Iterative Learning Control Framework Research Articles

Data‐based nonlinear learning control for aircraft trajectory tracking via Gaussian process regression

AbstractIn this article, a new data‐based iterative learning control (ILC) algorithm is proposed via Gaussian process regression (GPR) to accomplish the trajectory tracking objective of aircraft subject to completely unknown dynamics and strong nonlinearities. The nonlinear system input–output relationship of the unknown aircraft is formulated through GPR by leveraging historical data, based on which an optimal ILC framework is established. The monotonic convergence analysis of the GPR‐based ILC is explored such that high‐precision tracking tasks can be accomplished without prior model knowledge. Simulation tests are further conducted on a commercial aircraft performing a continuous climb operation to illustrate the effectiveness of the GPR‐based ILC approach.

Observer-Based Event-Triggered Iterative Learning Consensus for Locally Lipschitz Nonlinear MASs

This paper aims to realize the robust tracking for nonidentical locally Lipschitz nonlinear multiagent systems (MASs) with unmeasurable states, for which an observer-based distributed event-triggered iterative learning control (ILC) framework is proposed. With this framework, distributed state observers provide the indispensable state information for agents to learn to complete the task. An initial state learning strategy is implemented to relax consistent initial conditions, which can improve the learning accuracy. An event-triggering mechanism is designed to reduce the occupation of communication and computing resources during the iterative learning process of MASs. With locally Lipschitz nonlinearities and iteration-varying uncertainties caused by nonrepetitive initial states, the double-dynamics analysis (DDA) method is adopted to illustrate the convergence of the ILC process. By setting appropriate learning gains and constructing a quasi-globally Lipschitz condition via the DDA method, the robust convergence can be achieved for MASs in the presence of switching topologies. A numerical simulation is used to show the validity of the proposed framework.

Dissipativity-based iterative learning control for singular systems

In this paper, the framework of dissipativity-based iterative learning control for singular systems (SSs) is established for the first time. Firstly, under the P-type learning algorithm, it has been demonstrated that the dissipative SSs can achieve the accurate tracking for the desired trajectory in a finite time interval. Secondly, a sufficient condition for the SSs to satisfy dissipativity is given by using the linear matrix inequality (LMI) method, and the solvability criterion of the LMI is further presented. Moreover, the relationship between dissipativity and positive realness is revealed. Finally, two examples are given to verify the effectiveness of the proposed method.

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.

Q-learning based fault estimation and fault tolerant iterative learning control for MIMO systems

This paper proposes a Q-learning based fault estimation (FE) and fault tolerant control (FTC) scheme under iterative learning control (ILC) framework. Due to the repetitive demands on control actuators for repetitive tasks, ILC is sensitive to actuator faults. Moreover, unknown faults varying with both time and trial axes pose a challenge to the control performance of ILC. This paper introduces Q-learning algorithm for FE to continuously adjust the estimator and adapt the changing faults. Then, FTC is designed by adopting the norm-optimal iterative learning control (NOILC) framework, where the controller is adjusted based on the FE results from Q-learning to counteract the influence of faults. Finally, the simulation on the plant of a mobile robot verifies the effectiveness of the proposed algorithm.

Data-Based Optimization Control for Learning Systems

This paper is devoted to establishing a novel data-based optimization control framework of achieving the perfect tracking performances for learning systems in the absence of any model information. A modified Willems’ fundamental lemma is developed without the assumptions on the controllability and the input’s persistency of excitation, under which a data-based iterative learning control (ILC) framework is further presented. It is shown that the proposed data-based ILC can be employed to realize the perfect tracking tasks without any explicit model knowledge. A simulation example is provided to demonstrate the effectiveness of the proposed data-based ILC strategy.

Time-optimal coordination of multiple entering and departing ferries in terminals based on decentralized learning model predictive control

In large cities with harbors or rivers, ferry services have been an important part of public transport. In practice, many ferry terminals are subject to geographical and environmental conditions, limited space resources of the terminal pool, and restricted navigable waters of ships, which leads to constrained operations and increases the difficulty of docking when multiple ferries enter and depart from the terminal. Because of the distributed, real-time and dynamic characteristics of multi-ferry maneuvering, this paper proposes a decentralized, time-optimal control strategy to coordinate the maneuvering of multiple entering and departing ferries in restricted terminals. It combines nonlinear model predictive control (MPC) with an iterative learning control (ILC) framework. Based on the states and maneuver data of previously successfully performed trajectories, the coupled constraints among multiple ferries are decomposed with support vector machine (SVM). Therefore, it also does not require real-time information exchange during ferry operations and has the merits of low communication demand, as only local information is required in each ferry controller. Simulations are carried out to evaluate the effectiveness of the proposed method.

Internal-Model-Principle-Based Fast Adaptive Iterative Learning Trajectory Tracking Control for Autonomous Farming Vehicle Under Alignment Condition and Input Constraint

A novel adaptive iterative learning control (NAILC) strategy is proposed to enhance static and dynamic control performances for the autonomous farming vehicle tracking repetitive trajectories of alternating parallel straight and large curvature. The method integrates an exponential decay function, an internal model principle (IMP), and an input constraint auxiliary variable design system in an adaptive iterative learning control framework. The introduction of exponential decay improves the convergence rate of the iterative process and ensures the control system’s dynamic performance. The IMP enhances the static performance of the trajectory tracking control system and guarantees the alignment condition setting. The auxiliary variable design system reduces the adverse effects of input constraints on the control system performance during the iterative process. Moreover, the adaptive iterative learning updating law estimates the total time-varying disturbance to improve the robustness of the tracking process against the actual disturbance. Simulation comparisons with existing results verify the effectiveness and advantages of the designed NAILC strategy under the MATLAB/Simulink environment.

An Optimal Iterative Learning Control Approach for Linear Systems With Nonuniform Trial Lengths Under Input Constraints

In practical applications of iterative learning control (ILC), the repetitive process may end up early by accident during the performance improvement along the trial axis, which yields the nonuniform trial length problem. For such practical systems, input signals are usually constrained because of some certain physical limitations. This article proposes an optimal ILC algorithm for linear time-invariant multiple-input–multiple-output (MIMO) systems with nonuniform trial lengths under input constraints. The optimal ILC framework is specifically modified for the nonuniform trial length problem, where the primal–dual interior point method is introduced to deal with the input constraints. Hence, the constraint handling capability are improved compared with the conventional counterparts for nonuniform trial lengths. Also, the monotonic convergence property of the proposed optimal ILC algorithm is obtained in the sense of mathematical expectation. Finally, the effectiveness of the proposed algorithm is verified on the numerical simulation of a mobile robot.

Frequency Response Function-Based Learning Control: Analysis and Design for Finite-Time Convergence

Iterative learning control (ILC) enables substantial performance improvement by using past operational data in combination with approximate plant models. The aim of this article is to develop an ILC framework based on nonparametric frequency response function (FRF) models that requires very limited modeling effort. These FRF models describe the behavior of a system in periodic steady state, yet are employed for the control of arbitrary finite-length tasks. A detailed analysis and design framework is developed to construct noncausal learning filters directly from uncertain FRF models, that achieve ILC convergence for arbitrary tasks. The resulting framework provides a unification between ILC and iterative inversion-based control, where the latter is a learning method specifically developed for periodic tasks.

Iterative learning control for lane-changing trajectories upstream off-ramp bottlenecks and safety evaluation

This paper proposes an iterative learning control framework for lane changing to improve traffic operation and safety at a diverging area nearby a highway off-ramp in an environment with connected and automated vehicles (CAVs). This framework controls CAVs in the off-ramp bottlenecks by imitating the trajectories optimized by machine learning algorithms. Next Generation Simulation (NGSIM) dataset is utilized as the raw data and filtered by cost function. The traffic models, including lane-changing decision (LCD) models and lane-changing execution (LCE) models, are completed by Random Forest (RF) and Back Propagation Neural Network (BPNN) algorithms. Based on simulation results, simulation data satisfying the predetermined criterion will be added to dataset in the next iteration. Various metrics are considered to evaluate the proposed framework systematically from both lateral and longitudinal aspects, including time exposed time-to collision (TET), time integrated time-to-collision (TIT), rear-end collision risk indexes (RCRI) and lane-changing risk index (LCRI). The results present that the iterative framework can decrease the longitudinal risk of the system by a factor of two times, and can reduce the lateral risk by 28.7%. When the CAVs market penetration rate (MPR) reaches 100%, the longitudinal and lateral risk values of the off-ramp system can be reduced by 90% and 35%, respectively. However, it is worth noting that only when the CAVs MPR reaches 50% does the system's value at risk change significantly.

Echo-state-network-based iterative learning control of distributed systems

The paper proposes an effective modeling and control procedure for the distributed-parameter systems using the echo-state network. The main idea is to reconstruct the spatiotemporal dynamics defined in a given multi-dimensional domain. In the investigated problem positions of both sensors and actuators are fixed allowing to delegate the complex system dynamics to echo-state network. Imposing a proper partitioning of the spatial domain, a specific topology of a neural network is used to form a reservoir capable to follow not only temporal but also spatial dynamics of the system. Based on available historical data, neural network model is initially trained and then used to derive the control law in the framework of iterative learning control. The echo-state network can be retrained after a particular control iterate in order to reduce model uncertainty and to fit it to the current operating conditions as much as possible. The performance of the proposed approach is tested and evaluated on the example of the squared clamped plate control.

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.

Nonlinear Iterative Learning Control: A Frequency-Domain Approach for Fast Convergence and High Accuracy

Iterative learning control (ILC) involves a trade-off between perfect, fast attenuation of iteration-invariant disturbances and amplification of iteration-varying ones. The aim of this paper is to develop a nonlinear ILC framework that achieves fast convergence, robustness, and low converged error values in ILC. To this end, the method includes a deadzone nonlinearity in the learning update, which uses the difference in amplitude characteristics of repeating and varying disturbances to modify the learning gain for each error sample. A criterion for monotonic convergence of the nonlinear ILC algorithm is provided, which is used in combination with system measurements to select suitable design parameters. The proposed algorithm is validated using simulations, in which fast convergence to low error values is demonstrated.

Flexible-Time Receding Horizon Iterative Learning Control With Application to Marine Hydrokinetic Energy Systems

This brief presents an iterative learning control (ILC) framework for a class of repetitive control (RC) applications characterized by: 1) continuous operation; 2) flexible iteration time; and 3) an economic performance metric. Specifically, the effect of iteration-varying initial conditions, resulting from the continuous nature of the operation, is accounted for through an iteration domain receding horizon formulation. To address the need for flexible iteration times, the time-domain dynamics are transformed into path-domain dynamics characterized by a non-dimensional parameter spanning an iteration-invariant range. The resulting model is used to derive learning filters that minimize a multi-objective economic cost. The proposed methodology is applied to the control a kite-based marine hydrokinetic (MHK) system, which executes high-speed, repetitive flight paths with the objective of maximizing its lap-averaged power output. The proposed approach is validated via simulations of a medium-fidelity nonlinear model of a kite-based MHK system, and the results demonstrate robust and fast convergence of the kite to power-optimal flight patterns.

Iterative Learning Control for Output Tracking of Nonlinear Systems With Unavailable State Information.

This work presents a novel design framework of adaptive iterative learning control (ILC) approach for a class of uncertain nonlinear systems. By using the closed-loop reference model that can be viewed as an observer, the proposed adaptive ILC approach can be adapted to deal with the output tracking problem of nonlinear systems with unavailable system states. In the systems considered, two classes of uncertainties are taken into account, including parametric input disturbances and input distribution uncertainties. To facilitate the controller design and convergence analysis, the composite energy function (CEF) methodology is employed. The design framework in this brief is novel and widely applicable, which extends the CEF-based ILC approach to output tracking control of nonlinear systems without requiring full knowledge of state information and complicated observer design process. To show the effectiveness of the proposed design framework and control algorithms, two numerical examples are illustrated.

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.

Distributed Coordination for a Class of High-Order Multiagent Systems Subject to Actuator Saturations by Iterative Learning Control

This paper investigates a distributed coordination control for a class of high-order uncertain multiagent systems. Under the framework of iterative learning control, a novel fully distributed learning protocol is devised for the coordination problem of MASs including time-varying parameter uncertainties as well as actuator saturations. Meanwhile, the learning updating laws of various parameters are proposed. Utilizing Lyapunov theory and combining with Graph theory, the proposed algorithm can make each follower track a leader completely over a limited time interval even though each follower is without knowing the dynamics of the leader. Moreover, the extension to formation control is made. The validity and feasibility of the algorithm are verified conclusively by two examples.

Iterative learning control for intermittently sampled data: Monotonic convergence, design, and applications

The standard assumption that a measurement signal is available at each sample in iterative learning control (ILC) is not always justified, e.g., when exploiting time-stamped data from incremental encoders or in systems with data dropouts. The aim of this paper is to develop a computationally tractable ILC framework that is capable of exploiting intermittent data while maintaining favourable properties, including monotonic convergence. A controllability and observability analysis of the intermittent ILC framework leads to appropriate monotonic convergence conditions which allow for missing data. These conditions lead to a new explicit ILC controller design independent of the sampling instances, which is reminiscent of gradient-descent ILC. The approach is demonstrated on both an intuitive example and a practically relevant example which exploits time-varying timestamped data from an incremental encoder.

An sEMG based adaptive method for human-exoskeleton collaboration in variable walking environments

In this paper, a novel long short memory network – adaptive robust iterative learning control (LSTM-ARILC) framework is proposed to achieve accurate continuous motion estimation and adaptive following control for the exoskeleton robot, which is applied to offer assistance to human walking in variable environments. The LSTM network is established to estimate the human lower limb motion through the processed surface Electromyography (sEMG) signals, and the human-exoskeleton coupling fuzzy dynamic model is further developed. Then the closed-loop ARILC controller is designed to compensate the estimated errors and realize the adaptive and robust following control, and its asymptotic stability is rigorously proved via Lyapunov theory. The performance of the proposed method is evaluated with numerical experiments and compared with adaptive PID controller and adaptive fuzzy sliding mode controller (SMC). The maximum following errors of ARILC after 6 iterations can be reduced by more than 99% compared to the initial iteration, and the controller is quite less sensitive to the environment changes than the other two controllers, which proves that the proposed control framework is much more robust and effective in variable walking environments.