Variational Problems with State Variable Inequality Constraints

by Stuart E. Dreyfus


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Consideration of a problem requiring the determination of a control or decision function that, in conjunction with a set of differential equations of motion dependent upon the control, yields a maximal or minimal value of an objective function evaluated at an unspecified future time, at which certain specified final conditions are satisfied. This general problem is called the "Problem of Mayer" and is one of three completely equivalent formulations of any one-dimensional variational problem. New results are derived concerning the characterization of the optimal solution of a variational problem in which the variables involved are restricted, by an inequality constraint, to lie only in a specified region of space. The computational aspects of this problem lead to a rather thorough investigation of techniques of numerical solution of unconstrained optimal trajectory problems.

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