Parsimonious learning feed-forward control

We introduce the Learning Feed-Forward Control configuration. In this configuration, a B-spline neural network is contained, which suffers from the curse of dimensionality. We propose a method to avoid the occurrence of this problem. 1 Introduction In order to design a conventional feedback controller, like a state-feedback controller, detailed knowledge of the process under control is required. However, in many cases an accurate process model can only be obtained with considerable effort, time and cost. Modelling difficulties are likely to arise with processes that suffer from: a) uncertainty in process structure or in many parameters, b) strong non-linearities, or c) time-variance in process structure or in many parameters. With these kinds of processes, conventional controllers and even non-linear or adaptive controllers can show poor performance because their design relies heavily on the availability of an accurate process model. Even when a reasonable accurate model is available a-priori, feedback controllers often suffer from a trade-off between high performance and robust stability. Though feedback controllers are very capable of compensating disturbances, with good process knowledge available feed-forward control could be given preference over feedback control because feedback controllers are basically error driven. A feed-forward controller may be able to prevent control errors, because its output is based on the reference, instead of the error signal. When no accurate process model is available, learning feed-forward (LFF) controllers should be considered. LFF controllers hardly suffer from the mentioned trade-off and are capable of improving the performance of a feedback control system considerably [9]. They are not necessarily based on a physical process model and are potentially able to learn and reproduce an 'arbitrary' continuous function to any desired degree of accuracy, even if it concerns non-linear and/or time-variant functions. In this paper, we propose a method to deal with the curse of dimensionality [1, 4, 5] in the context of LFF. We first introduce the LFF configuration in section 2. Next, we discuss the B-spline network that is contained in this configuration and formulate the problems that are brought about by the curse of dimensionality. In section 4 we take a look at ASMOD [4, 5, 1], which is an effective way to avoid the curse of