Computationally Efficient Data-Driven Higher Order Optimal Iterative Learning Control

Dynamic Neural Network Predictive Compensation-Based Point-to-Point Iterative Learning Control With Nonuniform Batch Length

This article discusses the problem of nonuniform running length in incomplete tracking control, which often occurs in industrial processes due to artificial or environmental changes, such as chemical engineering. It affects the design and application of iterative learning control (ILC) that relies on the strictly repetitive property. Therefore, a dynamic neural network (NN) predictive compensation strategy is proposed under the point-to-point ILC framework. To handle the difficulty of establishing an accurate mechanism model for real process control, the data-driven approach is also introduced. First, applying the iterative dynamic linearization (IDL) technique and radial basis function NN (RBFNN) to construct the iterative dynamic predictive data model (IDPDM) relies on input-output (I/O) signal, and the extended variable is defined by a predictive model to compensate for the incomplete operation length. Then, a learning algorithm based on multiple iteration errors is proposed using an objective function. This learning gain is constantly updated through the NN to adapt to changes in the system. In addition, the composite energy function (CEF) and compression mapping prove that the system is convergent. Finally, two numerical simulation examples are given.

A Novel Accelerated Multistage Learning Control Mechanism via Virtual Performance Reduction

This study uses a multistage learning mechanism concept to investigate the accelerated learning control for stochastic systems. In this mechanism, the learning iterations are divided into successive stages, with each stage comprising several iterations. The learning gain is constant in each stage to accelerate the learning process and decreases it from one stage to another to eliminate the noise effect asymptotically. The critical issue is determining the switching iteration when a new stage starts. This study resolves this issue by calculating a virtual performance index of the mean-squared input error and its estimated upper bound. Specifically, the ideal, practical, and improved multistage learning control schemes are proposed to determine the switching iteration and generate the learning gain sequence. The ideal scheme achieves the best performance at the cost of a large computation burden, and the practical scheme saves computation cost, but the performance is not excellent. The improved scheme significantly approximates the best performance by introducing additional stretching parameters to the performance index. Illustrative simulations are provided to verify the theoretical results.

Data-Driven Tabulation for Chemistry Integration Using Recurrent Neural Networks

Due to the wide range of time scales involved in the ordinary differential equations (ODEs) describing chemical reaction kinetics, multidimensional numerical simulation of chemical reactive flows using detailed combustion mechanisms is computationally expensive. To confront this issue, this article presents an economic data-driven tabulation algorithm for fast combustion chemistry integration. It uses the recurrent neural networks (RNNs) to construct the tabulation from a series of current and past states to the next state, which takes full advantage of RNN in handling long-term dependencies of time series data. The training data are first generated from direct numerical integrations to form an initial state space, which is divided into several subregions by the K-means algorithm. The centroid of each cluster is also determined at the same time. Next, an Elman RNN is constructed in each of these subregions to approximate the expensive direct integration, in which the integration routine obtained from the centroid is regarded as the basis for a storing and retrieving solution to ODEs. Finally, the alpha-shape metrics with principal component analysis (PCA) are used to generate a set of reduced-order geometric constraints that characterize the applicable range of these RNN approximations. For online implementation, geometric constraints are frequently verified to determine which RNN network to be used to approximate the integration routine. The advantage of the proposed algorithm is to use a set of RNNs to replace the expensive direct integration, which allows to reduce both the memory consumption and computational cost. Numerical simulations of a H2/CO-air combustion process are performed to demonstrate the effectiveness of the proposed algorithm compared to the existing ODE solver.

Conic Input Mapping Design of Constrained Optimal Iterative Learning Controller for Uncertain Systems

In this article, we study the optimal iterative learning control (ILC) for constrained systems with bounded uncertainties via a novel conic input mapping (CIM) design methodology. Due to the limited understanding of the process of interest, modeling uncertainties are generally inevitable, significantly reducing the convergence rate of the control systems. However, huge amounts of measured process data interacting with model uncertainties can easily be collected. Incorporating these data into the optimal controller design could unlock new opportunities to reduce the error of the current trail optimization. Based on several existing optimal ILC methods, we incorporate the online process data into the optimal and robust optimal ILC design, respectively. Our methodology, called CIM, utilizes the process data for the first time by applying the convex cone theory and maps the data into the design of control inputs. CIM-based optimal ILC and robust optimal ILC methods are developed for uncertain systems to achieve better control performance and a faster convergence rate. Next, rigorous theoretical analyses for the two methods have been presented, respectively. Finally, two illustrative numerical examples are provided to validate our methods with improved performance.

A Probabilistically Quantized Learning Control Framework for Networked Linear Systems

In this article, we consider quantized learning control for linear networked systems with additive channel noise. Our objective is to achieve high tracking performance while reducing the communication burden on the communication network. To address this problem, we propose an integrated framework consisting of two modules: a probabilistic quantizer and a learning scheme. The employed probabilistic quantizer is developed by employing a Bernoulli distribution driven by the quantization errors. Three learning control schemes are studied, namely, a constant gain, a decreasing gain sequence satisfying certain conditions, and an optimal gain sequence that is recursively generated based on a performance index. We show that the control with a constant gain can only ensure the input error sequence to converge to a bounded sphere in a mean-square sense, where the radius of this sphere is proportional to the constant gain. On the contrary, we show that the control that employs any of the two proposed gain sequences drives the input error to zero in the mean-square sense. In addition, we show that the convergence rate associated with the constant gain is exponential, whereas the rate associated with the proposed gain sequences is not faster than a specific exponential trend. Illustrative simulations are provided to demonstrate the convergence rate properties and steady-state tracking performance associated with each gain, and their robustness against modeling uncertainties.

Design and Analysis of Data-Driven Learning Control: An Optimization-Based Approach

Learning to perform perfect tracking tasks based on measurement data is desirable in the controller design of systems operating repetitively. This motivates this article to seek an optimization-based design and analysis approach for data-driven learning control systems by focusing on iterative learning control (ILC) of repetitive systems with unknown nonlinear time-varying dynamics. It is shown that perfect output tracking can be realized with updating inputs, where no explicit model knowledge but only measured input-output data are leveraged. In particular, adaptive updating strategies are proposed to obtain parameter estimations of nonlinearities. A double-dynamics analysis approach is applied to establish ILC convergence, together with boundedness of input, output, and estimated parameters, which benefits from employing properties of nonnegative matrices. Simulations are implemented to verify the validity of our optimization-based adaptive ILC.

Model-Free Adaptive Iterative Learning Bipartite Containment Control for Multi-Agent Systems

This paper studies the bipartite containment tracking problem for a class of nonlinear multi-agent systems (MASs), where the interactions among agents can be both cooperative or antagonistic. Firstly, by the dynamic linearization method, we propose a novel model-free adaptive iterative learning control (MFAILC) to solve the bipartite containment problem of MASs. The designed controller only relies on the input and output data of the agent without requiring the model information of MASs. Secondly, we give the convergence condition that the containment error asymptotically converges to zero. The result shows that the output states of all followers will converge to the convex hull formed by the output states of leaders and the symmetric output states of leaders. Finally, the simulation verifies the effectiveness of the proposed method.

Data-Driven Adaptive Consensus Learning From Network Topologies

The problem of consensus learning from network topologies is studied for strongly connected nonlinear nonaffine multiagent systems (MASs). A linear spatial dynamic relationship (LSDR) is built at first to formulate the dynamic I/O relationship between an agent and all the other agents that are communicated through the networked topology. The LSDR consists of a linear parametric uncertain term and a residual nonlinear uncertain term. Utilizing the LSDR, a data-driven adaptive learning consensus protocol (DDALCP) is proposed to learn from both time dynamics of agent itself and spatial dynamics of the whole MAS. The parametric uncertainty and nonlinear uncertainty are estimated through an estimator and an observer respectively to improve robustness. The proposed DDALCP has a strong learning ability to improve the consensus performance because time dynamics and network topology information are both considered. The proposed consensus learning method is data-driven and has no dependence on the system model. The theoretical results are demonstrated by simulations.

Learning of Iterative Learning Control for Flexible Manufacturing of Batch Processes

Flexible manufacturing as an essential component of smart manufacturing implements the customized production mode, thereby requesting fast controller adaptation for producing different goods but still with high precision. This problem becomes even more acute for batch processes. Here we present a solution called learning of iterative learning control (ILC) based on neural networks. It is able to recommend control parameters for ILC controllers accordingly, so as to yield fast tracking error convergence and smaller steady-state error for disparate set-point profiles, which is deemed an abstraction of different production needs. The method substantially outperforms a benchmark ILC on a variety of systems and cases, thereby showing its potential for deployment in the industrial Internet of Things.

Quantitative Data-Driven Adaptive Iterative Learning Control: From Trajectory Tracking to Point-to-Point Tracking

This article reconsiders the data quantization problem in iterative learning control (ILC) for nonlinear nonaffine systems from four aspects: 1) use of available additional control knowledge; 2) different tracking tasks; 3) adaptation to uncertainties; and 4) data-driven design and analysis framework. An iterative linear data model (iLDM) is established first to represent the nonlinear nonaffine system for subsequent control algorithm design and analysis under a data-driven framework. A quantitative data-driven adaptive ILC (QDDAILC) is then developed using quantized tracking errors based on the nonlifted iLDM and, thus, additional available input information from previous time instants can be utilized to improve control performance. The parameter estimation derived from an adaptive updating law makes the learning gain of the QDDAILC adjustable, therefore improving the robustness to uncertainties. Due to the coupled dynamics among inputs and tracking errors, a new double-dynamics analysis method is introduced besides the contraction mapping principle to show error convergence. A quantized data-driven adaptive point-to-point ILC (QDDAPTPILC) is further presented using partial quantized measurements at the specified instants for multi-intermediate-point tracking. Simulation examples verify theoretical results and illustrate that the QDDAPTPILC outperforms the QDDAILC for multi-intermediate-point tracking tasks because it removes the unnecessary constraints.

Data-Driven Feedforward Learning With Force Ripple Compensation for Wafer Stages: A Variable-Gain Robust Approach

To meet the increasing demand for denser integrated circuits, feedforward control plays an important role in the achievement of high servo performance of wafer stages. The preexisting feedforward control methods, however, are subject to either inflexibility to reference variations or poor robustness. In this article, these deficiencies are removed by a novel variable-gain iterative feedforward tuning (VGIFFT) method. The proposed VGIFFT method attains: 1) no involvement of any parametric model through data-driven estimation; 2) high performance regardless of reference variations through feedforward parameterization; and 3) especially high robustness against stochastic disturbance as well as against model uncertainty through a variable learning gain. What is more, the tradeoff in which preexisting methods are subject to between fast convergence and high robustness is broken through by VGIFFT. Experimental results validate the proposed method and confirm its effectiveness and enhanced performance.

Spatial Linear Dynamic Relationship of Strongly Connected Multiagent Systems and Adaptive Learning Control for Different Formations

This article addresses an important problem of how to improve the learnability of an intelligent agent in a strongly connected multiagent network. A novel spatial-dimensional linear dynamic relationship (SLDR) is developed to formulate the spatial dynamic relationship of an agent with respect to all the related agents. The obtained SLDR virtually exists in the computer to describe the input-output (I/O) relationship in the spatial domain and an iterative adaptation mechanism is developed to update the SLDR using I/O information to show real-time dynamical behavior of multiagent systems with nonrepetitive initial states. Subsequently, an SLDR-based adaptive iterative learning control (SLDR-AILC) is presented with rigorous analysis for iteration-variant formation control targets. Not only the 3-D dynamic behavior of the multiagent network but also the control protocols of the communicated agents are incorporated in the learning mechanism and thus strong learnability of the proposed SLDR-AILC is achieved to improve control performance. The proposed SLDR-AILC is a data-driven scheme where no explicit model structure is needed. Simulations with strongly connected topologies verify the theoretical results.

Convergence Analysis of Robust Iterative Learning Control Against Nonrepetitive Uncertainties: System Equivalence Transformation

This article is concerned with the robust convergence analysis of iterative learning control (ILC) against nonrepetitive uncertainties, where the contradiction between convergence conditions for the output tracking error and the input signal (or error) is addressed. A system equivalence transformation (SET) is proposed for robust ILC such that given any desired reference trajectories, the output tracking problems for general nonsquare multi-input, multi-output (MIMO) systems can be equivalently transformed into those for the specific class of square MIMO systems with the same input and output numbers. As a benefit of SET, a unified condition is only needed to guarantee both the uniform boundedness of all system signals and the robust convergence of the output tracking error, which avoids causing the condition contradiction problem in implementing the double-dynamics analysis approach to ILC. Simulation examples are included to demonstrate the validity of our established robust ILC results.

Iterative Learning Model Predictive Control Based on Iterative Data-Driven Modeling

Iterative learning model predictive control (ILMPC) has been recognized as an effective approach to realize high-precision tracking for batch processes with repetitive nature because of its excellent learning ability and closed-loop stability property. However, as a model-based strategy, ILMPC suffers from the unavailability of accurate first principal model in many complex nonlinear batch systems. On account of the abundant process data, nonlinear dynamics of batch systems can be identified precisely along the trials by neural network (NN), making it enforceable to design a data-driven ILMPC. In this article, by using a control-affine feedforward neural network (CAFNN), the features in the process data of the former batch are extracted to form a nonlinear affine model for the controller design in the current batch. Based on the CAFNN model, the ILMPC is formulated in a tube framework to attenuate the influence of modeling errors and track the reference trajectory with sustained accuracy. Due to the control-affine structure, the gradients of the objective function can be analytically computed offline, so as to improve the online computational efficiency and optimization feasibility of the tube ILMPC. The robust stability and the convergence of the data-driven ILMPC system are analyzed theoretically. The simulation on a typical batch reactor verifies the effectiveness of the proposed control method.

Data-Driven Iterative Learning Control for Nonlinear Discrete-Time MIMO Systems

This article considers the tracking control of unknown nonlinear nonaffine repetitive discrete-time multi-input multi-output systems. Two data-driven iterative learning control (ILC) schemes are designed based on two equivalent dynamic linearization data models of an unknown ideal learning controller, which exists theoretically in the iteration domain. The two control schemes provide ways of selecting learning controllers based on the complexity of the controlled nonlinear systems. The learning control gain matrixes of the two learning controllers are optimized through the steepest descent method using only the measured input-output data of the nonlinear systems. The proposed ILC approaches are pure data-driven since no model information of the controlled systems is involved. The stability and convergence of the proposed ILC approaches are rigorously analyzed under reasonable conditions. Numerical simulation and an experiment based on a Gantry-type linear motor drive system are conducted to verify the effectiveness of the proposed data-driven ILC approaches.

Adjacent-Agent Dynamic Linearization-Based Iterative Learning Formation Control

The dynamical relationship of the multiple agents' behavior in a networked system is explored and utilized to enhance the control performance of the multiagent formation in this paper. An adjacent-agent dynamic linearization is first presented for nonlinear and nonaffine multiagent systems (MASs) and a virtual linear difference model is built between two adjacent agents communicating with each other. Considering causality, the agents are assigned as parent and child, respectively. Communication is from parent to child. Taking the advantage of the repetitive characteristics of a large class of MASs, an adjacent-agent dynamic linearization-based iterative learning formation control (ADL-ILFC) is proposed for the child agent using 3-D control knowledge from iterations, time instants, and the parent agent. The ADL-ILFC is a data-driven method and does not depend on a first-principle physical model but the virtual linear difference model. The validity of the proposed approach is demonstrated through rigorous analysis and extensive simulations.

An Active Repetitive Learning Control Method for Lateral Suspension Systems of High-Speed Trains

This article presents a novel perspective to improve the ride quality of high-speed trains (HSTs), namely, by virtue of the periodicity of lateral dynamics to suppress the lateral vibration of HST. To resolve the contradiction between the complex HST model and the effective controller design, a simplified three-degrees-of-freedom (3-DOF) quarter-vehicle model is first employed for controller design, while a 17-DOF full-vehicle model is built for efficiency verification, where periodic and random track irregularities are considered, respectively. An active repetitive learning control (RLC) method is proposed to achieve the periodic tracking control, where the learning convergence is proved rigorously in a Lyapunov way. The configuration of RLC-based lateral suspensions is economical in the sense that only four actuators and six sensors are needed. It is verified by simulation that, compared with the dynamic matrix controller, the proposed RLC controller has greatly reduced the lateral vibration of a vehicle body, especially the lateral acceleration in the frequency range of (0, 3] Hz to which human body is strongly sensitive.

Convergence Analysis of Saturated Iterative Learning Control Systems With Locally Lipschitz Nonlinearities

In this article, the robust trajectory tracking problem of iterative learning control (ILC) for uncertain nonlinear systems is considered, and the effects from locally Lipschitz nonlinearities, input saturations, and nonzero system relative degrees are treated. A saturated ILC algorithm is given, with the convergence analysis exploited using a composite energy function-based approach. It is shown that the tracking error can be guaranteed to converge both pointwisely and uniformly. Furthermore, the input updating signal can be ensured to eventually satisfy the input saturation requirements with increasing iterations. Two examples are given to demonstrate the validity of saturated ILC for systems with the relative degree of one, input saturation, and locally Lipschitz nonlinearity.

Performance Enhancement of Learning Tracking Systems Over Fading Channels With Multiplicative and Additive Randomness

This paper applies learning control to repetitive systems over fading channels at both output and input sides to improve tracking performance without applying restrictive fading conditions. Both multiplicative and additive randomness of the fading channel are addressed, and the effects of fading communication on the data are carefully analyzed. A decreasing gain sequence and a moving-average operator are introduced to modify the generic learning control algorithm to reduce the fading effect and improve control system performance. Results reveal that the tracking error converges to zero in the mean-square sense as the iteration number increases. Illustrative simulations are presented to verify the theoretical results.

3-D Learning-Enhanced Adaptive ILC for Iteration-Varying Formation Tasks

This paper explores the formation control problem of repetitive nonlinear homogeneous and asynchronous multiagent networks, where the early starting agent is designated as the parent, and the later starting agent with a small delayed time is designated as the child. Moreover, the desired formation reference is allowed to be different from iteration to iteration. A space-dimensional dynamic linearization method is presented to build the linear dynamic relationship between two parent-child agents in a networked system. Then, a 3-D learning-enhanced adaptive iterative learning control (3D-AILC) is proposed by utilizing the additional control information from previous time instants, iterative operations, and parent agents. In other words, the proposed method processes 3-D dynamics to strengthen its learnability, i.e., time dimension, iteration dimension, and space dimension. The desired formation signal is incorporated into the learning control law to compensate its iterative variation to achieve a fast and precise tracking performance. The proposed 3D-AILC is data based and does not use an explicit mechanistic model. The validity of the proposed approach is proven theoretically and tested through simulations as well. Moreover, the proposed method also works well with time-iteration-varying topologies and nonrepetitive uncertainties.

Convergence Conditions for Solving Robust Iterative Learning Control Problems Under Nonrepetitive Model Uncertainties

Learning from saved measurement and control data to refine the performance of output tracking is the core feature of iterative learning control (ILC). Even though this implementation process of ILC does not need any model knowledge, ILC typically requires the strict repetitiveness of the control systems, especially on the plant models of them. The questions of interest in this paper are: 1) whether and how can robust ILC problems be solved with respect to the nonrepetitive (or iteration-dependent) model uncertainties and 2) can convergence conditions be developed with the effective contraction mapping (CM)-based approach to ILC? The answers to these questions are affirmative, and the CM-based approach is applicable to robust ILC that accommodates certain nonrepetitive uncertainties, especially in the plant models. In particular, an H_∞ -norm condition is proposed to ensure the robust ILC convergence, which can be solved to determine learning gain matrices. Simulation tests are performed to illustrate the validity of our presented H_∞ -based analysis results.

Combination of Data-Driven Active Disturbance Rejection and Takagi-Sugeno Fuzzy Control with Experimental Validation on Tower Crane Systems

In this paper a second-order data-driven Active Disturbance Rejection Control (ADRC) is merged with a proportional-derivative Takagi-Sugeno Fuzzy (PDTSF) logic controller, resulting in two new control structures referred to as second-order data-driven Active Disturbance Rejection Control combined with Proportional-Derivative Takagi-Sugeno Fuzzy Control (ADRC–PDTSFC). The data-driven ADRC–PDTSFC structure was compared with a data-driven ADRC structure and the control system structures were validated by real-time experiments on a nonlinear Multi Input-Multi Output tower crane system (TCS) laboratory equipment, where the cart position and the arm angular position of TCS were controlled using two Single Input-Single Output control system structures running in parallel. The parameters of the data-driven algorithms were tuned in a model-based way using a metaheuristic algorithm in order to improve the efficiency of energy consumption.