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Optimal Control Problem

The minimization of the phase noise with respect to the design parameters and subject to Eqs. (gif) -- (gif) is an optimal control problem with as (constant) control function from a finite dimensional control space and and as state variables of the optimal control problem. The optimization problem is solved numerically by the direct collocation method DIRCOL [gif]. The method is based on a discretization of the state variables by piecewise cubic spline functions satisfying the dynamic equations at the grid points of a time grid and at the centers between (cf. Hargraves, Paris [gif] and [gif]). By this approach, the optimal control problem is transformed to a (finite dimensional) nonlinearly constrained optimization problem that can be solved by the Sequential Quadratic Programming method due to Gill et al. [gif]. Compared with other methods for solving optimal control problems the direct collocation method is easy-to-use (as knowledge of optimal control theory is not required), robust (not much information on the solution is a priori required) and reliable (if accuracy requirements are not too high) [gif].



Oskar von Stryk
Mon Aug 19 10:27:50 MET DST 1996