Automatic Domain Partitioning of Piecewise-Affine Simplicial Functions Implementing Model Predictive Controllers

This brief is concerned with the problem of mitigating the "curse of dimensionality" in the piecewise-affine simplicial approximation of multivariate model predictive control (MPC) functions by resorting to nonuniform domain partitions, in view of their implementation in high-speed embedded digital architectures. Two dual strategies are used to reduce the number of simplices with respect to uniform partitions, without reducing approximation accuracy. Both circuit implementation purposes and the MPC technique impose additional constraints, with respect to other techniques already available for multiresolution domain partitioning. The algorithms are tested on a benchmark example concerned with adaptive cruise control.