Data-driven Iterative Learning Control Research Articles

Pseudo-model-based iterative learning control for nonlinear multi-phase batch processes

In this article, a pseudo-model-based iterative learning control (ILC) is exploited for multi-phase batch processes which can be described as a nonlinear switched system with unknown functions and identical states in different phases. The nonlinear switched system is converted into a linear model whose system parameter matrix is approximated by minimizing the discrepancy from the real system output increment to the approximated system output increment. A data-driven ILC is constructed in an interactive form with system parameter matrix approximate algorithm. Meanwhile, the signs of the diagonal elements of system lower triangular parameter matrix are introduced into the construction of control input law. Theoretical analysis shows that the pseudo-model-based ILC (PM-ILC) concept can be extended to multi-phase batch processes with non-identical states in different phases. Furthermore, the approximation error of the system parameters matrix is bounded and the proposed PM-ILC is robust if the parameter is appropriately chosen. Simulation results illustrate the effectiveness and practicability of the proposed PM-ILC.

Data-driven robust iterative learning control of linear systems

We propose a data-driven robust iterative learning control (ILC) technique to multi-input-multi-output (MIMO) linear systems. Control of MIMO linear systems, particularly with strong cross-axis coupling, is challenging as modeling of a MIMO system can be complicated, time-consuming, and often requires a trade-off between robustness and performance. As such, limitations exist in current ILC techniques. The aim of this paper is to develop an efficient and easy-to-use data-driven ILC technique to output tracking of MIMO linear systems under random disturbance. Through the proposed technique, the complicated modeling process and the robustness-accuracy trade-off are avoided, and the up-to-now system dynamics is captured by constructing and updating the iteration gain using the input and output data in the last iteration. It is shown that monotonic convergence of the ILC algorithm is guaranteed, and an optimal gain can be obtained to maximize the convergence rate and minimize the residual tracking error. The proposed technique is illustrated through experiments on a three-input three-output piezoelectric actuator system, with comparison to the adaptive multi-axis inversion-based iterative control (A-MAIIC) technique. The experimental results show rapid convergence and improved formance of the proposed technique when the cross-axis coupling is strong.

Finite-Time Asymmetric Bipartite Consensus for Multi-Agent Systems Using Data-Driven Iterative Learning Control

Finite-Time Asymmetric Bipartite Consensus for Multi-Agent Systems Using Data-Driven Iterative Learning Control

Robust Data-Driven Iterative Learning Control for High-Speed Train With Aperiodic DoS Attacks and Communication Delays

Robust Data-Driven Iterative Learning Control for High-Speed Train With Aperiodic DoS Attacks and Communication Delays

Quantised data-driven iterative learning bipartite consensus control for unknown heterogeneous linear MASs with varying trial lengths

This paper aims to realise the robust output bipartite consensus for unknown heterogeneous linear time-varying multiagent systems (MASs) subject to varying trial lengths, unknown measurement disturbances and data quantisation. To this end, inspired by the idea of quantised control, a quantised data-driven adaptive iterative learning bipartite consensus (AILBC) method is proposed. Specifically, to address the problem of varying trial lengths, a distributed auxiliary output prediction system is constructed based on the agents' input-output (I/O) dynamic relationship. An adaptive update protocol is developed to estimate the measurement disturbances and unknown parameters of I/O dynamic relationship. Subsequently, a quantised distributed data-driven iterative learning control (ILC) approach based on the quantised output information is proposed for MASs to achieve robust bipartite consensus tracking, with an attempt to relax the need of explicit model information. The bipartite consensus tracking errors are ultimately bounded through rigorous analysis, and this result is further extended to switching topologies. Finally, numerical simulations are conducted to verify the validity of the AILBC method.

Compensating Aerodynamics of Over-Actuated Multi-Rotor Aerial Platform With Data-Driven Iterative Learning Control

Compensating Aerodynamics of Over-Actuated Multi-Rotor Aerial Platform With Data-Driven Iterative Learning Control

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.

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.

Kernel-based regularized iterative learning control of repetitive linear time-varying systems

For data-driven iterative learning control (ILC) methods, both the model estimation and controller design problems are converted to parameter estimation problems for some chosen model structures. It is well-known that if the model order is not chosen carefully, models with either large variance or large bias would be resulted, which is one of the obstacles to further improve the modeling and tracking performances of data-driven ILC in practice. An emerging trend in the system identification community to deal with this issue is using regularization instead of the statistical tests, e.g., AIC, BIC, and one of the representatives is the so-called kernel-based regularization method (KRM). In this paper, we integrate KRM into data-driven ILC to handle a class of repetitive linear time-varying systems, and moreover, we show that the proposed method has ultimately bounded tracking error in the iteration domain. The numerical simulation results show that in contrast with the least squares method and some existing data-driven ILC methods, the proposed one can give faster convergence speed, better accuracy and robustness in terms of the tracking performance.

Robust Data-Driven Iterative Learning Control for Linear-Time-Invariant and Hammerstein-Wiener Systems.

Iterative learning control (ILC) relies on a finite-time interval output predictor to determine the output trajectory in each trial. Robust ILCs intend to model the uncertainties in the predictor and to guarantee the convergence of the learning process subject to such model errors. Despite the vast literature in ILCs, parameterizing the uncertainties with the stochastic errors in the predictor parameters identified from system I/O data and thus robustifying the ILC have not yet been targeted. This work is devoted to solving such problems in a data-driven fashion. The main contributions are two-fold. First, a data-driven ILC method is developed for LTI systems. The relationship is established between the errors in the predictor matrix and the stochastic disturbances to the system. Its robust monotonic convergence (RMC) is then linked with the closed-loop learning gain matrix that contains the predictor uncertainties and is analyzed based on a closed-form expectation of this gain matrix multiplied with its own transpose, that is, in a mean-square sense (MS-RMC). Second, the data-driven ILC and MS-RMC analysis are extended to nonlinear Hammerstein-Wiener (H-W) systems. The advantages of the proposed methods are finally verified via extensive simulations in terms of their convergence and uncorrelated tracking performance with the stochastic parametric uncertainties.

Distributed Data-driven Iterative Learning Control for Consensus Tracking

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

Data-Driven Iterative Learning Control of Nonlinear Systems by Adaptive Model Matching

Iterative learning control (ILC) has proven successful in the industry for enhancing tracking performance of repetitive tasks. The high accuracy and fast convergence of ILC algorithms hinge on: 1) the knowledge of the system model and 2) an effective learning algorithm. For general industrial systems with nonlinear dynamics, this raises technical challenges because acquiring a nonlinear dynamical model or several linearized models at different operating points may be difficult and costly. It is also nontrivial to determine the learning algorithm for the complex model obtained. To address these challenges, this article proposes a novel data-driven ILC algorithm for single-input-single-output nonlinear systems. Without explicit nonlinear models, our algorithm treats the nonlinear system as an unknown linear time-varying system linearized on a specified input–output (I/O) trajectory in each ILC iteration. A linearly parameterized time-varying adaptive filter is constructed in each ILC iteration so that, when cascading with the nonlinear plant, the I/O dynamics around the specified trajectory follow a linear time-invariant reference model. The ILC error trajectory is then filtered by the adaptive time-varying filter, which represents the inverse dynamics with a bandwidth specified by the reference model, to render fast convergence. The benefits of the proposed data-driven algorithm is demonstrated by comparing to a gradient and Hessian-based data-driven ILC algorithm on a prototypical two-degree-of-freedom nonlinear pendulum.

Controller-Dynamic-Linearization-Based Data-Driven ILC for Nonlinear Discrete-Time Systems With RBFNN

In this article a novel data-driven iterative learning control (ILC) approach is proposed for unknown nonlinear nonaffine repetitive discrete-time systems, where the dynamic linearization (DL) technique in the iteration domain is applied both on the controlled nonlinear system and on the unknown nonlinear ideal learning controller. Through updating the weight matrix of a radial basis function neural network (RBFNN), the learning control gain of the obtained iterative learning law is automatically tuned in reaching the optimal learning controller using only the input-output data of the nonlinear system. The uniformly ultimately bounded property is established for the tracking error of the proposed ILC scheme in the iteration domain through rigorous theoretical analysis. The effectiveness and applicability are validated by a simulation example and further demonstrated by simulation on a high-speed train model.

Physiologic Data-Driven Iterative Learning Control for Left Ventricular Assist Devices.

Continuous flow ventricular assist devices (cfVADs) constitute a viable and increasingly used therapy for end-stage heart failure patients. However, they are still operating at a fixed-speed mode that precludes physiological cfVAD response and it is often related to adverse events of cfVAD therapy. To ameliorate this, various physiological controllers have been proposed, however, the majority of these controllers do not account for the lack of pulsatility in the cfVAD operation, which is supposed to be beneficial for the physiological function of the cardiovascular system. In this study, we present a physiological data-driven iterative learning controller (PDD-ILC) that accurately tracks predefined pump flow trajectories, aiming to achieve physiological, pulsatile, and treatment-driven response of cfVADs. The controller has been extensively tested in an in-silico environment under various physiological conditions, and compared with a physiologic pump flow proportional-integral-derivative controller (PF-PIDC) developed in this study as well as the constant speed (CS) control that is the current state of the art in clinical practice. Additionally, two treatment objectives were investigated to achieve pulsatility maximization and left ventricular stroke work (LVSW) minimization by implementing copulsation and counterpulsation pump modes, respectively. Under all experimental conditions, the PDD-ILC as well as the PF-PIDC demonstrated highly accurate tracking of the reference pump flow trajectories, outperforming existing model-based iterative learning control approaches. Additionally, the developed controllers achieved the predefined treatment objectives and resulted in improved hemodynamics and preload sensitivities compared to the CS support.

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.

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

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

Security data-driven iterative learning control for unknown nonlinear systems with hybrid attacks and fading measurements

To achieve the stabilization objective of a class of nonlinear systems with unknown dynamics, this paper studies the security data-driven control problem under iterative learning schemes, where the faded channels are suffering from randomly hybrid attacks. The networked attacks try to obstruct the data transmission by injecting the false data. The plant is transformed into a dynamic data-model with the iteration-related linearization method. Then, two data-driven control methods, including a compensation scheme multiplied by increasing gains, are designed by using incomplete I/O signals. The effectiveness of the algorithms and the influence brought by stochastic issues are analyzed theoretically. Finally, a numerical simulation and a tracking example of agricultural vehicles illustrate the validity of the design.

Symposium Title: The Very Young Brain and the Auditory World

This paper proposes a novel proportional-integral observer (PIO) based high-order data-driven iterative learning control (HODDILC) for nonlinear batch processes with non-repetitive disturbances subject to input constraints. First, an equivalent dynamic linearization data model (DLDM) with an uncertainty term arising from the nonrepetitive disturbances is constructed in the batch direction. Based on the established DLDM along with a gradient estimation algorithm, a data-driven PIO is then designed to estimate the uncertainty term along the batch direction, followed by designing a HODDILC law in terms of the tracking errors over more than one previous batches and control inputs in the previous time instants of the current batch. Using the contraction mapping principle and matrix theory, rigorous convergence analysis is conducted in the iteration domain. A notable advantage of the proposed design is that only input and output measurement data are used rather than a process model. Finally, an illustrative example from the literature is given to demonstrate the effectiveness and merit of the proposed method.

Quantisation compensated data-driven iterative learning control for nonlinear systems

This work presents a quantisation compensation-based data-driven iterative learning control (QC-DDILC) scheme by incorporating a uniform quantiser and an encoding–decoding mechanism (E-DM) to deal with the problem of limited communication resources in a networked control system. Since it is directly aimed at a nonlinear nonaffine system, an iterative dynamic linearisation method is employed to transfer it to a linear data model. Then, the QC-DDILC method is developed by the use of optimisation technique for the learning control law and the parameter updating law, respectively, where the quantised output from the E-DM is used. Since the direct output measurement of the system is unavailable, the linear data model is also acted as an iterative predictive model to estimate the system outputs utilised as the compensator in the consequent QC-DDILC. The proposed QC-DDILC is a data-driven method without relying on any explicit mechanism model information. The convergence analysis is conducted by using the mathematical tools of contraction mapping and induction. Simulations verify the theoretical results.

Auxiliary Predictive Compensation-Based ILC for Variable Pass Lengths

This paper reconsiders the iterative learning control (ILC) problem for variable trial lengths via compensating output data by using an auxiliary predictive model when the controlled process does not reach the desired trial length. Moreover, this paper aims to propose a general and data-driven ILC method without requiring any explicit mechanistic model information. Specifically, an iterative difference with state transition expression is performed at first over the desired trial length in iteration domain to build an auxiliary predictive model for the iterative input-output dynamics of the linear discrete-time system. Then, an auxiliary predictive compensation-based ILC (APC-ILC) method is presented by defining an expanded output variable in which the predictive output is incorporated to compensate the unavailable output data due to the shorter operation length. The learning gain is iteration-time-varying and is updated using real-time data to adapt to system changes. Furthermore, the proposed learning control law contains additional input information to further improve the control performance. Theoretical analysis and simulations further verify the effectiveness of the proposed APC-ILC.