Combinatorial optimization model and MIP formulation for the structural analysis of conditional differential-algebraic systems
In this paper we consider the structural analysis problem for differential-algebraic systems with conditional equations. This problem consists, given a conditional differential-algebraic system, in verifying if the system is structurally nonsingular for every state, and if not in finding a state in which the system is structurally singular. We give a formulation for this problem as an integer linear program. This is based on a transformation of the problem into a matching problem in an auxiliary graph. We also show that the linear relaxation of that formulation can be solved in polynomial time. using this, we develop a Branch-and-Cut algorithm for solving the problem and present some experimental results. (C) 2011 Elsevier Ltd. All rights reserved.
structural analysis differential-algebraic system integer linear program matching graph branch-and-cut algorithm