Efficient evaluation of mp-MIQP solutions using lifting

TL;DR

This paper introduces a novel lifted parameter space for mp-MIQP solutions, transforming piecewise quadratic functions into piecewise affine ones, enabling faster online evaluation through a single binary search tree, demonstrated by power electronics experiments.

Contribution

The paper proposes a lifted parameter space that simplifies mp-MIQP solution evaluation, significantly improving online speed and enabling trade-offs with offline computation.

Findings

Online evaluation speedup up to ten times

Single binary search tree for piecewise affine functions

Trade-off between online speed and offline computation

Abstract

This paper presents an efficient approach for the evaluation of multi-parametric mixed integer quadratic programming (mp-MIQP) solutions, occurring for instance in control problems involving discrete time hybrid systems with quadratic cost. Traditionally, the online evaluation requires a sequential comparison of piecewise quadratic value functions. As the main contribution, we introduce a lifted parameter space in which the piecewise quadratic value functions become piecewise affine and can be merged to a single value function defined over a single polyhedral partition without any overlaps. This enables efficient point location approaches using a single binary search tree. Numerical experiments include a power electronics application and demonstrate an online speedup up to an order of magnitude. We also show how the achievable online evaluation time can be traded off against the offline computational time.