Convergence stabilization by parameter tuning in Robust Fixed Point Transformation based adaptive control of underactuated MIMO systems

The classical approaches in the adaptive control of Classical Mechanical Systems as the “Adaptive Inverse Dynamics Controller (AIDC)” or the “Adaptive Slotine-Li Controller (ASLC)”, as well as several implementations of the idea of the “Model Reference Adaptive Control (MRAC)” have the common feature that they are designed by the use of Lyapunov´s 2^nd (“direct”) method that normally applies a quadratic Lyapunov function constructed of the tracking error and further additional terms. Though in the lack of unknown external disturbances this approach normally guarantees global asymptotic stability, it requires the use of complicated, slow, non-optimal tuning process with high computational burden. Furthermore, unknown external perturbations or the presence of not modeled, dynamically coupled subsystems can completely fob this sophisticated tuning. Recently an alternative problem tackling, the application of “Robust Fixed Point Transformations (RFPT)” were recommended for fully driven Classical Mechanical systems. This approach applies strongly saturated, multiplicative nonlinear terms causing a kind of “deformation” of the input of the available imprecise system model. Instead parameter tuning it operates with Cauchy sequences that are convergent only within a local basin of attraction. This technique can well compensate the simultaneous effects of modeling errors and unknown external disturbances. At first time, in this paper, as a completion, a convergence stabilizing tuning process is recommended and applied for underactuated Classical Mechanical systems. The conclusions of the paper are illustrated by simulation results.