Anti-windup design for internal model online constrained optimization

Abstract: This paper proposes a novel algorithmic design procedure for online constrained optimization grounded in control-theoretic principles. By integrating the Internal Model Principle (IMP) with an anti-windup compensation mechanism, the proposed Projected-Internal Model Anti-Windup (P-IMAW) gradient descent exploits a partial knowledge of the temporal evolution of the cost function to enhance tracking performance. The algorithm is developed through a structured synthesis procedure: first, a robust controller leveraging the IMP ensures asymptotic convergence in the unconstrained setting. Second, an anti-windup augmentation guarantees stability and performance in the presence of the projection operator needed to satisfy the constraints. The effectiveness of the proposed approach is demonstrated through numerical simulations comparing it against other classical techniques.