Optimization problems for dynamic systems with path constraints

In Chapter 2 we discussed optimization problems for nonlinear dynamic systems with end-point constraints; i.e., functions of the state variables were prescribed at the terminal point and the state variables were prescribed at the initial point. In this chapter we are going to consider problems with path constraints, i.e., constraints that apply at intermediate points or over the whole path, t₀≤ t ≤ t_f , rather than just at the end points. We shall first consider equality constraints and then inequality constraints.