ABSTRACT
As in the previous chapters, let PWC(a, b;Rm) denote the space of all Rm-valued piecewise continuous functions defined on [a, b]. Also, PWC(a,+∞;Rm) denotes the set of all functions u(·) : [a,+∞) → Rm such that u(·) ∈ PWC(a, T ;Rm) for all a < T < +∞. A function u(·) ∈ PWC(t0,+∞;Rm) is called a control or control function. We start with a statement of the Simplest Problem in Optimal Control (SPOC) and state the basic Maximum Principle for this simplest problem.
