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Symbolic controller synthesis is a fully-automated and correct-by-designsynthesis scheme whose limitations are its immense memory and runtimerequirements. A current trend to compensate for this downside is to developtechniques for parallel execution of the scheme both in mathematical foundationand in software implementation. In this paper we present a generalizedBellman-Ford algorithm to be used in the so-called symbolic optimal control,which is an extension of the aforementioned synthesis scheme. Compared to thewidely used Dijkstra algorithm our algorithm has two advantages. It allows forcost functions taking arbitrary (e.g. negative) values and for parallelexecution with the ability for trading processing speed for memory consumption.We motivate the usefulness of negative cost values on a scenario of aerialfirefighting with unmanned aerial vehicles. In addition, this four-dimensionalnumerical example, which is rich in detail, demonstrates the great performanceof our algorithm.

A generalized Bellman-Ford Algorithm for Application in Symbolic Optimal Control