Structural Analysis for Differential-Algebraic Systems: Complexity, Formulation and Facets
暂无分享,去创建一个
Abstract In this paper we consider the structural analysis problem for differential-algebraic systems with conditional equations. This consists, given a conditional differential algebraic system, in verifying if the system is well-constrained for every state and if not in finding a state for which the system is bad-constrained. We first show that the problem reduces to the perfect matching free subgraph problem in a bipartite graph. We then show the NP-completeness of this problem and give a formulation as an integer linear program. We also discuss the polytope of the solutions of this problem and propose a Branch-and-Cut algorithm.
[1] A. Mahjoub,et al. Structural analysis in differential-algebraic systems and combinatorial optimization , 2009, 2009 International Conference on Computers & Industrial Engineering.
[2] Kazuo Murota,et al. Matrices and Matroids for Systems Analysis , 2000 .
[3] Kazuo Murota,et al. Systems Analysis by Graphs and Matroids , 1987 .
[4] Peter A. Fritzson,et al. Principles of object-oriented modeling and simulation with Modelica 2.1 , 2004 .