The Pontryagin Maximum Principle and Some of Its Applications

Abstract

Publisher Summary This chapter discusses the Pontryagin maximum principle and a few of its applications. An especially appealing feature of this principle from the control system designer's viewpoint is its utility in establishing certain properties of optimal controls with a minimum of mathematical manipulation. The chapter presents a few fundamental results of the maximum principle and discusses the way in which they may be exploited in control system studies. If an optimal control exists for a given problem, it must satisfy the conditions of the theorem relevant to the problem formulation. Satisfaction of the conditions of the maximum principle by an admissible control does not necessarily imply that the control is optimal. From the problem formulation and the statement of the theorems, it is clear that application of the maximum principle to a given problem will, in general, lead to a nonlinear, two-point boundary value problem. The chapter presents a particular example to show how the maximum principle can be used to effect a preliminary design.