Iterative Learning Control Scheme Research Articles

Combined Iterative Learning and Model Predictive Control Scheme for Nonlinear Systems

Combined Iterative Learning and Model Predictive Control Scheme for Nonlinear Systems

Robust tracking of discrete-time linear switched systems with disturbance via second-order ILC with data loss

The purpose of this article is to investigate the second-order P-type iterative learning control (ILC) scheme in the presence of data loss for a class of linear discrete-time switched systems with disturbances. Employing the super-vector representation technique, the discrete-time linear switched system is reformulated as an input-output transmission equation. The robustness of the resulting switched system driven by a second-order P-type ILC scheme is guaranteed through the use of the super-vector representation technique. Importantly, the article also explores cases of data loss occurring during data transmission. The proposed methodology exhibits significantly improved convergence performance compared to the P-type ILC scheme (Yang et al., 2022, Robust finite-iteration tracking of discrete-time systems in repetitive process setting via ILC scheme. International Journal of Robust and Nonlinear Control, 32(5), 2585–2602. https://doi.org/10.1002/rnc.5782). Simulation examples are provided to demonstrate the effectiveness of the proposed scheme.

Iterative-learning-based tracking control of a two-wheeled mobile robot with model uncertainties and unknown periodic disturbances

In this paper, we develop an adaptive iterative learning approach to investigate the trajectory tracking control issue for a class of two-wheeled mobile robots subject to model uncertainties and unknown disturbances. First, we derive the nonlinear velocity error dynamics. Then a parameterization-based adaptive iterative learning control scheme is adopted to achieve precise tracking, along with logic-based update law for the estimated period and bound of the disturbance. Moreover, the boundness of all the closed-loop signals is rigorously analyzed based on the Lyapunov stability theory to provide the theoretical foundation for the proposed method. The experimental results show the efficacy and viability of our results.

Almost sure and mean square convergence of iterative learning control system with state feedback under random packet dropouts

This paper investigates the almost sure and mean square convergence of a state feedback-based iterative learning control scheme for a class of discrete-time multi-input–multi-output linear systems with a direct feedback term in the presence of random data dropouts. Firstly, the realisability of the control system is considered. It is shown that the realisability of the control system is only determined by the direct feedback matrix, which has nothing to do with the input–output coupling matrix, and the direct feedback matrix to be full-row rank is enough to guarantee the system realisable. Secondly, the convergence of output tracking errors is analysed in both the almost sure and mean square senses, respectively. By the contraction mapping method combined with matrix decomposition and transformation techniques, it is strictly proved that the output sequence can converge to any given desired trajectory in the sense of almost sure and mean square, respectively, if and only if the general spectral radius condition is satisfied. Finally, an example is given to show the correctness of the theoretical analysis.

An integrated tube robust iterative learning model predictive control strategy based on dynamic partial least squares algorithm for batch processes

AbstractIn this paper, an integrated tube robust iterative learning model predictive control (Tube‐RILMPC) strategy based on the dynamic partial least squares (DyPLS) identified algorithm is proposed. The problems of large amount of online data calculation and input and output variable dimensions disaster in the original variable space are solved. This integrated Tube‐RILMPC strategy enhances the tracking performance and robustness of two‐dimensional (2D) control system. The output trajectories of system are located in the tube the nominal trajectory, which reduces the modelling error caused by the uncertain model. Based on the worst‐case performance index of ellipsoidal uncertainty and polytopic uncertainty, a robust iterative learning control (ILC) strategy is designed. Finally, the superiority of the proposed control algorithm is verified by comparative simulation.

Iterative learning control approach for linear discrete time-varying systems with different initial time points

Different from the existing iterative learning control (ILC) works for dynamical systems with iteration-varying trial lengths, in which the terminal time points are not identical, this paper presents an ILC approach for linear discrete time-varying (LDTV) systems with different initial time points. A piecewise ILC law is designed by using the segment compensation techniques in time axis. Through a rigorous mathematical analysis, it is theoretically proved that as the mathematical expectation of the iterative initial state equals to the desired initial state, the ILC tracking error at the maximum universal time interval can be driven into a bounded region in mathematical expectation sense. Particularly, the mathematical expectation of the ILC tracking error at the maximum universal time interval can even be driven to zero under a certain initial state condition. Numerical simulations are provided to verify the effectiveness of the proposed ILC scheme.

Neural network compensator-based robust iterative learning control scheme for mobile robots nonlinear systems with disturbances and uncertain parameters

Aiming at the problem of trajectory tracking control for mobile robot nonlinear systems with non-repetitive uncertain parameters, we propose a novel neural network compensator-based robust iterative learning control (NNRILC) scheme to achieve excellent tracking performance and uncertainty compensation. The NNRILC scheme consists of a parallel structure that includes a robust iterative learning control (RILC) term and a neural network (NN) compensator. The RILC term is used to ensure robust control performance and promise closed-loop stability. The compensator based on the neural network is employed to handle the uncertainties resulted from the nonlinear dynamics as well as the suppressed disturbances in the mobile robot nonlinear systems. Additionally, the fourth-order Runge-Kutta algorithm is employed to solve the state differential equation of the mobile robot. Consequently, The H∞ robust technique is used to construct an iterative learning control update rule to reduce the impact of disturbances. Meanwhile, the RILC scheme is designed to optimize the neural network initial parameters and weights of the NN compensator at each trial. Then the convergence of the proposed NNRILC scheme is analyzed, and the results are incorporated into the control update for the next process trial. Finally, the effectiveness of the proposed method is verified by mobile robot simulation.

Adaptive iterative learning control for a class of parameterized fractional-order systems subjected to backlash-like hysteresis

In this article, a fractional-order adaptive iterative learning control scheme is proposed for a class of parameterized fractional-order systems with unknown control gain and backlash-like hysteresis nonlinearity under disturbance. Based on the sufficient condition for the stability of linear fractional-order systems, a sliding mode surface of tracking errors is constructed to facilitate the controller design and stability analysis. A new boundary layer function is designed by using Mittag-Leffler function to relax the restriction of the identical initial condition of iterative learning control design. The fractional-order differential-type adaptive laws and difference-type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. To deal with the influence of backlash-like hysteresis nonlinearity reminder term and unknown bounded external disturbance, a robust control term is designed by employing the hyperbolic tangent function with a convergent series sequence which can guarantee the learning convergence along iteration axis. By constructing Lyapunov-like composite energy function, the stability analysis is presented to prove the convergence of the system output to a small neighborhood of the desired trajectory and the boundedness of all the closed-loop signals. Finally, a simulation example of second-order nonlinear fractional-order system is presented, which demonstrates the effectiveness of the proposed fractional-order adaptive iterative learning control scheme.

Predictive State Observer-Based Set-Point Learning Control for Batch Manufacturing Processes With Delay Response

A predictive state observer (PSO) based iterative learning control (ILC) scheme is proposed for industrial batch manufacturing processes with delay response suffering from nonrepetitive uncertainties and disturbances. Combining with a delay-free output predictor, a PSO based feedback control structure is firstly presented to improve set-point tracking and disturbance rejection performance against nonrepetitive process uncertainties and disturbances for the initial batch run. Then an ILC law is introduced to update the closed-loop system set-point in order to improve the tracking performance from batch to batch. A delay-independent sufficient condition is established to ensure the convergence of output tracking error along the batch-direction, based on double-dynamic analysis. Moreover, another delay-dependent sufficient condition is constructed by linear matrix inequality to assess robust stability of the proposed two-dimensional control system along both the time- and batch-directions. Finally, an illustrative example and a real application to the batch temperature regulation of a 4-litre crystallizer are shown to validate the effect and advantage of the proposed ILC scheme.

Cross-coupling indirect iterative learning control method for batch processes with time-varying uncertainties

For batch time-varying processeswith non-repetitive disturbances, a cross-coupling indirect iterative learning control (CC-iILC) is proposed. The set trajectory of the system on the single axis is accurately tracked by an indirect iterative learning control strategy with a PI controller for its time direction and a closed-loop feedback control strategy for the batch direction. Under the asymptotically stable condition of the two-dimensional (2D) dynamic model, the optimal control law is obtained by optimizing the H-infinity control function. To avoid the contour error during coupling, the cross-coupling technique is used to distribute the contour error to each axis for compensation. The stability condition of the indirect iterative learning controller is analyzed by a two-dimensional Fornasini-Marchesini (FM) batch dynamics model and two-dimensional robust H-infinity control theory. The feasibility and superiority of the proposed control method are verified by numerical simulation and experimental tests.

A two-dimensional model predictive iterative learning control based on the set point learning strategy for batch processes

Although conventional two-dimensional model predictive iterative learning control (2D-MPILC) based on an extended non-minimum state space (ENMSS) model can avoid designing an observer, it only relies on feedback to passively deal with time delay. This passive treatment for time delay hinders the further improvement of control performance. To address this shortcoming, a two-dimensional model predictive iterative learning control strategy based on the set point learning (2D-SPL-MPILC) is proposed. Firstly, a set point learning strategy is developed to improve the ability to deal with time delay. Based on the error of the previous batch, the set point learning strategy perceives the system dynamics in advance, and then outputs this advance perception in the form of the predictive set point. Secondly, a novel ENMSS model is constructed on the basis of the predictive tracking error between the predictive set point and the actual output. Since the predictive tracking error integrates the predictive set point, this novel ENMSS model has certain predictive ability. Finally, based on this novel ENMSS model, a novel two-dimensional model predictive iterative learning control (2D-MPILC) method, which is called 2D-SPL-MPILC method, is designed. Because this controller contains the perception of future process dynamics, it can reduce the impact of time delay and improve the control performance. The case studies on the packing pressure control in injection molding process and batch reactors demonstrate the effectiveness of the presented 2D-SPL-MPILC strategy.

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.

Repetitive process based indirect-type iterative learning control for batch processes with model uncertainty and input delay

This paper develops an indirect iterative learning control scheme for batch processes with time-varying uncertainties, input delay, and disturbances. In this paper, a predictor based on a state observer is designed to estimate the future state and to compensate for the input delay. Then a feedback controller based on the estimated state and the set-point error is used to track the specified reference trajectory, where, of the options available, a robust H∞ controller is designed in the presence of time-varying uncertainties and load disturbances. Then a proportional plus derivative type iterative learning control law is designed. An injection molding process model demonstrates the new method’s effectiveness, and a comparison with a direct-type design is given.

Two-dimensional iterative learning control with deep reinforcement learning compensation for the non-repetitive uncertain batch processes

Iterative learning control (ILC) is an advantage control strategy widely used in batch systems. Nevertheless, designing an effective iterative learning control scheme remains crucial for complex batch systems with model mismatch and non-repetitive nature. In this paper, we propose a two-dimensional iterative learning control-reinforcement learning (2D ILC-RL) control scheme composed of a two-dimensional ILC controller and a two-dimensional DRL compensator. Based on the 2D system theory, the 2D ILC controller is proposed to ensure the primary control performance and its stability and convergence are verified. Meanwhile, the DRL compensator counteracts the negative impact of the model mismatch and the non-repetitive nature. In addition, we proposed a real-time implementation scheme to guarantee the safety of the practical batch systems compared to the conventional online training method. Finally, the simulation results in the injection molding batch process and the nonlinear continuously stirred tank reactor demonstrate the proposed control scheme’s effectiveness, significant control performance, and strong robustness.

Data-Driven Spatial Adaptive Terminal Iterative Learning Predictive Control for Automatic Stop Control of Subway Train With Actuator Saturation

A data-driven spatial adaptive terminal iterative learning predictive control (SATILPC) scheme with actuator saturation is proposed for automatic stop control of the subway train. Considering the outstanding repetitive operation pattern and the unavailable accurate model of a subway train, the unknown train dynamics is firstly transformed into a nonlinear discrete form in spatial domain via the spatial differential operator. Since the train automatic stop control (TASC) only concentrates on the tracking performances of the terminal position and terminal speed, an iterative dynamic linearization approach considering the terminal operation point is devised to formulate the relationship of the train input and output (I/O) into a linear affine form. Then, a terminal iterative learning prediction mechanism is introduced to reconstruct the developed train data model to forecast the future train behaviors through rolling optimization process. As a result, by removing the constraints on the unimportant points, the optimal control input (braking force) can be obtained by minimizing the objective function through terminal I/O data. Further, actuator saturation is considered to address the passenger comfort and the reliable operation of the train. The proposed SATILPC approach is a pure data-driven iterative learning control scheme and no model information is involved in the whole design processes. By utilizing a newly space-based contraction mapping method, the convergence of the proposed approach is strictly proved. Finally, the simulation results further demonstrate the feasibility of the proposed algorithm.

Multi-phase iterative learning control for high-order systems with arbitrary initial shifts

Aiming at the second-order tracking system with arbitrary initial shifts, this paper presents a multi-phase iterative learning control strategy. Firstly, utilizing the form of solution of the second-order non-homogeneous linear differential equation with constant coefficients and the initial shifts, we can select the appropriate control gain to ensure that the second-order systems are stable and reach the stable output after a fixed time. Secondly, on the premise that the second-order systems have reached the fixed output, two methods are proposed for rectifying the fixed shift, namely, shifts rectifying control and varied trajectory control. Theoretical analysis shows that the multi-stage iterative learning control strategy proposed in this paper can ensure that the second-order systems achieve complete tracking in the specified interval. Finally, the simulation examples affirm the validation of the designed algorithms.

Fractional-order iterative learning control for fractional-order systems with initialization non-repeatability

The effect of initialization non-repeatability on iterative learning control performance for fractional-order systems has not been sufficiently investigated. It is a hidden deficiency that leads directly to the breaking of perfect tracking conditions in both theoretical analysis and real-world applications. Therefore, under the framework of general fractional-order nonlinear systems, this paper proposes an open-close loop Dα-type iterative learning control scheme based on system preconditioning and strictly derives two convergence conditions. By applying the preconditioning optimization strategy based on the short-memory principle, the tracking error due to initialization nonrepetition can converge to any desired range. Compared with the existing results, the proposed iteration scheme fully considers the complexity of the initialization and initial conditions of fractional-order systems, and provides several practical preconditioning methods to improve the tracking efficiency. Two numerical examples are presented to validate the above conclusions.

Experimental Validation of Iterative Learning Control for DC/DC Power Converters

In order to solve the problem that the parameters of traditional proportional–integral (PI) control are not easy to adjust, an iterative learning control (ILC) technique for a DC/DC power converter is proposed in this paper. Firstly, we have developed a system which is composed of two different states of DC/DC converter in order to obtain its equivalent linear time-varying system, and then the open-loop PD-type ILC law has been used to control it. Secondly, an experimental setup is arranged to verify and compare the simulated results. The experimental results show that, as compared with the traditional PI control, the proposed strategy is easy to implement and optimal with regard to debugging parameters, and it can achieve zero steady-state tracking errors without overshooting. Finally, the experimental results have also proven that our proposed scheme of iterative learning control for a DC/DC power converter is robust as compared to traditional PI control.

A novel iterative learning control scheme based on Broyden‐class optimization method

SummaryThis study proposes a novel iterative learning control scheme for discrete‐time linear systems based on the Broyden‐class optimization method. To overcome the difficulty of lacking system information, a cost function is introduced for the performance index by constructing a positive‐definite matrix with little system information. An optimization‐based learning control algorithm is proposed using a Hessian matrix approximation and the generated input sequence is demonstrated to exhibit a superlinear convergence rate. The proposed scheme is extended to address the point‐to‐point tracking problem. Numerical simulations are provided to verify the effectiveness of the proposed approach.

Event-Triggered Cooperative Model-Free Adaptive Iterative Learning Control for Multiple Subway Trains With Actuator Faults.

This article investigates the issue of speed tracking and dynamic adjustment of headway for the repeatable multiple subway trains (MSTs) system in the case of actuator faults. First, the repeatable nonlinear subway train system is transformed into an iteration-related full-form dynamic linearization (IFFDL) data model. Then, the event-triggered cooperative model-free adaptive iterative learning control (ET-CMFAILC) scheme based on the IFFDL data model for MSTs is designed. The control scheme includes the following four parts: 1) the cooperative control algorithm is derived by the cost function to realize cooperation of MSTs; 2) the radial basis function neural network (RBFNN) algorithm along the iteration axis is constructed to compensate the effects of iteration-time-varying actuator faults; 3) the projection algorithm is employed to estimate unknown complex nonlinear terms; and 4) the asynchronous event-triggered mechanism operated along the time domain and iteration domain is applied to lessen the communication and computational burden. Theoretical analysis and simulation results show that the effectiveness of the proposed ET-CMFAILC scheme, which can ensure that the speed tracking errors of MSTs are bounded and the distances of adjacent subway trains are stabilized in the safe range.