Tackling mismatched uncertainty in robust constraint-following control of underactuated systems

The mismatched uncertainty makes the control for underactuated systems an intractable problem in the control field. This paper targets this problem based on constraint-following. The uncertainty is (possibly fast) time-varying and bounded. The control goal is to drive underactuated systems to follow prescribed constraints, which may be holonomic or non-holonomic, linear or nonlinear with respect to the velocity. The control is designed in two steps. First, the nominal control without addressing uncertainties and initial condition deviations is investigated. Second, we meticulously decompose uncertainty into matched and mismatched portions. This decomposition makes the mismatched uncertainty "disappear" in the stability analysis. Consequently, we are able to design a class of robust constraint-following controls free from mismatched uncertainty and only based on matched uncertainty. By the Lyapunov approach, we show that the proposed robust controls guarantee uniform boundedness and uniform ultimate boundedness for underactuated systems. Simulation results on a mobile robot are given for demonstrations. (c) 2020 Elsevier Inc. All rights reserved.