On robust iterative learning control against iteration-varying uncertain plant parameters

This paper deals with the problem of iterative learning control for large-scale interconnected linear systems in the presence of fixed initial shifts. According to the characteristics of the systems, iterative learning control laws are proposed for such large-scale interconnected linear systems based on the PD-type learning schemes. The proposed controller of each subsystem only relies on local output variables without any information exchanges with other subsystems. Using the contraction mapping method, we show that the schemes can guarantee the output of the system converges uniformly to the corresponding output limiting trajectory over the whole time interval along the iteration axis. Simulation examples illustrate the effectiveness of the proposed method.

The problem of iterative learning control (ILC) is considered for a class of time-varying systems with random packet dropouts. It is assumed that an ILC scheme is implemented via a remote control system and that packet dropout occurs during the packet transmission between the ILC controller and the actuator of remote plant. The packet dropout is viewed as a binary switching sequence which is subject to the Bernoulli distribution. In order to eliminate the effect of packet dropouts on the convergence property of output error, the hold-input scheme is adopted to compensate the packet dropout at the actuator. It is shown that the hold-input scheme with average ILC can achieve asymptotical convergence along the iteration axis for discrete time-varying linear system. Numerical examples are provided to show the effectiveness of the proposed method.

This note considers the problem of iterative learning control (ILC) for a class of linear continuous-time multiple-input multiple-output (MIMO) systems with vector relative degree, where the trail length of control input is different from that of system state and output for a specific iteration. An iteration-average operator is included in the proposed ILC law to address the varying trail lengths. The proposed ILC algorithm allows that the control input length is iteration-varying during the ILC process, and can achieve desired trajectory tracking at control time interval. A numerical example is carried out to illustrate the effectiveness of the proposed ILC scheme.

In this paper we present a mathematical formulation of the problem of robust iterative learning control (ILC) design when the system is subject to data dropout. It is assumed that an ILC scheme is implemented via a networked control system (NCS) and that during the data transfer from the remote plant to the ILC controller data dropout occurs, resulting in what we call intermittent measurement. Using the Kalman filtering approach, we show that it is possible to design a learning gain such that the system eventually converges to a desired trajectory as long as there is not complete data dropout.

Based on Nesterov accelerated gradient method, the problem of iterative learning control for a class of linear discrete-time systems is considered in this paper. Firstly, the iterative learning control problem of linear discrete-time systems is transformed into an iterative least-squares problem. Then, the Nesterov accelerated gradient method is introduced into the iterative learning control framework. Note that the Nesterov accelerated gradient learning algorithm has the capability of fast convergence. It is shown that the algorithm presented in this paper can guarantee the output tracking error converges to zero with rate O(1/k) , where k is the iteration counter. Moreover, the monotonic convergence of the Nesterov accelerated gradient learning algorithm is analyzed and discussed. Finally, the effectiveness of the proposed method is verified by two simulation examples.

ABSTRACTThis paper addresses the problem of iterative learning control (ILC) for a class of nonlinear continuous‐time systems with higher relative degree. The proposed ILC solution is a family of updating laws using differentiations of tracking error with the order less than the system relative degree. A unified convergence condition for this family of ILC updating laws is provided and proved to be independent of the highest order of differentiation. The application to path tracking of a robotic manipulator is presented to illustrate the effectiveness of the proposed method.

The problem of iterative learning control is considered for linear discrete-time systems with multiple time delays. In this paper, it is assumed that the initial condition for discrete time-delay systems is unknown at each iteration. For such a class of discrete time-delay systems, a method is presented whereby a class of P-type discrete iterative learning control schemes can be constructed. It is shown that under some given conditions, the constructed iterative learning controllers can guarantee the asymptotic convergence of the output error between the given desired output and the actual output through the iterative learning process. Finally, a numerical example is given to demonstrate the validity of the results.

Although originally motivated by applications such as image processing, multidimensional (nD) systems have mainly attracted the attention of the research community due to the richness of new theoretical questions raised by their treatment, and are often replaced by other settings when it comes to modelling, identifying and controlling processes in practical situations. The aim of this special issue is to illustrate the application potential of nD systems by presenting several contributions where the nD framework is successfully used either to deal with practical problems or to solve practically relevant questions that arise in other contexts that are not at first sight related to multidimensional systems. In the paper Multidimensional Control Systems: Case Studies in Design and Evaluation, by Rogers et al., after introducing the most commonly used models for the analysis and control of discrete nD linear systems, a series of case studies is presented with the aim of demonstrating the advantages of the nD systems approach in solving certain control problems. Namely, applications in the fields of sensor grid networks, iterative learning control, civil engineering and agriculture are considered. The paper Two-dimensional Generalized Predictive Control (2D-GPC) Scheme for the Batch Processes with Two-dimensional (2D)Dynamics, Shi et al. studies the problem of iterative learning control (ILC) design for batch processes. Based on 2Dcontrolled auto-regressive moving average (2D-CARMA) model, a novel two-dimensional generalized predictive control (2D-GPC) is proposed. The feasibility and effectiveness of the proposed method is validated by the experimental results on packing pressure control of the injection molding process.

This paper addresses the problem of iterative learning control with well‐defined relative degree. The solution is a family of sampled‐data learning algorithms using lower‐order differentiations of the tracking error with the order less than the relative degree. A unified convergence condition for the family of learning algorithms is derived and is proved to be independent of the highest order of the differentiations. In the presence of initial condition errors, the system output is ensured to converge to the desired trajectory with a specified error bound at each sampling instant. The bound will reduce to zero whenever the bound on initial condition errors tends to zero. Numerical examples are provided to illustrate the tracking performance of the proposed learning algorithms. Copyright © 2004 John Wiley & Sons, Ltd.

An iterative learning control (ILC) framework based on two-degree-of-freedom control is presented for a linear plant with perturbations. A sufficient condition in the frequency domain is obtained for robust convergence with the bounded asymptotic error in the existence of input disturbance, output disturbance and errors in initial states. Based on the sufficient condition, the problem of designing ILC can be converted to a robust performance problem and a robust ILC against disturbances and initialization errors is derived by structured singular value and mu synthesis

In this paper, a robust adaptive iterative learning control (ILC) scheme is developed for the high-precision attitude tracking control of spacecraft in the presence of parametric uncertainties and external disturbances. The proposed robust adaptive ILC law consists of three parts, i.e., the classic proportional-derivative (PD) feedback control term, the PD-type feedforward learning term, and the robust term. The adaptive updating laws are designed for the gain matrices of both the classic PD feedback control term and the PD-type feedforward learning term. The asymptotic stability of the whole closed-loop system is proved through the Lyapunov function–based convergence analysis. The proposed robust adaptive ILC scheme can not only compensate for the parametric uncertainties and repetitive disturbance, but also handle the nonrepetitive disturbance owing to the robust control concept. Moreover, the proposed robust adaptive ILC scheme can achieve the fast convergence speed benefiting from the adaptive technique. Numerical simulations illustrate the effectiveness and superiority of the proposed ILC scheme.

This paper addresses robust performance analysis and synthesis of lifted system iterative learning control (ILC). By applying the full block S-procedure, sufficient conditions for the robust performance of ILC with both unstructured and structured uncertainty are derived. In the synthesis problem, we consider the design of the learning filter Q for modelinversion based ILC. The problem is reformulated as a convex optimization problem such that the converged tracking error is minimized subject to the monotonic convergence condition. This synthesis approach enables full automation of the ILC design since neither an uncertainty model has to be identified nor a robustness filter has to be chosen. The advantages of this novel robust performance ILC technique are demonstrated on an experimental linear motor test setup.

Here the authors concerned with robust iterative learning control (ILC) for uncertain time-delay systems. They demonstrate that the design of a robust ILC is straightforward based on a performance index for the error system. The ILC algorithms under consideration are rather simple. They show that after the two-dimensional analysis of ILC, a Lyapunov-like approach can be used to directly obtain a stable algorithm that achieves monotonic convergence of the control input error. Sufficient stability conditions are provided in terms of linear matrix inequalities, which can determine learning gains as well. They also show that the Lyapunov-like approach can be applied to design robust ILC for uncertain systems with time-varying delay or multiple time delays. Numerical simulation results are presented to illustrate the effectiveness of the proposed ILC approach.

This paper proposes an adaptive learning control scheme to solve high-precision velocity tracking problem for tank gun control servo systems. Lyapunov approach is used to design the learning controller, with alignment condition used to cope with initial problem of iterative learning control. Robust control technique and adaptive learning control technique are synthesized to handle nonlinear uncertainties and external disturbances. The unknown parameters are estimated according to the full saturation difference learning strategy. As the iteration number increases, the system state can accurately track the reference signal over the whole time interval, and all signal are guaranteed to be bounded.

In this paper, we consider an iterative learning control (ILC) problem for a class of multiinput-multioutput (MIMO) second-order hyperbolic distributed parameter systems with uncertainties. A P-type ILC scheme is proposed in the iteration procedure for distributed systems with an initial deviation in the state. A convergence of tracking error with respect to the iteration index can be guaranteed in the sense of $\mathbf{L}^{2}$ norm. Feasibility in theory of the iterative learning algorithm with difference method is proposed. Numerical simulation results are presented to illustrate the effectiveness of the proposed ILC approach.