Punctual and Global Constraints

Abstract

In this chapter we consider punctual and global constraints which concern the values taken on by the state and control variables at each time instants inside the control interval. First we consider punctual and global equality constraints and assume that the controlled system possesses more than one control variable. This assumption is needed because, otherwise, the problems will be either trivial or unsolvable. Then we tackle punctual and global inequality constraints. The main features of the relevant problems are: (1) the initial state is always given; (2) the final state is either given or partially specified or constrained to belong to a set which is not a regular variety; (3) the final time is given in one problem and is free in all the remaining ones; (4) other complex constraints (punctual and isolated equality constraints, integral inequality constraints) are also occasionally present.