Adaptive robust control for dual avoidance–arrival performance for uncertain mechanical systems

An unprecedented dual avoidance–arrival problem is addressed for uncertain mechanical systems. The concerned system uncertainty is (possibly fast) time-varying but within an unknown bound. The objective is to design a control to simultaneously guarantee two seemingly opposite system performance: avoidance (with respect to a region) and arrival (with respect to another region). This is formulated as an approximate constraint-following control problem, in which formulation, the desired constraint is creatively divided into two categories as the avoidance constraint and the arrival constraint. An adaptive robust control is then put forward under the consideration of the system uncertainty. It is proved that, with the proposed control input, the avoidance constraint is completely followed and the arrival constraint is closely followed; hence, the dual avoidance–arrival problem is carried out.