ON DYNAMIC PROGRAMMING TEACHING IN OPTIMAL CONTROL COURSES - COMMENTS ON ITS APPLICABILITY.

Dynamic programming is a fundamental technique in optimal control theory since it provides a computationally attractive solution to several problems of practical interest. A key concept for its derivation is the principle of optimality. It is well known that a sufficient condition for the latter to hold is that the minimizing functional satisfies the additivity property, which is clearly valid for integral functionals. However, this requirement is overseen in standard optimal control textbooks, leading the students to the erroneous belief that it is true in all instances. A simple minimization problem given provides an example where application of the optimality principles gives an erroneous solution.