Symplectic Geometry Based Simple Algebraic Possibilities for Developing Adaptive Control for Mechanical Systems
József K. Tar, Imre J. Rudas*, János F. Bitó* and Seppo J. Torvinen**
*John von Neumann Faculty of Informatics, Budapest Polytechnic, H-1081 Budapest, Npsznh z utca 8, Hungary
**Tampere University of Technology, 33101 Tampere, P.O.Box 589, Finland
The paper is a report on the development of a new special branch of Soft Computing (SC) developed for the control of mechanical devices. Like “traditional” SC this method also uses uniformized structures and procedures applicable for a whole class of problems rather than the precise model of a given, particular system. In contrast to the structures of traditional SC (e.g. typical Neural Network Architectures, and/or fuzzy membership functions and relations) the present approach obtains its structures and procedures from the fundamental symmetry group of Classical Mechanics, the Symplectic Group. Another essential novelty is in dealing with the indefinite, unconstrained parameters of the possible Symplectic Transformations used in the control, resulting in very limited number of shrinks/stretches, conventional rotations in an abstract space eliminating any unnecessary transformation and permutation characteristic to the former solution based on the “Standard Symplectizing Algorithm”. For the price of limited circle of applicability (mechanical systems control) drastic reduction in the number of free parameters, a priori known ranges, reduced computational complexity and lucidity is obtained. As an application example a technological task, polishing of a plane surface is considered via simulation.