Optimal complexity reduction of polyhedral piecewise affine systems

This paper focuses on the NP-hard problem of reducing the complexity of piecewise polyhedral systems (e.g. polyhedral piecewise affine (PWA) systems). The results are fourfold. Firstly, the paper presents two computationally attractive algorithms for optimal complexity reduction that, under the assumption that the system is defined over the cells of a hyperplane arrangement, derive an equivalent polyhedral piecewise system that is minimal in the number of polyhedra. The algorithms are based on the cells and the markings of the hyperplane arrangement. In particular, the first algorithm yields a set of disjoint (non overlapping) merged polyhedra by executing a branch and bound search on the markings of the cells. The second approach leads to non-disjoint (overlapping) polyhedra by formulating and solving an equivalent (and well-studied) logic minimization problem. Secondly, the results are extended to systems defined on general polyhedral partitions (and not on cells of hyperplane

• Type: Journal
• Year: 2008
• Where: AUTOMATICA
• Authors: Tobias Geyer, Fabio Danilo Torrisi, Manfred Morari
• Keywords: AUTOMATICA 2008, Hyperplane Arrangement, Polyhedral Piecewise, Polyhedral Piecewise Affine