Nonlinear functional analysis and its applications
Nonlinear functional analysis and its applications
Automatic qualitative analysis of dynamic systems using piecewise linear approximations
Artificial Intelligence
A dynamic systems perspective on qualitative simulation
Artificial Intelligence
Differential equations and dynamical systems
Differential equations and dynamical systems
Mathematical problems arising in qualitative simulation of a differential equation
Artificial Intelligence
Qualitative and quantitative simulation: bridging the gap
Artificial Intelligence
An approach by graphs for the recognition of temporal scenarios
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Qualitative simulation and related approaches for the analysis of dynamic systems
The Knowledge Engineering Review
Experiment selection for the discrimination of semi-quantitative models of dynamical systems
Artificial Intelligence
Constraint-Based Approach for Analysis of Hybrid Systems
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Box invariance in biologically-inspired dynamical systems
Automatica (Journal of IFAC)
Experiment selection for the discrimination of semi-quantitative models of dynamical systems
Artificial Intelligence
Using qualitative description for the dynamic analysis of virus inflection
SEAL'06 Proceedings of the 6th international conference on Simulated Evolution And Learning
Computation of polytopic invariants for polynomial dynamical systems using linear programming
Automatica (Journal of IFAC)
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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.