Global qualitative description of a class of nonlinear dynamical systems

In this paper we propose a methodology to derive a qualitative description of the behavior of a system from an incompletely known nonlinear dynamical model. The model is written as an algebraic structure with unknown parameters and/or functions. Under some hypotheses, we obtain a graph describing the possible transitions between regions, defined by the trends of the state variables and their relative positions. A qualitative simulation of the model can be compared with on-line data for fault detection purpose. We give the example of a nonlinear biological model (in dimension three) for the growth of cells in a bioreactor.  2001 Elsevier Science B.V. All rights reserved.