Robustness of the minimal control synthesis algorithm to non-linear plant with regard to the position control of manipulators

This paper presents new, more rigorous, proofs of the stability and robustness of the adaptive minimal control synthesis (MCS) and decentralized MCS (DMCS) algorithms, applied to plant subject to internal state-dependent non-linear disturbances. The concept of arbitrary dissipativity, and the restriction on the high frequency gain of the plant introduced by Hodgson and Stoten in 1996, is used as a basis for the analysis. We also extend the stability result to the position control of manipulators composed of prismatic and revolute joints, by making use of the passive structure of the manipulator dynamics.