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Motivated by the prototypical problem of a marching band, this paper studies a class of multi-agent formation problems characterized by two features: (i) the agents attempt to complete a finite duration, coordinated formation task with high precision by repeating the task and (ii) the feedback mechanism by which the agents control their motions is based on relative differences between nearest neighbors, but the underlying graph topology can vary both during a repetition and from one repetition to the next. Adopting the framework of iterative learning control leads to the notion of multi-agent networks with switching topologies along two directions: a finite time axis and an infinite iteration axis. For such systems, we present distributed algorithms using nearest neighbor information whose exponential convergence can be demonstrated. It is shown that as the number of repetition increases, the relative formation between agents approaches the desired formation exponentially fast if and only if at each time step, the union of the interaction graphs has a spanning tree frequently enough along the iteration axis. That is, the agents can “learn to cooperate.” The remarkable point of this result is that it is not necessary to have a spanning tree at any specific time step or iteration in order for the system to converge. Two examples are given to illustrate the ideas, including a general example, where through iteration the agents can form a desired formation, and a special case of it, where an additional agent specifies a reference to regulate the formation shape simultaneously. [ABSTRACT FROM AUTHOR]

The article focuses on the recent trends in iterative learning control (ILC) research and analyzes the literature published on ILC, between 1998 and 2004. It reports that the ILC is an intelligent control tool for enhancing transient responses of dynamic systems and provides a technical specification of ILC's methodology. It categorizes the literature into various subcategories based on their theory-focused results and application focused results. It reports on the development of ILC application after analyzing the application-related as well as theory-focused literature on ILC. Also mentioned are three surveys, conducted previously on ILC systems.

Abstract: This paper presents a stability analysis of the iterative learning control (ILC) problem for discrete-time systems when the plant Markov parameters are subject to interval uncertainty. Using the so-called super-vector approach to ILC, vertex impulse response matrices are employed to develop sufficient conditions for both asymptotic stability and monotonic convergence of the ILC process. It is shown that the stability of such interval ILC systems can be determined by checking the stability of the system using only the vertex points of the interval Markov parameters. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

Editorial. Discusses issues pertaining to the use of iterative learning control (ILC) in dealing with difficulties associated with performance design of control systems. Background on the ILC concept; Formulation of the ILC problem.

Learning control is an iterative approach to the problem of improving transient behavior for processes that are repetitive in nature. In this article, we present some results on iterative learning control. A complete review of the literature is given first. Then, a general formulation of the problem is given. Next, we present a complete analysis of the learning control problem for the case of linear, time-invariant plants and controllers. This analysis offers: (1) insight into the nature of the solution of the learning control problem by deriving sufficient convergence conditions: (2) an approach to learning control for linear systems based on parameter estimation; and (3) an analysis that shows that for finite-horizon problems it is possible to design a learning control algorithm that converges, with memory, in one step. Finally, a time-varying learning controller is given for controlling the trajectory of a nonlinear robot manipulator. A brief simulation example is presented to illustrate the effectiveness of this scheme. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present two iterative learning control (ILC) frameworks for tracking problems with specified data points that are desired points at certain time instants. To design ILC systems for such problems, unlike traditional ILC approaches, we first develop an algorithm in which not only the control signal but also the reference trajectory is updated at each trial. We investigate the relationship between the reference trajectory and ILC tracking control as it relates to the rate of convergence. Second, a new ILC scheme is proposed to produce output curves that pass close to the desired points. Here, the control signals are generated by solving an optimal ILC problem with respect to the desired sampling points. One of the key advantages of the proposed approaches is a significant reduction of the computational cost. [Copyright &y& Elsevier]