Real-time Optimal Resource Allocation using Online Primal Decomposition*

Abstract

Many industrial processes consist of several subsystems (i.e., clusters) that share common constraints. Typically, each subsystem strives for its objective by competing in obtaining the shared resource, e.g., electrical power, steam, and water. A distributed optimization can solve such a problem, however, it involves solving a numerical optimization problem online and is usually computationally extensive. One can utilize an online iteration of Dual decomposition (without a numerical solver) to solve such a problem. However, in this approach, the constraint is typically controlled on a slow time scale causing significant dynamic constraint violation in the transient, especially in active constraint region switching. In practice, a ”back-of” strategy is necessary, and it may lead to profit loss in the long run. To address this issue, we propose to utilize online Primal decomposition instead, where the problem turns into a feedback-based problem, and the constraint controller(s) distribute local setpoints without violating the common constraint. The simulation results show that the proposed approach can reach the ideal steady-state optimum.