Anti-windup higher derivative Newton-based extremum seeking under input saturation

The physical constraint of actuators in practical systems, such as actuator magnitude saturation, can significantly impact the behaviour of control systems. To address this issue, a fast learning mechanism is introduced in this paper for constrained input in higher derivatives Newton-based extremum seeking. The approach employs a constrained optimisation method with an anti-windup loop based on a wide range of penalty functions to adapt the search and prevent the violation of constraints, thereby avoiding windup of integral action in a controller. The practical asymptotic stability of the proposed algorithm is proven through a modified singular perturbation method, and its effectiveness is validated through simulations.