Equivalence of optimal control problems and the use of parameterization methods

A notion of equivalence for optimal control synthesis problems is defined and partially characterized. If the dynamical constraint satisfies certain well-known conditions, a solution can be obtained by solving a related problem involving a linear constraint. The linearity can be exploited when using functional approximation techniques to obtain a solution. A class of interpolating polynomials is suggested that possess certain characteristics that make them useful when solving the equivalent problem by one of the mathematical programming methodologies