A DIRECT SECOND VARIATIONAL METHOD FOR FREE-ENDPOINT FREE-TIME OPTIMAL CONTROL PROBLEMS BY NEWTONS METHOD IN FUNCTION SPACE

A direct second-variational method is proposed for solving free-time, free-endpoint optimal control problems. By introducing a time-scaling factor and a reduced-time coordinate, the original free-endpoint problem is transformed into a fixed-time problem in the reduced-time domain. In this framework, Newton's method is applied to the optimality criterion and the transversality condition, in order to arrive at a scheme for simultaneous correction in the control policy and in final time. The resulting algorithm does not involve a Riccati transformation nor requires the solution of other sensitivity equations, and is therefore a decided improvement over existing methods. For illustrative purposes the method is applied to the temperature optimization of a tubular reactor of unspecified length. © 1969 Taylor and Francis Group, LLC.