<h2>AAS 97-151</h2>
<h2>APPROXIMATE SOLUTION OF OPTIMAL CONTROL PROBLEMS                                                                                                 </h2>
<h4> D. G. Hull, The University of Texas at Austin                                                                                                                            </h4>
<h2> Abstract </h2>
 A standard method for obtaining approximate analytical solutions of optimal control  problems is regular perturbation theory.  Here, a small parameter is identified;  the equations are expanded in a Taylor series, and equations defining the zeroth- order, first-order,.... parts of the solution are obtained.  The solutions of each  part are combined to form an approximate solution.  In this paper, it is shown that  this proccess is the same as taking variations and obtaining a neighboring  extremal.  A simple problem which has an analytical solution is used to issustrate  the process.