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SIAM Journal on Computing
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Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
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ACM '52 Proceedings of the 1952 ACM national meeting (Pittsburgh)
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HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
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Automatica (Journal of IFAC)
Dynamic programming for constrained optimal control of discrete-time linear hybrid systems
Automatica (Journal of IFAC)
Technical Communique: Evaluation of piecewise affine control via binary search tree
Automatica (Journal of IFAC)
Convexity recognition of the union of polyhedra
Computational Geometry: Theory and Applications
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Automatica (Journal of IFAC)
Stabilizing polynomial approximation of explicit MPC
Automatica (Journal of IFAC)
Brief paper: Explicit predictive control with non-convex polyhedral constraints
Automatica (Journal of IFAC)
Complexity reduction of explicit model predictive control via separation
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
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 arrangements). Thirdly, the paper proposes a technique to further reduce the complexity of piecewise polyhedral systems if the introduction of an adjustable degree of error is acceptable. Fourthly, the paper shows that based on the notion of the hyperplane arrangement PWA state feedback control laws can be implemented efficiently. Three examples, including a challenging industrial problem, illustrate the algorithms and show their computational effectiveness in reducing the complexity by up to one order of magnitude.