Iterative learning control and repetitive control

This special issue contains selected contributions originating from the ‘Symposium on Learning Control’ which took place immediately prior to the 2009 IEEE Conference on Decision and Control in Shanghai. This two day event was held at Shanghai Jiaotong University to commemorate 25 years of highly creative and productive research since the concept of Iterative Learning Control (ILC) was formally proposed by Professor Arimoto in the seminar paper (Arimoto, Kawamura, and Miyazaki 1984). The symposium was organised by up-and-coming members of the ILC research community, aided by an advisory committee of leading figures in the field. As well as being guest of honour at the event, Professor Arimoto delivered one of the plenary lectures. In Arimoto, Kawamura and Miyazaki (1984) a controller was presented that was applicable to systems which were required to track a desired reference trajectory that was of a fixed length T, and specified a priori. After each trial of the task, resetting of the system states occurred, during which time the measured output was used to construct the next control output. The system dynamics were assumed trial-invariant and invertible. In postulating the six tenets of ILC that are highlighted in bold, Professor Arimoto succeeded in creating a fertile framework which went on to rapidly attract research interest from multiple quarters around the world. ‘Bettering Operation of Robots by Learning’ has since been cited over 1258 times by researchers in over 45 counties. Prior to the formalisation of ILC, similar ideas of learning can be traced back to a patent filed in 1967 which proposed correcting command signals using characteristics of actuators which were learnt over time (United States Patent 3,555,252 1971). Closely related papers appeared on the control of multipass processes in Edwards (1974) and in a Japanese language paper which used a similar algorithm to control a mechanical arm in Uchiyama (1978). As well as providing a framework to support the rich stream of research which followed, Professor Arimoto has made substantial contributions to learning control applied to robotics, learning under geometric constraints, higher level learning, passivity and impedance, and control of multiple manipulators and hands. In the course of over a quarter-century, ILC has broadened in breadth and depth, fusing with established fields such as robust, adaptive, and optimal control, as well as neural networks, fuzzy logic and many others. Application areas have also expanded, most heavily in robotics, rotary systems, process control, bio-applications, power systems and semiconductors. Whilst ILC is still a relatively young field, with a combined body of research work amassing around 1/30th of more established areas, there is a strong linear trend in increasing year on year publications continually pushing the realms of both theory and applications. For recent state of the art, the review paper (Ahn, Chen, and Moore 2007) contains 515 references, with a further review paper containing 135 (Bristow, Tharayil, and Alleyne 2006). Numerous events have punctuated the rise in ILC research activity, including special sessions at the American Control Conference and IFAC World Congress over multiple years, tutorials and workshops at the Conference on Decision and Control, International Conference on Control, Automation, Robotics and Vision, and International Conference on Mechatronics and Automation. Several of Arimoto’s original six postulates have been relaxed in recent years, whilst the concept of learning from experience gained over repetitions of a task remains unchanged. This is especially true for linear ILC applied to linear plants, in the domain of which algorithms have emerged with variable trial length, imprecise resetting, a reference and output which are only defined over a subset of data points, and application of constraints of various forms. The mature algorithmic development in this area has given rise to a concerted effort on pushing the bounds of achievable performance, together with new analytical methods often inspired by practical demands. For nonlinear systems, the primarily focus of linear ILC has shifted towards practical control problems and associated theoretical challenges, whilst interest in nonlinear methodologies has gathered pace. Similar observations apply for Repetitive Control (RC), a closely related methodology in which no resetting occurs between trials. The seven papers in this special issue cover a broad spectrum of the current research landscape for ILC and RC. The collection starts with two papers on RC which are associated with a broadening in scope and performance. An RC approach for uncertain systems is