Irredundant lattice representations of continuous piecewise affine functions
نویسندگان
چکیده
In this paper, we revisit the lattice representation of continuous piecewise affine (PWA) function and give a formal proof of its representation ability. Based on this, we derive the irredundant lattice PWA representation through removal of redundant terms and literals. Necessary and sufficient conditions for irredundancy are proposed. Besides, we explain how to remove terms and literals in order to ensure irredundancy. An algorithm is given to obtain an irredundant lattice PWA representation. Both the offline and online complexity as well as the storage requirement of the irredundant lattice PWA representation are analyzed. In the worked examples, the irredundant lattice PWA representation is used to express the optimal solution of the explicit model predictive control, and the results turn out to be much more compact than those given by a state-of-the-art algorithm.
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ورودعنوان ژورنال:
- Automatica
دوره 70 شماره
صفحات -
تاریخ انتشار 2016