Symbiosis of RFPT-Based Adaptivity and the Modified Adaptive Inverse Dynamics Controller

The use of Lyapunov’s “direct” method for designing globally asymptotically stable controllers generates numerous, practically disadvantageous restrictions. The “Adaptive Inverse Dynamic Controller for Robots (AIDCR)” therefore suffers from various difficulties. As alternative design approach the “Robust Fixed Point Transformations (RFPT)” were introduced that instead of parameter tuning adaptively deforms the control signals computed by the use of a fixed approximate system model by observing the behaviour of the controlled system. It cannot guarantee global asymptotic stability but it is robust to the simultaneous presence of the unknown external disturbances and modelling imprecisions. In the paper it is shown that the RFPT-based design can co-operate with a modified version of the AIDCR controller in the control of “Multiple Input-Multiple Output (MIMO)” Systems. On the basis of certain function approximation theorems it is expected that this symbiosis works well in a wider class of physical systems than robots.