Accelerating space traversal methods for explicit model predictive control via space partitioning trees

The paper elaborates an approach for acceleration of space traversal methods for solving a point location problem involved in the evaluation of explicit model predictive control laws. The idea is to improve the initialisation of the space traversal algorithms by providing initial estimates that restrict the search over a fraction of the original space. The reduction of the search space ensures that the space traversal algorithms can find the solution significantly faster as if sought over the full space. The proposed approach comprises two algorithms. The first algorithm generates an orthogonal partition of the search space off-line which is represented by a quadtree. In the second algorithm, the quadtree is traversed on-line and a particular space traversal method is initialised. The paper provides complexity analysis of both algorithms in the runtime and storage requirements. The approach is tested numerically on multiple examples and achieves significant reduction of iterations in the space traversal methods.