Region of attraction comparison for gradient projection anti-windup compensated systems

Abstract

Abstract-The gradient projection anti-windup (GPAW) scheme was recently proposed for saturated multi-input-multioutput (MIMO) nonlinear systems driven by MIMO nonlinear controllers, a topic recognized as an open problem in a recent survey paper. Thus far, stability results for GPAW compensated systems are restricted to the simple case of a saturated first order linear time invariant (LTI) plant driven by a first order LTI controller. Here, we present a region of attraction (ROA) comparison result for general GPAW compensated regulatory systems. The ROA comparison result is demonstrated on a simple planar nonlinear system, which also highlights the limitations of existing state-of-the-art anti-windup results.

PI control of stable nonlinear plants using projected dynamical systems

“…On the other hand, the (natural) link between PDS theory and AW design has been pointed out before. Investigations in a similar direction have been carried out in Teo and How (2011), where a gradient projection AW (GPAW) scheme has been proposed. In particular, they provide sufficient conditions under which the following holds: Assume that the nominal unconstrained closed-loop system is stable and achieves tracking in correspondence of a certain equilibrium point, then the region of attraction of the same equilibrium point in the associated GPAW closed-loop system is "larger" than the one of the unconstrained system.…”