Anti-windup and Model Predictive Control: Reflections and Connections*

Anti-windup strategies for dealing with input constraints date from the earliest stages of automatic control. They are ad-hoc procedures which achieve input saturation in an instantaneous fashion. Not surprisingly, anti-windup methods have a strong appeal to practitioners because of their simplicity. On the other hand, model predictive control (MPC) is a well established strategy for dealing with input constraint problems. The essential feature of the method is a receding horizon optimal quadratic control problem which is solved subject to input constraints. Both methods are known to perform well in practice and each has its strong advocates. In this paper, we explore connections between the methods for constrained single-input linear systems. In particular, we show that there are cases in which anti-windup schemes are identical to MPC schemes. In other cases, we show that anti-windup has performance which is close to that of MPC strategies. These comparisons are facilitated by formulating a general class of anti-windup algorithms in a form which highlights the connection with the state space formulations which are traditionally used in the MPC area.