Stable and optimal fuzzy control of linear systems

In this paper, a stable and an optimal fuzzy controllers are developed for linear systems. Based on some classical results in control theory, we design the structure and parameters of fuzzy controllers such that the closed-loop fuzzy control systems are stable if the process under control is linear and satisfies certain conditions. It turns out that if stability is the only concern, there is much freedom in choosing the fuzzy controller parameters. Therefore, a performance criterion is set to optimalize the parameters. Using the Pontryagin minimum principle, we design an optimal fuzzy controller for linear systems with quadratic cost function. Finally, the optimal fuzzy controller is applied to the ball-and-beam system.