Lyapunov Based Reasoning Methods

Semiquantitative simulation is a novel approach for the analysis of uncertain dynamic systems that performs a comprehensive simulation study based on automated reasoning methods (for example with the SQSIM algorithm). Semiquantitative simulation of complex models is, however, hindered by the limited automated reasoning capabilities of the currently available semiquantitative simulation techniques. This paper describes the extension of semiquantitative simulation techniques on the basis of Lyapunov methods. This extension improves automated reasoning by utilizing generalized energy functions, called Lyapunov functions. Automated reasoning based on Lyapunov functions can be seen as a generalization of the energy considerations employed by engineers. It has the advantage that it can be used to analyze systems where it does not make sense to speak about energy in the physical sense. The difficult task of deducing a Lyapunov function for the semiquantitatively modeled dynamic system is solved by reformulating methods from nonlinear control theory. A procedure for an automatic deduction of a Lyapunov function and Lyapunov-based reasoning methods using this deduced Lyapunov function are given. The improved automated reasoning capabilities of our extended SQSIM simulation platform are demonstrated by example.