RFPT-based Adaptive Control Stabilized by Fuzzy Parameter Tuning

An alternative of Lyapunov's "direct" method, the "Robust Fixed Point Transformation (RFPT)" based adaptive controller is stabilized by adaptively tuning only one parameter of a single fuzzy membership function. As an application, decentralized control of two dynamically coupled, incompletely and imprecisely modeled mechanical systems is studied via simulation. Each subsystem consists of a cart and a double pendulum provided with a local controller having no information on the existence and the physical state of its own second pendulum and on the existence of and dynamic coupling with the other cart and double pendulum. Instead developing complete and generally useful system model this approach extracts information on the present and recent behavior of the controlled system only in the given control situation by using only three adaptive control parameters. Two of them can be kept xed but the third one may need ne tuning for stable control. In this paper a formerly proposed intricate tuning strategy is replaced by simple fuzzy tuning. It is illustrated by simulations that via observing and controlling the state propagation only of the modeled axles the uncorrelated controllers can precisely track their prescribed trajectories even in the presence of considerable measurement noises.