A new method for analysis and design of iterative learning control algorithms in the time-domain

In this paper, a novel analysis method for iterative learning control (ILC) algorithms is presented. Even though expressed in the lifted system representation and hence in the time-domain, the convergence rate as a function of the frequency content of the error signal can be determined. Subsequently, based on the analysis method, a novel ILC algorithm (F-ILC) is proposed. The convergence rate at specific frequencies can be set directly in the design process, which allows simple tuning and a priori known convergence rates. Using the F-ILC design, it is shown how to predict the required number of iterations until convergence is achieved, depending on the reference trajectory and information on the system repeatability. Numerical examples are given and experimental results obtained on an internal combustion engine test bench are shown for validation.     

Adaptive ILC algorithms of nonlinear continuous systems with non-parametric uncertainties for non-repetitive trajectory tracking

In this article, two adaptive iterative learning control (ILC) algorithms are presented for nonlinear continuous systems with non-parametric uncertainties. Unlike general ILC techniques, the proposed adaptive ILC algorithms allow that both the initial error at each iteration and the reference trajectory are iteration-varying in the ILC process, and can achieve non-repetitive trajectory tracking beyond a small initial time interval. Compared to the neural network or fuzzy system-based adaptive ILC schemes and the classical ILC methods, in which the number of iterative variables is generally larger than or equal to the number of control inputs, the first adaptive ILC algorithm proposed in this paper uses just two iterative variables, while the second even uses a single iterative variable provided that some bound information on system dynamics is known. As a result, the memory space in real-time ILC implementations is greatly reduced.     

A non-standard iterative learning control approach to tracking periodic signals in discrete-time non-linear systems

In this paper we use the formalism of iterative learning control (ILC) to solve the repetitive control problem of forcing a system to track a prescribed periodic reference signal. Although the systems we consider operate continuously in time, rather than with trials that have distinct starting and ending times, we use the ILC approach by defining a 'trial' in terms of completion of a single 'period' of the output trajectory, where a period is an interval from the start of the trial until the system returns to its initial state. The ILC scheme we develop does not use the standard assumption of uniform trial length. In the final result the periodic motion is achieved by 'repetition' of the learned ILC input signal for a single period. Analysis of the convergence of the algorithm uses an intermediate convergence result for the typical ILC problem. This intermediate result is based on a multi-loop control interpretation of the signal flow in ILC. The idea is demonstrated on an example and it is noted that it may be possible to generalize the ideas to broader classes of systems and ILC algorithms.     

Iterative Learning Control for Nonlinear Systems with Data Dropouts at Both Measurement and Actuator Sides

This paper discusses the iterative learning control (ILC) for nonlinear systems under a general networked control structure, in which random data dropouts occur independently at both measurement and actuator sides. Both updating algorithms are proposed for the computed input signal at the learning controller and the real input signal at the plant, respectively. The system output is strictly proved to converge to the desired reference with probability one as the iteration number goes to infinity. A numerical simulation is provided to verify the effectiveness of the proposed mechanism and algorithms.     

Genetic algorithms based approach to database vertical partition

Vertical partition clusters attributes of a relation to generate fragments suitable for subsequent allocation over a distributed platform with the goal of improving performance. Vertical partition is an optimization problem that can resort to genetic algorithms (GA). However, the performance of the classical GA application to vertical partition as well as to similar problems such as clustering and grouping suffers from two major drawbacks—redundant encoding and non-group oriented genetic operations. This paper applies the restricted growth (RG) string Ruskey (1993) constraint to manipulate the chromosomes so that redundant chromosomes are excluded during the GA process. On RG string compliant chromosomes, the group oriented crossover and mutation become realizable. We thus propose a novel approach called Group oriented Restricted Growth String GA (GRGS-GA) which incorporates the two above features. Finally, we compare the proposed approach with a rudimental RG string based approach and a classical GA based approach. The conducted experiments demonstrate a significant improvement of GRGS-GA on partition speed and result, especially for large size vertical partition problems.     

Output tracking for nonlinear stochastic systems by iterative learning control

An iterative learning control (ILC) algorithm, which in essence is a stochastic approximation algorithm, is proposed for output tracking for nonlinear stochastic systems with unknown dynamics and unknown noise statistics. The nonlinear function of the system dynamics is allowed to grow up as fast as a polynomial of any degree, but the system is linear with respect to control. It is proved that the ILC generated by the algorithm a.s. converges to the optimal one at each time t/spl isin/[0,1,...,N] and the output tracking error is asymptotically minimized in the mean square sense as the number of iterates tends to infinity, although the convergence rate is rather slow. The only information used in the algorithm is the noisy observation of the system output and the reference signal y/sub d/(t). When the system state equation is free of noise and the system output is realizable, then the exact state tracking is asymptotically achieved and the tracking error is purely due to the observation noise.     

Optimal <Emphasis Type="Italic">N</Emphasis>-Parametric Type Iterative Learning Control

One of the most important problems in the field of the iterative learning control (ILC) is to design algorithms, in order to achieve a desired convergence rate. In this paper a new type of the ILC algorithm is introduced, which is called N-parametric type ILC with optimal gains. The convergence of the proposed algorithm is analyzed and an optimal design method is presented to determine its gains. The effect of the number of the parameters on the convergence rate of the presented ILC is investigated. It is shown that N parametric type of this ILC has a better performance than the N-1 one. Illustrative simulation examples are given to verify the theoretical analysis.     

ILC for non-minimum phase system

In this paper we propose a design method of an iterative learning controller (ILC) for a non-minimum phase (NMP) system by model-matching theory. The ILC consists of two learning filters acting on both the previous input signal and the previous error signal. To design the learning filters, we convert the convergence condition of the ILC into the model-matching problem and get the stable and proper learning filter by solving the Nevanlinna's algorithm. To show the usefulness of the proposed algorithm, some design examples are included.     

Initial state iterative learning for final state control in motion systems

In this work, an initial state iterative learning control (ILC) approach is proposed for final state control of motion systems. ILC is applied to learn the desired initial states in the presence of system uncertainties. Four cases are considered where the initial position or speed is a manipulated variable and the final displacement or speed is a controlled variable. Since the control task is specified spatially in states, a state transformation is introduced such that the final state control problems are formulated in the phase plane to facilitate spatial ILC design and analysis. An illustrative example is provided to verify the validity of the proposed ILC algorithms.     

Formation control for multi‐agent systems through an iterative learning design approach

This paper deals with formation control problems for multi‐agent systems by using iterative learning control (ILC) design approaches. Distributed formation ILC algorithms are presented to enable all agents in directed graphs to achieve the desired relative formations perfectly over a finite‐time interval. It is shown that not only asymptotic stability but also monotonic convergence of multi‐agent formation ILC can be accomplished, and the convergence conditions in terms of linear matrix inequalities can be simultaneously established. The derived results are also applicable to multi‐agent systems that are subject to stochastic disturbances and model uncertainties. Furthermore, the feasibility of convergence conditions and the effect of communication delays are discussed for the proposed multi‐agent formation ILC algorithms. Simulation results are given for uncertain multi‐agent systems to verify the theoretical study. Copyright © 2012 John Wiley & Sons, Ltd.     

Iterative learning control for constrained linear systems

This article considers iterative learning control (ILC) for linear systems with convex control input constraints. First, the constrained ILC problem is formulated in a novel successive projection framework. Then, based on this projection method, two algorithms are proposed to solve this constrained ILC problem. The results show that, when perfect tracking is possible, both algorithms can achieve perfect tracking. The two algorithms differ, however, in that one algorithm needs much less computation than the other. When perfect tracking is not possible, both algorithms can exhibit a form of practical convergence to a ‘best approximation’. The effect of weighting matrices on the performance of the algorithms is also discussed and finally, numerical simulations are given to demonstrate the effectiveness of the proposed methods.     

Learning control for discrete-time nonlinear systems with sensor saturation and measurement noises

The iterative learning control (ILC) is investigated for a class of nonlinear systems with measurement noises where the output is subject to sensor saturation. An ILC algorithm is introduced based on the measured output information rather than the actual output signal. A decreasing sequence is also incorporated into the learning algorithm to ensure a stable convergence under stochastic noises. It is strictly proved with the help of the stochastic approximation technique that the input sequence converges to the desired input almost surely along the iteration axis. Illustrative simulations are exploited to verify the effectiveness of the proposed algorithm.     

Linear computational complexity robust ILC for lifted systems

In this paper we propose a new methodology to synthesize and implement robust monotonically convergent ILC for lifted systems, with the computational complexity that is linear in the trial length. Starting from the model uncertainty of the local sample to sample LTI or LTV models, and using the randomized algorithm, we compute the bound on the model uncertainty of the ILC system representation in the trial domain (lifted ILC). Based on this computed uncertainty bound, we design weighting matrices of the Norm Optimal ILC, such that the robust monotonic convergence condition is satisfied. Since we compute the uncertainty bound, rather than assuming its value in the trial domain, we reduce the conservatism of the robust design. The linear computational complexity of the algorithms for computation of the uncertainty bound and implementation of the Norm Optimal ILC law, is achieved through exploiting the sequentially semi-separable structure of the lifted system matrices. Therefore the framework proposed in this paper is especially suitable for the LTI and LTV uncertain systems with a large number of samples in the trial. We have performed numerical experiments to demonstrate the robustness and linear computational complexity of the proposed method.     

Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system

To improve stability and convergence, feedback control is often incorporated with iterative learning control (ILC), resulting in feedback feed-forward ILC (FFILC). In this paper, a general form of FFILC is studied, comprising of two feedback controllers, a state feedback controller and a tracking error compensator, for the robustness and convergence along time direction, and an ILC for performance along the cycle direction. The integrated design of this FFILC scheme is transformed into a robust control problem of an uncertain 2D Roesser system. To describe the stability and convergence quantitatively along the time and the cycle direction, the concepts of robust stability and convergence along the two axes are introduced. A series of algorithms are established for the FFILC design. These algorithms allow the designer to balance and choose optimization objectives to meet the FFILC performance requirements. The applications to injection molding velocity control show the good effectiveness and feasibility of the proposed design methods.     

Adaptive fuzzy ILC of nonlinear discrete-time systems with unknown dead zones and control directions

This paper presents an adaptive fuzzy iterative learning control (ILC) design for non-parametrized nonlinear discrete-time systems with unknown input dead zones and control directions. In the proposed adaptive fuzzy ILC algorithm, a fuzzy logic system (FLS) is used to approximate the desired control signal, and an additional adaptive mechanism is designed to compensate for the unknown input dead zone. In dealing with the unknown control direction of the nonlinear discrete-time system, a discrete Nussbaum gain technique is exploited along the iteration axis and applied to the adaptive fuzzy ILC algorithm. As a result, it is proved that the proposed adaptive fuzzy ILC scheme can drive the ILC tracking errors beyond the initial time instants into a tunable residual set as iteration number goes to infinity, and keep all the system signals bounded in the adaptive ILC process. Finally, a simulation example is used to demonstrate the feasibility and effectiveness of the adaptive fuzzy ILC scheme.     

Interference level configuration in CDMA-based cellular networks

The accommodation of various traffic load situations in W-CDMA-based cellular systems requires the engineering of the allowed interference levels per cell. This paper presents functionality that can complement the design and management as well as the mechanisms required. The overall scheme is called Interference Level Configuration (ILC). It relies on the solution of problems, which will be concisely defined, optimally formulated and solved by computationally efficient algorithms. The proposed herewith algorithms are also able to co-operate with soft computing (SC) methods to the solution of problems in the power control domain. Numerical results will be presented.     

Identification based adaptive iterative learning controller

In recent years, more research in the control field has been in the area of self‐learning and adaptable systems, such as a robot that can teach itself to improve its performance. One of the more promising algorithms for self‐learning control systems is Iterative Learning Control (ILC), which is an algorithm capable of tracking a desired trajectory within a specified error limit. Conventional ILC algorithms have the problem of relatively slow convergence rate and adaptability. This paper suggests a novel approach by combining system identification techniques with the proposed ILC approach to overcome the aforementioned problems. The ensuing design procedure is explained and results are accrued from a number of simulation examples. A key point in the proposed scheme is the computation of gain matrices using the steepest descent approach. It has been found that the learning rule can be guaranteed to converge if certain conditions are satisfied. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

局部对称积分型迭代学习控制

提出了一个新的迭代学习控制（ＩＬＣ）更新律用于连续线性系统的有限时间区间跟踪控制,迭代学习控制作为一个前馈控制,迭代学习控制作为一个前馈控制器加在已有的反馈控制器之上,对于上倥 的反馈控制信号作局部对称积分,所提出的迭代学习控制更新律具备较简单的形式且仅含有两个设计参数,即：学习增益和局部积分的区间长度,给出了收敛性分析以及设计步骤。     

Iterative Learning Control Via Weighted Local-Symmetrical-Integration

A new iterative learning control (ILC) updating law is proposed for tracking control of continuous linear system over a finite time interval. The ILC is applied as a feedforward controller to the existing feedback controller. By using the weighted local symmetrical integral (WLSI) of feedback control signal of previous iteration, the ILC updating law takes a simple form with only two design parameters: the learning gain and the range of local integration. Convergence analysis is presented together with a design procedure. A set of experimental results are presented to illustrate the effectiveness of the proposed WLSI-ILC scheme.