Anti-windup for Extremum Seeking

At the heart of Extremum Seeking Control (ESC) is an integrator to modify an adapted parameter. This integrator may drive the adapted parameter outside its physically realistic domain. Such a finite domain may represent the operational limits of an actuator or similar. In this note an anti-windup ESC is proposed to ensure that the adapted parameter remains within a given domain. Furthermore it is demonstrated that this anti-windup ESC can be viewed as an approximation for an appropriate penalty-function-based ESC. The link between the anti-windup compensator and the penalty function is further explored. Finally, some simulations are described to illustrate the results.