Generalization of a sigmoid generated Fixed Point Transformation from SISO to MIMO systems

Recently a systematic method was presented for the generation of whole families of “Fixed Point Transformations” that can be used in nonlinear adaptive control of “Single Input - Single Output (SISO)” systems as alternatives of Lyapunov´s “direct method”. In the present paper further development of this alternative method is considered. It consists in the generalization of the method for “Multiple Input - Multiple Output (MIMO)” systems. The applicability of the novel method is demonstrated by the adaptive control of a 2 “Degree of Freedom (DoF)” system, a cart indirectly driven in the horizontal direction by a rotated pendulum. Results of numerical simulations illustrate and substantiate the usability of the suggested approach.