Global solutions for nonlinear systems using qualitative reasoning

This paper explores how qualitative information can be used to improve the performance of global optimization procedures. Specifically, we have constr ucted a nonlinear parameter estimation reasoner (NPER) for finding paramete r values that match an ordinary differential equation (ODE) model to observ ed data. Qualitative reasoning is used within the NPER, for instance, to in telligently choose starting values for the unknown parameters and to empiri cally determine when the system appears to be chaotic. This enables odrpack , the nonlinear least-squares solver that lies at the heart of this NPER, t o avoid terminating at local extrema in the regression landscape. odrpack i s uniquely suited to this task because of its efficiency and stability. The NPER's robustness is demonstrated via a Monte Carlo analysis of simulated examples drawn from across the domain of dynamics, including systems that a re nonlinear, chaotic, and noisy. It is shown to locate solutions for noisy , incomplete real-world sensor data from radio-controlled cars used in the University of British Columbia's soccer-playing robot project. The paramete r estimation scheme described in this paper is a component of pret, an impl emented computer program that uses a variety of artificial intelligence tec hniques to automate system identification - the process of inferring an int ernal ODE model from external observations of a system - a routine and diff icult problem faced by engineers from various disciplines.