H. Tolle – författare

Since heavily non-linear and/or very complex processes still pose a problem for automatic control, they can often be handled easily by human operators. The book describes re- sults from ten years of research on learning control loops, which imitate these abilities. After discussing the diffe- rencesto adaptive control some background on human informa- tion processing and behaviour is put forward and some lear- ning control loop structure related to these ideas is shown. The ability to learn is due to memories, which are able to interpolate for multi-dimensional input spaces between scat- tered output values. A neuronally and mathematically inspi- red memory lay out-are compared and it is shown that they learn much faster thanbackpropagation neural networks, which can also be used. For the learning control loop diffe- rent architectures are given. Their usefulness is demonstra- ted by simulation and results from applications to real pi- lot plants. The book should be of interest for control engi- neers as well as researchers in neural net applications and/or artificial intelligence. The usual mathematical back- ground of engineers is sufficient.

Variational problems which are interesting from physical and technical viewpoints are often supplemented with ordinary differential equations as constraints, e. g. , in the form of Newton''s equations of motion. Since analytical solutions for such problems are possible only in exceptional cases and numerical treat­ ment of extensive systems of differential equations formerly caused computational difficulties, in the classical calculus of variations these problems have generally been considered only with respect to their theoretical aspects. However, the advent of digital computer installations has enabled us, approximately since 1950, to make more practical use of the formulas provided by the calculus of variations, and also to proceed from relationships which are oriented more numerically than analytically. This has proved very fruitful since there are areas, in particular, in automatic control and space flight technology, where occasionally even relatively small optimization gains are of interest. Further on, if in a problem we have a free function of time which we may choose as advantageously as possible, then determination of the absolutely optimal course of this function appears always advisable, even if it gives only small improve­ ments or if it leads to technical difficulties, since: i) we must in any case choose some course for free functions; a criterion which gives an optimal course for that is very practical ii) also, when choosing a certain technically advantageous course we mostly want to know to which extent the performance of the system can further be increased by variation of the free function.