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.