Abstract

This chapter analyzes the control problem and its connection with the classical theory. Any control problem of the Pontryagin type can be expressed as a problem of Lagrange, and it is possible to deduce the necessary conditions for the control problem—including the maximum principle—from those for the problem of Lagrange. This is the procedure that should be followed to develop a rigorous proof of the necessary conditions for control problems. The chapter also describes conversion of a control problem into a problem of Lagrange. The control problem can be converted into a problem of Lagrange. The chapter discusses the classical theory that deals only with variables which are piecewise smooth and also discusses transition conditions.

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