Avoidance-Arrival Control for Mechanical Systems Under Constraint-Following

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 problem by dividing the desired constraint into the avoidance constraint and the arrival constraint. An adaptive robust control is then put forward, with which the avoidance constraint is completely followed and the arrival constraint is closely followed; hence, the dual avoidance-arrival problem is solved.