A mathematical formulation of hierarchical systems using fuzzy logic systems

In this paper, we use fuzzy logic systems to model higher levels of hierarchical systems. Specifically, we consider three-level hierarchical systems where the lowest level comprises the plant and convertional feedback controllers, the middle level performs supervisory operations to guarantee the stability of the whole system, and the top level is a planning level which provides control targets for the lower levels and communicates with the environment. The plant is modeled by differential equations, and the supervision and planning levels are modeled by fuzzy logic systems. The advantage of this model is that all the levels are formulated in a same mathematical framework (due to the dual role of fuzzy logic systems), therefore it is possible to analyze the hierarchical systems in a mathematically rigorous fashion. Two case studies are presented: integrated planning and control of mobile robots, and intelligent vehicle/highway systems