed algorithm is out-of-the-box and uses a point-to-point method to calculate the control input for each relative time of the system iteration, driving the tracking error of the system to approach zero. In addition, it is proved that the tracking error of the system under the proposed control algorithm is uniformly ultimately bounded. Finally, a numerical example shows the effectiveness and superiority of the control algorithm, and a path tracking experiment of an unmanned vehicle further verifies its practicability.

Cascaded iterative learning motion control of precision maglev planar motor with experimental investigation

Cascaded iterative learning control (CILC) is explored for a magnetically levitated (maglev) planar motor to achieve excellent tracking motion performance in this paper. The CILC control method is based on traditional iterative learning control (ILC) with deeper iterations. CILC solves the difficulty of ILC in constructing perfect learning filter and low-pass filter to obtain excellent accuracy. Specifically, in CILC, the traditional ILC strategy is implemented several times by the operation of feedforward signal registering and clearing in a cascaded structure, which makes the motion error reach an accuracy level superior to traditional ILC even though the filters are imperfect. The fundamental principle, convergence and stability of CILC strategy are explicitly presented and analyzed. Through the structure of CILC, the repetitive component of the convergence error can be completely eliminated in theory, while the non-repetitive component is accumulated but the sum is bounded. Simulation investigation and comparative experimental investigation on maglev planar motor are both conducted. The results consistently show that the CILC strategy is not only superior to PID and model-based feedforward control, but also obviously outperforms traditional ILC. The CILC investigations on maglev planar motor also provide a clue that CILC has appreciable application prospect for precision/ultra-precision systems requiring extreme motion accuracy.

Frequency-Domain Based Iterative Learning Control for 2-D Discrete Systems

In the existing of traditional iterative learning control (ILC) results for two-dimensional (2-D) discrete systems with time-domain based analysis approach, fixed boundary states do not affect the complete convergence of P-type ILC law. However, it does affect the ILC convergence properties in the frequency domain. This paper first investigates the frequency-domain ILC tracking problem for 2-D discrete systems with different boundary states. An extended P-type ILC law is designed and a sufficient convergence condition of which can be derived through a rigorous mathematical proof. A simulation example is given to verify the effectiveness and validation of the proposed extended P-type ILC law. Finally, some comparison results on traditional P-type ILC law and D-type ILC law are presented.

Iterative Learning Control for Actuator Fault Uncertain Systems

An iterative learning fault-tolerant control method is designed for an actuator fault intermittent process with simultaneous uncertainties for the system parameters. First, an intermittent fault tolerance controller is designed using 2D system theory, and the iterative learning control (ILC) intermittent process is transformed into a 2D Roesser model. Secondly, sufficient conditions for the controller’s existence are analyzed using the linear matrix inequality (LMI) technique, and the control gain matrices are obtained by convex optimization with LMI constraints. Under these conditions for all additive uncertainties for the system parameters and admissible failures, the controller can ensure closed-loop fault-tolerant performance in both the time and batch directions, and it can also meet the H∞ robust performance level against outside disturbances. Eventually, the algorithm’s computational complexity is analyzed, and the effectiveness of the algorithm is verified by simulation with respect to an injection molding machine model. Compared with traditional ILC laws, which do not consider actuator faults, the proposed algorithm has a better convergence speed and stability when the time-invariant and time-variant actuator faults occur during implementation.

A learning control scheme for upper-limb exoskeleton via adaptive sliding mode technique

This paper investigates an iterative learning approach integrated with sliding mode control method to accomplish passive rehabilitation therapy tasks for wearable 6 degrees of freedom (DOF) upper-limb exoskeleton. Firstly, the motion data of human body is collected from a healthy subject through VICON motion capture system and reasonable trajectories in joint space are generated by fitting functions. Secondly, an iterative learning controller is developed to estimate the iteration-invariant dynamic parameters which are complicated and difficult to be obtained precisely in practice. Note that the identical initial condition (i.i.c) in traditional iterative learning control (ILC) is released by applying the polynomial reconstruction method. Considering the uncertainties and disturbances which affect the system in the form of friction, backlash and unexpected tissue torques from human body, an adaptive law is proposed to estimate the upper bound of the lumped non-periodic disturbances. Based on that, sliding mode controller is conducted to achieve the robustness over the time domain, while the chattering phenomenon is attenuated by applying tanh function. Afterwards, the stability and convergence of the overall system is rigorously proved with a composite energy function (CEF) composed of tracking and estimating errors. Finally, co-simulation and experiment results are presented to demonstrate the effectiveness of the proposed control scheme.

Iterative Learning for Heterogeneous Systems

Iterative learning control (ILC) aims to improve a system’s performance by learning from previous iterations in repetitive operations. Traditional ILC requires the system to operate in a strictly repetitive way and the learning process is within the confines of one single system. This article proposes an iterative learning method that extends traditional ILC from a temporal learning process within one single system to a spatial learning process between two heterogeneous systems. This learning mechanism is made viable by designing learning filters which bridge the dynamics of different systems. To design such learning filters, first, a dynamic system that consists of two heterogeneous systems and two learning filters is constructed; second, the two learning filters are decoupled from the known dynamics step by step. Each filter is successfully placed in the feedback loop of a reconstructed system consecutively, which enables us to transfer the filter design problem into a controller design problem that can be solved by leveraging the H-infinity optimal control theory. Meanwhile, the solvability of the learning filters, the stability of the system, and the learning convergence are rigorously analyzed. The proposed new algorithm is applied to the trajectory tracking problem of quadrotor drones. Both numerical and experimental studies have been conducted to validate the effectiveness of the proposed iterative learning method for multiple heterogeneous systems.

An Iterative Learning Controller for a Switched Cooperative Allocation Strategy during Sit-to-Stand Tasks with a Hybrid Exoskeleton.

A hybrid exoskeleton that combines functional electrical stimulation (FES) and a powered exoskeleton is an emerging technology for assisting people with mobility disorders. The cooperative use of FES and the exoskeleton allows active muscle contractions via FES while robustifying torque generation to reduce FES-induced muscle fatigue. In this paper, a switched distribution of allocation ratios between FES and electric motors in a closed-loop adaptive control design is explored for the first time. The new controller uses an iterative learning neural network (NN)-based control law to compensate for structured and unstructured parametric uncertainties in the hybrid exoskeleton model. A discrete Lyapunov-like stability analysis that uses a common energy function proves asymptotic stability for the switched system with iterative learning update laws. Five human participants, including a person with complete spinal cord injury, performed sit-to-stand tasks with the new controller. The experimental results showed that the synthesized controller, in a few iterations, reduced the root mean square error between desired positions and actual positions of the knee and hip joints by 46.20% and 53.34%, respectively. The sit-to-stand experimental results also show that the proposed NN-based iterative learning control (NNILC) approach can recover the asymptotically trajectory tracking performance despite the switching of allocation levels between FES and electric motor. Compared to a proportional-derivative controller and traditional iterative learning control, the findings showed that the new controller can potentially simplify the clinical implementation of the hybrid exoskeleton with minimal parameters tuning.

A New Iterative Learning Control Algorithm for Final Error Reduction*

Iterative learning control (ILC) is a powerful technique for tracking performance improvement by adding the iteratively updated learning signal to the feedforward loop of a repetitively operated system. To increase the robustness to uncertainties and noises, usually a low-pass filter is needed in the learning law which can result in a final steady-state error as a trade-off. This study proposes a new ILC algorithm to further reduce the final error associated with the traditional ILC design. This new algorithm can be easily applied to most ILC systems. In the proposed learning algorithm, when the learning converges and a final error is obtained, the learning law is updated by adding a compensating term which consists of a compensatory filter and the obtained final error. The to-be-designed compensatory filter introduces no more design trade-offs and uncertainties. By updating the learning law, the reached learning convergence can be broken and the final error is further reduced. The compensatory filter design guideline along with four different designs are provided and analyzed. Numerical studies with the four designs have been conducted, and the results are compared to that with the traditional ILC design. It shows that the proposed learning algorithm is able to further reduce the final error effectively.

Time‐iteration‐domain integrated learning control for robust trajectory tracking and disturbance rejection: With application to a PMLSM

Iterative learning control (ILC) has been widely used to improve motion performance when reference trajectories and external disturbances are strictly repetitive. However, the occurrence of non-repetitive trajectories and disturbances would significantly deteriorate the performance of traditional ILC methods. To solve this problem, a time-iteration-domain integrated learning control (TIDLC) scheme is proposed for enhancing robustness against non-repetitive trajectories and disturbances. The TIDLC scheme consists of an ILC term and a time-domain compensator (TC) term. While the ILC term that performs learning in the iteration-domain preserves excellent performance under repetitive tasks, the TC term that is updated in the time-domain can compensate for the variations of trajectories and disturbances. Stability and performance analyses are discussed in both the time-domain and iteration-domain. Experimental results on a permanent magnet linear synchronous motor (PMLSM) positioning system verify the validity of the proposed scheme.

Consensus of fractional‐order multi‐agent systems using iterative learning control in the sense of Lebesgue‐p norm

AbstractIn this paper, open loop and closed loop PDα‐type fractional‐order iterative learning control algorithms with fixed topology for the fractional‐order distributed multi‐agent systems are proposed. In the sense of Lebesgue‐p norm, the convergences of the proposed methods are discussed by using the generalized Young inequality of convolution, and their convergence conditions are presented. The proposed algorithm extends the application scope of traditional iterative learning control theory. Theoretical analysis shows that by selecting the appropriate learning gain matrix, the output of each agent can completely track the desired trajectory in a limited time interval as the number of iterations increases. The feasibility and theoretical correctness of the presented algorithm are verified by numerical simulations.

Iterative learning control realized using an iteration-varying forgetting factor based on optimal gains

Iterative learning control with forgetting factor (ILCFF) is widely used in control engineering. However, choosing the optimal parameters of ILCFF to improve system-output characteristics has been a challenging issue for controller designers. This paper proposes an iterative learning control (ILC) algorithm that involves a variable forgetting factor based on optimal gains for a class of discrete linear time-invariant systems with aperiodic disturbances. The convergence of the algorithm is analyzed, and the necessary and sufficient condition for its convergence is derived in terms of proportional–integral–derivative coefficients. A design method based on optimal gains is established to determine the algorithm coefficients and to accelerate system convergence. Furthermore, the influence of the forgetting factor on both the system-output error and the scope of the proposed algorithm is analyzed. Additionally, the most suitable system type for the application of the forgetting factor is determined. The effectiveness of the algorithm is verified by performing a theoretical analysis and a case-based simulation. The proposed iteration-varying optimal forgetting-factor-based ILC algorithm undergoes fast convergence with a small system-output error. The findings disrupt the conventional view that the use of the forgetting factor increases system-output error. In fact, in a system with small trajectory and increased disturbances, the error induced by the forgetting factor may be smaller than that of the traditional optimal ILC algorithm.

Adaptive Iterative Learning Control for Robot Manipulators With Time-Varying Parameters and Arbitrary Initial Errors

In this paper, a novel error-tracking adaptive iterative learning control scheme is proposed to solve trajectory-tracking problem for a class of robot manipulators with time-varying parameters and arbitrary initial errors. Firstly, desired error trajectories are constructed for implementing error tracking strategy in the robotic systems, so as to relax the requirement of zero initial errors, which is usually assumed to be met in traditional iterative learning control algorithms. Secondly, with the help of reasonable parameterization to the robotic dynamics, the adaptive iterative control law is designed by using Lyapunov approach. Projection-free combined time-domain and iteration-domain adaptive learning strategy is adopted to estimate the unknown time-invariant parametric uncertainties, and difference learning strategy is adopted to estimate unknown time-varying parametric uncertainties. As the iteration number increases, the system error follows its desired error trajectory over the whole interval. As a result, system state can perfectly track the reference signal in the predetermined part interval. In the end, several numerical simulations are presented to demonstrate the effectiveness of the designed control scheme.

Optimised data-driven terminal iterative learning control based on neural network for distributed parameter systems

In this paper, a data-driven iterative learning control with neural network-based optimisation method for distributed parameter systems is presented to solve a class of problems caused by the imprecise mathematical model. The forward difference format is used to establish a linear relationship between input and output data, which is the only information available. However, this also leads to an unknown parameter matrix of the system. To overcome this problem, the radial basis function neural network is used to form a mapping relation from the desired output to the desired input, and the iterative learning algorithm of neural network weight is obtained by optimising the system performance indexes. Then, a detailed theoretical analysis based on composite energy function is given. Moreover, unlike traditional iterative learning control task tracking the whole trajectory, tracking time terminal is taken into account in this paper. Finally, simulation results show the feasibility of the theory.

A periodic iterative learning scheme for finite-iteration tracking of discrete networks based on FlexRay communication protocol

In this study, the finite-iteration tracking of discrete networks is analyzed by designing a new kind of periodic iterative learning control (ILC) strategy. In the proposed ILC scheme, the FlexRay communication protocol with both static and dynamic segments is introduced in the design. The design has the advantage to reduce the communication channel bandwidth load and hence improve the performance of finite-iteration tracking. This paper provides the first integrating approach to iterative learning design based on the dynamic capability of FlexRay communication channels, and can be generalized to other learning process in network control design. Simulation results are shown to clarify the effectiveness of the obtained criteria, and demonstrate that the proposed periodic ILC scheme performs better than the traditional ILC schemes.