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  • Author: Ulrich Appel, x
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Abstract

Aminolysis of the P-chlorofunctional carbodiphosphorane Ph3P = C = PPh2Cl (1) affords the diorganylamino substituted phosphonium salts (3a-e, R = alkyl), which can be dehydrohalogenated in good yield by NaH to give the neutral compounds Ph3P = C - PP2(NR2) (4a-e). The structure of the hitherto unknown amino-carbodiphosphoranes has been confirmed by 31P{1H} and 13C{1H} NMR data as well as by hydrolysis to give 5, hydrochlorination to 6b, e and methylation to 7a, e.

Abstract

Many systems like manufacturing systems, biological processes and even stock markets can be seen as networks of coupled decision makers and thus be described as networked discrete event systems (DES) or multi-agent discrete event systems (MADES). Information interchange between agents is usually performed indirectly via competition for shared resources. The problem of trajectory planning for MADES is about finding an optimal sequence of decisions for the particular agents. The planning process can be performed in a distributed manner. To encode the trajectory planning problem, we utilize Petri net models and present a formal way to derive integer linear programs (ILPs) that exhibit a bordered block-diagonal structure. We apply Dantzig’s decomposition method to decompose the LP-relaxed problem into multiple subproblems that can be solved locally by their corresponding agents. In general, the obtained LP solutions are non-integer. Therefore, we ensure feasibility to the original ILP using a superior Branch-and-Bound algorithm. Hence, we end up with a so called Branch-and-Price algorithm, tailored to solve trajectory planning problems for general MADES via distributed optimization.