Stable and optimal fuzzy control of linear systems

A number of stable and 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, provided that the process under control is linear and satisfies certain conditions. It turns out that if stability is the only requirement, 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 a ball-and-beam system.