Geometric properties of gradient projection anti-windup compensated systems

The gradient projection anti-windup (GPAW) scheme was recently proposed as an anti-windup method for nonlinear multi-input-multi-output systems/controllers, which was recognized as a largely open problem in a recent survey paper. Here, we show that for controllers whose output equation depends only on its state, the GPAW compensated controller achieves exact state-output consistency when appropriately initialized. In a related paper analyzing the GPAW scheme on a simple constrained system, this property was crucial in proving that the GPAW scheme can only maintain/enlarge the exact region of attraction of the uncompensated system. When the nominal controller does not have the required structure, an arbitrarily close approximating controller can be constructed. Further geometric properties of GPAW compensated systems are then presented, which illuminates the role of the GPAW tuning parameter.