Given the well known concept that optimal control problems may be solved either by the maximum principle or by the dynamic programming technique which employs many numerical algorithms, this paper attempts to show that the exact penalty function method may be used to transform a constrained optimal control problem into an unconstrained optimal control problem. Under certain conditions the constrained optimal control problem is shown to be equivalent to an unconstrained optimal control problem, which can be easily solved by a numerical technique.
Abstract.A constructive process is presented which leads to a class of quadrature formulas with any preassigned compound precision for the numerical integration of rapidly oscillating functions on (0, oo) of the form e-X F(x, 2x), where 2 is a large parameter and F(., y) is periodic of period unity in y.
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