Decentralized Adaptive Control with Fractional Order Elimination of Obsolete Information

In this paper an alternative of Lyapunov’s complicated “direct” method, “Robust Fixed Point Transformation (RFPT)” based adaptive controller is applied in decentralized manner for the control of two dynamically coupled, imperfectly and imprecisely modeled mechanical systems. Each subsystem consists of a cart plus a double pendulum provided with a local controller having no information on the existence and the physical state of the 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 only 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 the use of “recent experiences” with properly fading obsolete information is a viable solution. For this purpose parametric, discrete numerical approximation of Caputo’s fractional order derivatives with “memory properties” are successfully used. It is shown by convincing simulation results that via observing and controlling the state propagation only of the modeled axles the uncorrelated controllers can precisely track their prescribed trajectories.