Equivalence between Approximate Dynamic Inversion and Proportional-Integral control

Approximate dynamic inversion is a method applicable to control of minimum phase, nonaffine-in-control systems. We show that if all the system states are available for feedback, the approximate dynamic Inversion controller can be realized as a linear Proportional-Integral model reference controller without knowledge of the nonlinear system beyond the sign of the control effectiveness, and without any approximations. Similarities with earlier work on high-gain feedback and variable structure control of affine-in-control nonlinear systems are highlighted, which suggests a possible link between approximate dynamic Inversion and variable structure control for nonaffine-in-control systems.