Qualitative analysis of system behaviour.

摘要

In this thesis, we provide a rigorous definition for the term "qualitative" in the context of static and dynamic systems. Based on these definitions, we develop mathematical and computational tools for reasoning about qualitative properties of models. The dissertation makes contributions to three problems of qualitative reasoning: Qualitative Comparative Statics, Qualitative Stability, and, Qualitative Analysis of Differential Equations.; 1. The problem of solving for the direction of change of an equilibrium point when the Jacobian of she system of equations about the equilibrium point is specified only in terms of signs is plagued with multiple solutions. In this thesis we introduced the use of the dimensions of variables to constrain the number of solutions. We present a set of conditions under which the information of the dimensions is sufficient to solve for the direction of change uniquely.; 2. We can reason about stability of systems when the interactions between the state variables is specified in terms of signs only if the feedback loops are of length 2. In this thesis we introduce representations which allow equality and order of magnitude relations between the interactions and derive two new stable structures with feedback loops of length greater than 2. These structures are encountered in the startup of chemical process plants.; 3. Lastly, we have developed a program ANDRONOV, which integrates the use of symbolic and numeric computation to automatically analyze the qualitative behavior of second order, nonlinear, autonomous differential equations. We have illustrated the capability of this program to analyze complex differential equations with illustrative examples.