Mixed-Integer Optimization and Model Predictive Control Applied to Hybrid Vehicles

In my PhD dissertation, three different algorithms will be presented and evaluated with the help of a series of numerical experiments. The first algorithm takes the name of Proximal Outer Approximation (POA). POA results from the merging and harmonization of the characteristics of two different approaches to mixed-integer convex optimization: Outer Approximation (OA) and Feasibility Pump (FP). The algorithm seeks to find an adaptive balance between the more feasibility-focused FP-like iterations and the more optimality-focused OA-like iterations. The collected empirical evidence suggests that, on the analyzed benchmark, Proximal Outer Approximation is capable of yielding faster and more robust convergence with respect to the classical OA algorithm. Next to be presented is the Mixed-Integer Real-Time Optimal Control (MIRT-OC) algorithm, a mixed-integer convex Model Predictive Control (MPC) approach that, inspired from the success of single-tree optimization schemes for mixed-integer convex optimal control, reduces the whole MPC process to a single tree search. The algorithm, rather than dealing with each MPC iteration separately, makes use of two specialized routines in order to adapt the optimization data and the search-tree collected during one MPC iterationo into optimization data and a partially explored search-tree for the subsequent iteration. Such strategy allows for maximal reuse of the collected information and, as confirmed by the performed numerical experiments, provides sizeable computational savings. Finally, the thesis presents the Disjunctive Outer Approximation for Optimal Control (DOA-OC) scheme, a specialized variation of Outer Approximation capable of efficiently solving a certain class of mixed-integer non-convex optimal control problems. The algorithm exploits the peculiar structure of the optimization problems that arise from optimal control applications and where the constraints result convex only on the continuous variables of the system. The distinctive feature of DOA-OC is its ability of efficiently generating linear relaxations for the non-convex constraints of the considered problems. The result is the possibility of avoiding the use of extremely expensive mixed-integer non-convex solution schemes or fiddly reformulations techniques, and thus, of obtaining vast reductions in computational complexity.status: accepte