General principles for design of robust non-linear controllers for AI-, ANN- or fuzzy approach-based realization

Development of adaptive and robust controllers for nonlinear coupled systems is inspired by new possibilities of hardware-realization, It concerns each kind of artificial intelligence: “classical” knowledge-based systems (KBSs), and artificial neural network- (ANN) and fuzzy set- (FS) based formulations. While common and general roots of these approaches became transparent, in each case complexity of the control rules, number of ANN processor units or fuzzy sets, or complexity of fuzzy rules essentially depend on the generalized coordinates used for describing the system to be controlled. It is pointed out, that in a wide class of control tasks relatively simple kinds of coordinate transformation can be applied to achieve effective simplification of the control rules and reduction of the number of necessary processor units or fuzzy sets. As an example, dynamics of robot arms are considered, where the appropriate coordinate transformation is approximate diagonalization of the inertia matrix of the robot arms. It serves as a satisfactory basis for working out a general method and principles for dealing with the quadratic coupling not eliminated by the diagonalization. It shows strong robustness with respect to the unknown inertia of the manipulated body and easily can be realized by ANN or fuzzy rule-based solutions of very limited number of processor units or fuzzy rules. The method is demonstrated by results of numerical simulation. Effects of imprecise modeling of the mass of the work-piece are considered