A Structure Exploiting Branch-and-Bound Algorithm for Mixed-Integer Model Predictive Control
For practitioners in automotive, aerospace, and hybrid systems requiring real-time mixed-integer MPC, this algorithm offers a structure-exploiting approach that significantly reduces computation time.
This paper presents a branch-and-bound algorithm for mixed-integer model predictive control that exploits the block-sparse optimal control structure and uses warm-starting from previous time steps. The algorithm achieves computational speedups of up to 10x compared to state-of-the-art solvers in preliminary MATLAB and C implementations.
Mixed-integer model predictive control (MI-MPC) requires the solution of a mixed-integer quadratic program (MIQP) at each sampling instant under strict timing constraints, where part of the state and control variables can only assume a discrete set of values. Several applications in automotive, aerospace and hybrid systems are practical examples of how such discrete-valued variables arise. We utilize the sequential nature and the problem structure of MI-MPC in order to provide a branch-and-bound algorithm that can exploit not only the block-sparse optimal control structure of the problem but that can also be warm started by propagating information from branch-and-bound trees and solution paths at previous time steps. We illustrate the computational performance of the proposed algorithm and compare against current state-of-the-art solvers for multiple MPC case studies, based on a preliminary implementation in MATLAB and C code.