Accelerating Explicit Model Predictive Control by Constraint Sorting

Abstract Explicit MPC represents one of the fastest ways of real-time MPC implementation. As the explicit MPC policy is optimization-free in real-time control, its efficiency is determined by solving a point location problem. This paper proposes the novel concept of accelerating explicit MPC that significantly speeds up the real-time evaluation of the point location problem. The introduced strategy has two layers: (i) an offline phase determines a smart order of the regions to be explored, and (ii) an online phase removes further regions to be explored on the fly based on the current value of the value function. The main advantage of layer (i) is that the order is evaluated offline, therefore, it does not increase the real-time implementation of explicit MPC. The implementation of layer (ii) slightly increases the real-time evaluation but leads to further speed-up of the point location problem. As the proposed layers are based just on the evaluation of some appropriate value function, the main benefit is that these layers are fully applicable also for higher-dimensional systems. Although the accelerated explicit MPC variant does not reduce the worst-case time of solving the point location problem, an extensive case study demonstrates the efficiency of the proposed strategy.