Hyperbolic optimal control and fuzzy control

In this paper, we consider a new approach to fuzzy control which entails the formulation of a novel state-space representation and a new form of optimal control problem. Basically, in this new formulation, linear functions in the conventional state-space representation and cost functional are replaced by hyperbolic functions. We give a solution for this new, infinite-time, optimal control problem, which we call hyperbolic optimal control. Furthermore, we show that the resulting optimal controller is in fact a Mamdani-type fuzzy controller with Gaussian membership functions and center of gravity defuzzification. These results enable us to investigate analytically important issues, such as stability and robustness, pertaining to fuzzy controllers as well as add a powerful theoretical framework to the field of fuzzy control.