Interior variations method for solving optimal control problems

Abstract

In this article, the author examines the properties of interior variations and indicates how to use them in order to formulate the necessary condition of optimality (in the form of maximum principle) for optimal control problems in the class of smooth and bounded functions with fixed end-points. For such optimal control problems, an optimization technique based on interior variations and polynomial approximations is suggested and then illustrated by an explanatory example.

Keywords:

• optimal control
• smooth and bounded controls
• interior variations
• maximum principle

AMS Subject Classifications::

• 49K30
• 49K15
• 65K10