Iteration Domain Research Articles

Iterative Learning Identification/Iterative Learning Control for Linear Time-Varying Systems

This paper integrates a previously developed iterative learning identification (ILI) (Liu, N., and Alleyne, A. G., 2016, “Iterative Learning Identification for Linear Time-Varying Systems,” IEEE Trans. Control Syst. Technol., 24(1), pp. 310–317) and iterative learning control (ILC) algorithms (Bristow, D. A., Tharayil, M., and Alleyne, A. G., 2006, “A Survey of Iterative Learning Control,” IEEE Control Syst. Mag., 26(3), pp. 96–114), into a single norm-optimal framework. Similar to the classical separation principle in linear systems, this work provides conditions under which the identification and control can be combined and guaranteed to converge. The algorithm is applicable to a class of linear time-varying (LTV) systems with parameters that vary rapidly and analysis provides a sufficient condition for algorithm convergence. The benefit of the integrated ILI/ILC algorithm is a faster tracking error convergence in the iteration domain when compared with an ILC using fixed parameter estimates. A simple example is introduced to illustrate the primary benefits. Simulations and experiments are consistent and demonstrate the convergence speed benefit.

Adaptive iterative learning control for high-order nonlinear multi-agent systems consensus tracking

In this work, we present a new distributed adaptive iterative learning control (AILC) scheme for a class of high-order nonlinear multi-agent systems (MAS) under alignment condition with both parametric and nonparametric system uncertainties, where the actuators may be faulty and the control input gain functions are not fully known. Backstepping design with the composite energy function (CEF) structure is used in the discussion. Through rigorous analysis, we show that under this new AILC scheme, uniform convergence of agents output tracking error over the iteration domain is guaranteed. In the end, an illustrative example is presented to demonstrate the efficacy of the proposed AILC scheme.

Robust adaptive iterative learning control for discrete‐time nonlinear systems with both parametric and nonparametric uncertainties

SummaryA new robust adaptive iterative learning control approach is proposed for discrete‐time nonlinear systems with both parametric and nonparametric uncertainties. By virtue of a well‐designed dead‐zone function, the learning of the parametric and nonparametric uncertainties can be performed concurrently. Rigorous Lyapunov function‐based analysis ensures that the effect of system uncertainties can be fully compensated, and the tracking error will converge to zero asymptotically in the iteration domain, even under random initial conditions and iteration‐varying reference trajectories. The efficacy of the proposed controller is demonstrated by simulating a single‐link robot manipulator with unknown frictions. Copyright © 2015 John Wiley & Sons, Ltd.

High‐order data‐driven optimal TILC approach for fed‐batch processes

A high‐order data‐driven optimal terminal iterative learning control (H‐DDOTILC) is proposed for fed‐batch processes, which are considered a general class of nonlinear and non‐affine systems. A new dynamical linearization is introduced to the iteration domain to reveal the relationship of system terminal output and control input among batches. The proposed H‐DDOTILC consists of a high‐order learning control law, an iterative parameter estimator, and a rest algorithm, together. The learning control law with a high‐order form is capable of utilizing more control knowledge of the previous l batches to improve control performance. The parameter updating law is used to estimate the unknown derivatives of the nonlinear system to control input, which is the main part of the nonlinear learning gain function of the control law. Essentially, the proposed approach is a data‐driven control strategy, and the controller design and analysis only depend on the I/O data of the plant, which is a distinct feature for the control problems of practical nonlinear and non‐affine systems. Both the rigorous analysis and the simulation results illustrate the applicability and effectiveness of the proposed approach.

A high-order internal model based iterative learning control scheme for discrete linear time-varying systems

In this paper, an iterative learning control algorithm is proposed for discrete linear time-varying systems to track iteration-varying desired trajectories. A high-order internal model (HOIM) is utilized to describe the variation of desired trajectories in the iteration domain. In the sequel, the HOIM is incorporated into the design of learning gains. The learning convergence in the iteration axis can be guaranteed with rigorous proof. The simulation results with permanent magnet linear motors (PMLM) demonstrate that the proposed HOIM based approach yields good performance and achieves perfect tracking.

Adaptive iterative learning control for nonlinearly parameterised systems with unknown time-varying delays and input saturations

In this work, an adaptive iterative learning control (AILC) scheme is proposed to address a class of nonlinearly parameterised systems with both unknown time-varying delays and input saturations. By incorporating a saturation function, a novel iterative learning control mechanism is constructed with a feedback term in the time domain and a fully saturated adaptive learning term in the iteration domain, which is used to estimate the unknown time-varying system uncertainty. A new time-weighted Lyapunov–Krasovskii-like composite energy function (LKL-CEF) is designed for the convergence analysis where time-weighted inputs, states and estimates of system uncertainty are all considered. Despite the existence of time-varying parametric uncertainties, time-varying delays, input saturations and local Lipschitz nonlinearities, the learning convergence is guaranteed with rigorous mathematical analysis. Simulation results verify the correctness and effectiveness of the proposed method further.

Data‐driven terminal iterative learning control with high‐order learning law for a class of non‐linear discrete‐time multiple‐input–multiple output systems

In this study, a novel data-driven terminal iterative learning control with high-order learning law is proposed for a class of non-linear non-affine discrete-time multiple-input-multiple output systems, where only the system state or output at the endpoint is measurable and the control input is time-varying. A new data-driven dynamical linearisation is proposed in the iteration domain and the linearisation data model can be updated by a designed parameter updating law iteratively. The high-order learning control law makes it possible to utilise more control knowledge of previous runs to improve control performance. The design and analysis of the proposed approach only depends on the I/O data of the control plant without requiring any explicit model information. Both theoretical analysis and extensive simulations are provided to confirm the effectiveness and applicability of this novel approach.

A unified data-driven design framework of optimality-based generalized iterative learning control

This paper proposes a unified design framework for data-driven optimality-based generalized iterative learning control (DDOGILC), including data-driven optimal ILC (DDOILC), data-driven optimal point-to-point ILC (DDOPTPILC), and data-driven optimal terminal ILC (DDTILC). First, a dynamical linearization in the iteration domain is developed. Then three specific DDOGILC approaches are proposed. Both design and analysis of the controller only require the measured I/O data without relying on any explicit model information. The optimal learning gain can be updated iteratively, which makes the proposed DDOGILC more adaptable to the changes in the plant. Furthermore, the proposed DDOPTPILC and DDOTILC only depend on the tracking error at specific points, and thus they can deal with the scenario when the system outputs are measured only at some time instants. Moreover, the proposed DDOPTPILC and DDOTILC approaches do not need to track the unnecessary output reference points so that the convergence performance is improved.

Convergence Analysis of Wireless Remote Iterative Learning Control Systems with Channel Noise

AbstractChannel noise, including sensor‐to‐controller(SC) noise and controller‐to‐actuator(CA) noise, impacts the convergence of wireless remote iterative learning control (ILC) system significantly. In this paper, the relationship between output error, SC noise and CA noise is obtained firstly by super‐vector formulation, and then the norm of output error vector covariance matrix is employed to analyze the convergence of the system in presence of SC noise and CA noise. Upper bound of the norm at any sample time reveals that the SC noise is accumulated only in iteration domain, while the CA noise is accumulated not only in iteration domain but also in time domain. Furthermore, the accumulated effect of the CA noise in time domain is ruled by system matrices, so the values of which determine the effect of the CA noise is greater or less than that of the SC noise on convergence of the system. Finally, some simulation results are given to illustrate correctness of the result.

Adaptive Iterative Learning Control for Complex Dynamical Networks

A new adaptive iterative learning control scheme is proposed for complex dynamical networks with repetitive operation over a fixed time interval. By designing difference type updating laws for unknown time-varying parameters and coupling strength, the state of each node in complex dynamical networks can track the reference signal. By constructing a composite energy function, a sufficient condition of the convergence of tracking error sequence is achieved in the iteration domain. Finally, a numerical example is given to show the effectiveness of the designed method.

Iterative learning control of inhomogeneous distributed parameter systems—frequency domain design and analysis

This paper aims to construct a design and analysis framework for iterative learning control of linear inhomogeneous distributed parameter systems (LIDPSs), which may be hyperbolic, parabolic, or elliptic, and include many important physical processes such as diffusion, vibration, heat conduction and wave propagation as special cases. Owing to the system model characteristics, LIDPSs are first reformulated into a matrix form in the Laplace transform domain. Then, through the determination of a fundamental matrix, the transfer function of LIDPS is precisely evaluated in a closed form. The derived transfer function provides the direct input–output relationship of the LIDPS, and thus facilitates the consequent ILC design and convergence analysis in the frequency domain. The proposed control design scheme is able to deal with parametric and non-parametric uncertainties and make full use of the process repetition, while avoid any simplification or discretization for the 3D dynamics of LIDPS in the time, space, and iteration domains. In the end, two illustrative processes are addressed to demonstrate the efficacy of the proposed iterative learning control scheme.

Improved data-driven optimal TILC using time-varying input signals

A new improved data-driven optimal TILC (DDOTILC) is proposed for a class of nonlinear discrete-time systems by using time-varying control input signals to enhance control performance. An equivalent dynamical linear presentation is developed in the iteration domain for the repeatable nonlinear system, where the time-varying partial derivatives of the system with respect to the time-varying control inputs reflect the dynamical characters of the plant. Both the time-varying input signals and time-varying partial derivatives over the entire finite time interval are updated in batches, respectively. The proposed approach is a data-driven control scheme and only the boundedness of the partial derivatives is needed for control system design and analysis. Both rigorous mathematical analysis and the simulation results are provide to verify the applicability and effectiveness of the proposed approach further.

An Iterative Learning Control Approach for Linear Systems With Randomly Varying Trial Lengths

This technical note addresses an iterative learning control (ILC) design problem for discrete-time linear systems where the trial lengths could be randomly varying in the iteration domain. An ILC scheme with an iteration-average operator is introduced for tracking tasks with non-uniform trial lengths, which thus mitigates the requirement on classic ILC that all trial lengths must be identical. In addition, the identical initialization condition can be absolutely removed. The learning convergence condition of ILC in mathematical expectation is derived through rigorous analysis. As a result, the proposed ILC scheme is applicable to more practical systems. In the end, two illustrative examples are presented to demonstrate the performance and the effectiveness of the averaging ILC scheme for both time-invariant and time-varying linear systems.

Adaptive iterative learning control for a class of non-linearly parameterised systems with input saturations

In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov–Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L2[0, T] convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.

Iterative learning control for spatially interconnected systems

Iterative learning control (ILC) has been successfully employed for trajectory tracking of uncertain dynamic systems with less system information. This paper attempts to adopt the benefits of ILC to improve the trajectory tracking performance of spatially interconnected systems. By utilizing the ILC update law along the iteration domain repetitively, a perfect reference trajectory tracking can be ensured. It is the key benefit of using ILC that less system model information is used in the design of a trajectory tracking controller for spatially interconnected systems. Through a numerical simulation, the validity of the proposed control scheme is illustrated.

Iterative Learning Control for a Class of Modeling Undesirable Single Degree of Freedom System

A class of modeling undesirable single degree of freedom system is studied by using iterative learning control. The proposed iterative learning algorithm constantly updates the control input according to output error until the desired output occurred. So the system with designed controller can achieve perfect accuracy. We have proved convergence properties in iteration domain and simulation results demonstrate the effectiveness of the presented method.

Iterative Learning Control for a Class of Linear Discrete-time Switched Systems

In this paper,the iterative learning control(ILC) is considered for a class of linear discrete-time switched systems with arbitrary switching signals.It is assumed that the switched system is operated during a finite time interval repetitively,and then the first order P-type ILC scheme can be used to achieve perfect tracking over the whole time interval.By the super vector approach,a convergence condition for such ILC systems in the iteration domain can be given.The theoretical analysis is supported by simulations.

Pareto iterative learning control: Optimized control for multiple performance objectives

Iterative learning control (ILC) is a 2-degree-of-freedom technique that seeks to improve system performance along the time and iteration domains. Traditionally, ILC has been implemented to minimize trajectory-tracking errors across an entire cycle period. However, there are applications in which the necessity for improved tracking performance can be limited to a few specific locations. For such systems, a modified learning controller focused on improved tracking at the selected points can be leveraged to address multiple performance metrics, resulting in systems that exhibit significantly improved behaviors across a wide variety of performance metrics. This paper presents a pareto learning control framework that incorporates multiple objectives into a single design architecture.

High-Performance Tracking of Piezoelectric Positioning Stage Using Current-Cycle Iterative Learning Control With Gain Scheduling

In this paper, two types of sampled-data current-cycle iterative learning control (ILC) (CILC) schemes are exploited to perform high-performance tracking control for piezoelectric positioning stage systems. The proposed CILC schemes consist of a direct feedback control (FC) loop and an add-on ILC loop and thus can simultaneously deal with repeatable and nonrepeatable components in tracking error. Based on the modeling result of the control system, gain-scheduling technique is further incorporated in the learning filter design of the ILC loop to speed up the learning convergence. In consequence, low tracking error in the time domain and fast convergence speed in the iteration domain are achieved concurrently. In the end, to illustrate the respective characteristics of CILC schemes and verify their superiorities to pure FC or pure ILC, a set of experiments including low-frequency (2 Hz) tracking and high-frequency (100 Hz) tracking is conducted with detailed comparisons among proportional/proportional-plus-integral control, pure ILC with robust design, pure ILC with gain scheduling, and CILC with gain scheduling.

Composite iterative learning controller design for gradually varying references with applications in an AFM system

Learning control for gradually varying references in iteration domain was considered in this research, and a composite iterative learning control strategy was proposed to enable a plant to track unknown iteration-dependent trajectories. Specifically, by decoupling the current reference into the desired trajectory of the last trial and a disturbance signal with small magnitude, the learning and feedback parts were designed respectively to ensure fine tracking performance. After some theoretical analysis, the judging condition on whether the composite iterative learning control approach achieves better control results than pure feedback control was obtained for varying references. The convergence property of the closed-loop system was rigorously studied and the saturation problem was also addressed in the controller. The designed composite iterative learning control strategy is successfully employed in an atomic force microscope system, with both simulation and experimental results clearly demonstrating its superior performance.