Revisiting reachability-driven explicit MPC for embedded control

Abstract

The real-time implementation of the explicit MPC suffers from the evaluation of the, potentially large, lookup table. The paper revisits the original approach and presents an efficient reachability-sets-driven-based explicit MPC method addressing this issue by splitting the look-up table into the set of the “relevant” subsets. Simultaneously, effective binary encoding is introduced to minimize the runtimes and the memory footprint. Further acceleration is achieved by introducing the “smart” order of the considered critical regions. Then, the significant real-time complexity reduction is ensured by online pruning and traversing the sorted lookup table associated with the optimal control law evaluation. Technically, the number of critical regions to be explored is reduced and the order is redefined to accelerate the point location problem and minimize the computational effort. While the optimality of the control law is still preserved, the cost that we need to pay for the accelerated point location problem lies in an additional offline computation effort and a minor increase in memory requirements of the underlying controller. The benefits of the proposed method are demonstrated using an extensive case study. The complexity reduction strategy was investigated on two fast-dynamic benchmark systems and the computational burden was analyzed by implementing the designed controllers on an embedded hardware.