Punctual and Isolated Constrains

Abstract

In this chapter we consider punctual and isolated equality constraints which concern the values taken on by the state variables at isolated time instants inside the control interval. These instants may or may not be specified. First we present seven problems where the initial and final state are given. Furthermore: (1) the constraints are either functions of the state only or also functions of time; (2) the final time is given or free; (3) different scenarios are discussed according to whether the time of constraints satisfaction is given or free; (4) occasionally the comparison with the constraint-free situation is presented. We end this chapter by considering a problem which leads to a seemingly contradictory conclusion because the necessary conditions can not be satisfied, even if an optimal solution is shown to exist.