In the previous chapters, we have discussed classical prescribed performance control and our proposed tunnel prescribed control. However, there exists an implicit assumption in these performance control results, that is, the tracking error should be constrained from the beginning of the system operation, indicating that the knowledge of initial condition is completely known. If the initial condition violation occurs, these methods becomes invalid since they are not defined outside the allowable set. From a global perspective, it yields local tracking results. However, Entry Capture Problem (ECP) is frequently encountered in practical scenarios, where the tracking error may violate the performance constraints initially, then is regulated into an allowable set within a reasonable user-specified time [21]. A representative example is a manipulator system, starting from an unconstrained region for some time, then is expected to track and grasp an object in a specified performance.