A generalized Markov Chain modeling approach for on board applications

This paper deals with a new class of Markov Chain type models that can be effectively used for real time modeling and on-line learning of nonlinear systems with uncertainties. We expand the concept of the generalized Markov Chain - a probabilistic model that synergistically combines the idea of transition probabilities with the information granulation paradigm. We consider generalized Markov chains based on two different types of information granules - intervals and fuzzy subsets - and the methods for their learning from data. We also analyze the relationship between the Markov chains and the fuzzy models and derive an alternative formulation of the Chapman-Kolmogorov equation that applies to stochastic models in fuzzy environment. As this approach is motivated by and intended for in-vehicle applications, results are illustrated on examples of granular models of vehicle speed and road grade.