On the tuning of predictive controllers: Application of generalized Benders decomposition to the ELOC problem

• Solve economic linear optimal control problem using the generalized Benders decomposition algorithm.
• Develop a novel method to convexify constraints in the relaxed master problem while retaining global solution properties.
• Illustrate computational advantage of the proposed GBD based scheme over the existing branch and bound approach.
• Illustrate that the new approach will allow for easy incorporation of nonlinear steady-state models within the ELOC problem.

This work investigates the computational procedures used to obtain global solution to the economic linear optimal control (ELOC) problem. The proposed method employs the generalized Benders decomposition (GBD) algorithm. Compared to the previous branch and bound approach, a naive application of GBD to the ELOC problem will improve computational performance, due to less frequent calls to computationally slow semi-definite programming (SDP) routines. However, the reverse-convex constraints of the original problem will reappear in the relaxed master problem. In response, a convexification of the relaxed master constraints has been developed and proven to preserve global solution characteristics. The result is a multi-fold improvement in computational performance. A technological benefit of decomposing the problem into steady-state and dynamic parts is the ability to utilize nonlinear steady-state models, since the relaxed master problem is free of SDP type constraints and can be solved using any global nonlinear programming algorithm.