An algorithm for automatic domain partitioning of piecewise-affine model predictive control laws

This paper proposes an algorithm for the automatic selection of a non-uniform simplicial partition of the domain of a piecewise-affine function used as an approximate Model Predictive Control law. The main goal is to obtain good approximations reducing the so-called “curse of dimensionality”, which affects the uniform partition case. The partition is chosen according to geometric considerations and by minimizing a proper cost function. The effectiveness of the algorithm and its advantages with respect to employing uniform domain partitions are discussed through an example.