The look-up table controllers and a particular class of Mamdani fuzzy controllers are equivalent - Implications to real-world applications

We focused on a new direction of fuzzy control that, we believe, has received little, if any, attention. We explored how the look-up table (LUT) controllers and one special type of Mamdani fuzzy controllers were mathematically related and how to represent the former by the latter. A LUT controller is one of the most widely used tools in industry, especially in automotive engineering. The reasons for its popularity are the strong nonlineraity and multimodal behaviors that can be, in many cases, formalized only by experimentally measured data. Our approach was inspired by the similarity between the fuzzy controllers and LUTs and we used the theory of fuzzy controllers to bring new light to the LUT-based engineering technique that is usually considered as a low tech or “black art” type of control tool. We developed a local stability criterion for feedback control systems with LUT controllers. Based on this, we developed a practical design procedure for constructing a LUT control system that is guaranteed to be at least locally stable under the assumptions that (1) the nonlinear system's mathematical model is unknown, and (2) the system is linearizable at the equilibrium (most practical systems meet this assumption).

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