A. Firooznia, R. Bourdais, and B. De Schutter, "A distributed algorithm to determine lower and upper bounds in branch and bound for hybrid model predictive control," Proceedings of the 54th IEEE Conference on Decision and Control, Osaka, Japan, pp. 1736-1741, Dec. 2015.
In this work, a class of model predictive control problems with mixed real-valued and binary control signals is considered. The optimization problem to be solved is a constrained Mixed Integer Quadratic Programming (MIQP) problem. The main objective is to derive a distributed algorithm for limiting the search space in branch and bound approaches by tightening the lower and upper bounds of objective function. To this aim, a distributed algorithm is proposed for the convex relaxation of the MIQP problem via dual decomposition. The effectiveness of the approach is illustrated with a case study.