Situation-dependent adaptive control polynomially eliminating the past information of fading relevance

In this paper an alternative of Lyapunov´s complicated “direct” method, the “Robust Fixed Point Transformation (RFPT)” based adaptive controller is applied in decentralized manner for the control of two dynamically coupled, incompletely and imprecisely modeled mechanical systems. 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 connection to the other cart+pendulums system. Instead trying to develop a complete and generally useful system model the RFPT-based solution extracts information on the present and recent behavior of the controlled system only in the given control situation. Insisting only on the use of the “present experiences” makes the method noise-sensitive. To improve the situation by the use of “recent experiences” with properly fading obsolete information is a viable solution. For this purpose a parametric, discrete, polynomial weighting of the past information is successfully used. The applied weights evidently have some “memory properties” with controllable forgetting rate. It is shown by convincing simulations that via observing and controlling the state propagation only of the modeled axles the uncorrelated controllers can precisely track their prescribed trajectories in spite of the presence of considerable measurement noises.