Abstract
Suppose that the state variables x = (x 1,…,x n )′ where the dot refers to derivatives with respect to time t, and u ∊ U is a vector of controls. The object is to transfer x to x 1 by choosing the controls so that the functional takes on its minimum value J(x) called the Bellman function (although we shall define it in a different way). The Dynamic Programming Principle leads to the maximisation with respect to u of and equality is obtained upon maximisation.
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