Online Feedback-based Optimization with Multi-input Direct Constraint Control

Abstract

The starting point of this paper is to solve a steady-state optimization problem with simple feedback controllers using the Primal-Dual approach. However, this approach controls the constraint indirectly and on a slow time scale by manipulating the Dual variables (Lagrange multipliers). This control strategy may lead to unacceptable dynamic violations. The main contribution of this paper is to reduce the violations by introducing direct constraint control on the fast time scale using a selector. To get consistency with the steady-state optimization, we need to change the constraints in the Primal-Dual approach to involve the input used for direct constraint control. As a further refinement of this idea, we propose a multi-input direct constraint control for cases where many inputs affect the constraint value, and where pairing with a single input may lead to input rate saturation. The proposed control structure is applied to a subsea oil production network, showing that the proposed approach can minimize the dynamic violation during transient, and can achieve optimal steady-state conditions using simple feedback controllers.