Using ADMM for Hybrid System MPC

Model Predictive control (MPC) has been studied extensively because of its ability to handle constraints and its great properties in terms of stability and performance [Mayne et al., 2000]. We have in this thesis focused on MPC of Hybrid Systems, i.e. systems with both continuous and discrete dynamics. More specifically, we look at problems that can be cast as Mixed Integer Quadratic Programming (MIQP) problems which we are solving using a Branch and Bound technique. The problem is in this way reduced to solving a large number of constrained quadratic problems. However, the use in real time systems puts a requirement on the speed and efficiency of the optimization methods used. Because of its low computational cost, there have recently been a rising interest in the Alternating Direction Method of Multiplies (ADMM) for solving constrained optimization problems. We are in this thesis looking at how the different properties of ADMM can be used and improved for these problems, as well as how the Branch and Bound solver can be tailored to accompany ADMM. We have two main contributions to ADMM that mitigate some of the downsides with the often ill-conditioned problems that arise from Hybrid Systems. Firstly, a technique for greatly improving the conditioning of the problems, and secondly, a method to perform fast line search within the solver. We show that these methods are very efficient and can be used to solve problems that are otherwise hard or impossible to precondition properly