Synthesis of invariant nonlinear single-channel sigmoid feedback tracking systems ensuring given tracking accuracy

We consider the tracking problem under exogenous and parametric disturbances for nonlinear single-channel plants with mathematical model representable in a triangular input–output form. Within the framework of the block approach, we develop a decomposition procedure for nonlinear feedback synthesis that provides tracking of the target signal by the output variable with given accuracy in given time. We formalize a new type of sigmoid local feedbacks in the class of smooth everywhere bounded S-shaped functions that ensure invariance with respect to uncontrolled bounded disturbances not belonging to the control space without any assumptions about their smoothness. The results of numerical simulation of our algorithms for an inverted pendulum control system are presented.