(204x) On the Computational Efficiency of the Economic Linear Optimal Control Problem

The method of Economic Linear Optimal Control (ELOC) can be used to serve as a surrogate for Economic Model Predictive Control (EMPC) and is fundamental in the development of the infinite horizon formulation of EMPC (IH-EMPC). In addition, ELOC can be extended to address certain classes of simultaneous controller and system design problems.

The computational challenge associated with ELOC is that the optimization problem used to synthesize the controller contains linear matrix inequality constraints along with a set of scalar reverse convex inequalities. While this class of problems can be solved using a simple application of the branch-and-bound algorithm, computational times can become excessive for moderate sized problems. In this work we illustrate two approaches to improve the computational efficiency of solving the ELOC problem. The first is a conceptually simple heuristic algorithm that possesses not guarantee with respect to global optimality, but to our knowledge has yet to arrive at a solution other than the global optimum. The second is an application of the generalized Bender decomposition, which is guaranteed to yield a globally optimal solution.