Managing time-storage complexity in point location problem: Application to explicit model predictive control

The online computational burden of linear model predictive control (MPC) can be moved offline by using multi-parametric programming, so called explicit MPC. The explicit MPC is a piecewise affine (PWA) function defined over a polyhedral subdivision of the set of feasible states. The online evaluation of such a control law needs to determine the polyhedral region in which the current state lies. This procedure is called the point location problem and its computational complexity is challenging. In this paper a new flexible algorithm is proposed which enables the designer to tradeoff between time and storage complexities. Utilizing the concept of hash tables and the associate hash functions the proposed method is modified to solve an aggregated point location problem in processing complexity independent of the number of polyhedral regions while the storage needs remains tractable. The effectiveness of this approach is supported by several numerical examples.