Formal application of dummy parameters in a soft computing-based control of mechanical devices

Several variants of a special approach aiming at the development of a new branch of soft computing (SC) for the adaptive control of approximately and partially known mechanical systems are under investigation since 1995. Like "traditional" SC it uses "uniform structures" for modeling, but these structures are obtained from the symplectic group (SG) as a mathematical means describing the inner symmetry of conservative mechanical systems. It considerably reduces the number of free parameters in the model in comparison with that of the neural networks or ample sets of fuzzy rules. It also replaces the process of parameter tuning with simple, lucid, and explicit algebraic operations of limited steps. Further considerations reveals that on the basis of quite formal mathematical observations SG can either be replaced by several Lie groups not representing any symmetry of the physical systems under consideration, or it can be used in a different way not based on the symmetry principle. This approach eliminates certain measurability problems, and the existence of certain singularities related to the symmetry-based application can be evaded using it by building in dummy parameters into the control. In this paper the robustness of this new formal approach is demonstrated in the adaptive control of a SCARA-type robot arm with one introduced dummy parameter