# University of Twente Student Theses

## On training strategies for parsimonious learning feed-forward controllers

Valkenburg, Govert
(2001)
*On training strategies for parsimonious learning feed-forward controllers.*

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Abstract: | This thesis addresses the question how to train a Parsimonious Learning Feed-Forward Controller (PLFFC). In Learning Feed-Forward control (LFFC) generally a well-conditioned feedback control signal is used to train a feed-forward controller, which mainly performs a function approximation. Then the feedback control signal is seen as an approximation of the inverse plant dynamics with respect to a particular reference signal. The feed-forward controller generally converges to the inverse plant dynamics. In a PLFFC a so-called parsimonious B-spline network (P-BSN) is used for the function approximation. In a second order BSN, (the only type used in this research) a function is approximated part-wise by straight lines. In a P-BSN a multivariate function is approximated by the sum of a set of univariate (or lower-variate) sub-BSNs. It is not obvious what information should be stored in what sub-BSN. If information is stored into the wrong network, we speak of interference. It turns out that the quality of training a PLFFC mainly depends on symmetry in the training paths. Due to symmetry, some effects add up to zero, which is important for avoiding interference between the sub-BSNs. The theory was applied both in simulations and in experiments. The simulations turn out to be successful: a significant decrease of the error is achieved. It turns out that the error reduction by poor paths is about equal to the reduction by well-conditioned paths, whereas the extent to which they extract the correct mappings from the plants is really smaller, in this sense that the mappings learnt by the BSN do not equal the target functions. Furthermore it was shown that a poorly conditioned path can even cause divergence. In experiments it was found that discontinuous relations in the plant disable the LFFC to learn the correct relations. This remains the same when PLFFC is used. This is the main reason why the performance PLFFC when applied to a real plant according to the presented theory, is limited. Furthermore in some cases the difference between reference and system states is too large. Still a significant error reduction is achieved. The theory was proven to be correct, with some remarks to its applicability. A training procedure for PLFFC is proposed in the end. |

Item Type: | Essay (Master) |

Faculty: | EEMCS: Electrical Engineering, Mathematics and Computer Science |

Subject: | 53 electrotechnology |

Programme: | Electrical Engineering MSc (60353) |

Link to this item: | http://purl.utwente.nl/essays/56897 |

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