SHOULD CONTROLS BE ELIMINATED WHILE SOLVING OPTIMAL-CONTROL PROBLEMS VIA DIRECT-METHODS

Direct methods of solving optimal control problems include techniques based on control discretization, where the control function of time is parameterized, and collocation, where both the control and state func tions of time are parameterized. A recently introduced direct approach of solving optimal control problems via differential inclusions param eterizes only the state, and constrains the state rates to lie in a fe asible hodograph space. In this method, the controls, which are just a rtifacts used to parameterize the feasible hodograph space, are comple tely eliminated from the optimization process. Explicit and implicit s chemes of control elimination are discussed. Comparison of the differe ntial inclusions method is made to collocation in terms of number of p arameters, number of constraints, CPU time required for solution, and ease of calculation of analytical gradients, A minimum time-to-climb p roblem for an F-15 aircraft is used as an example for comparison. For a special class of optimal control problems with linearly appearing bo unded controls, it is observed that the differential inclusion scheme is better in terms of number of parameters and constraints. Increased robustness of the differential inclusion methodology over collocation for the Goddard problem with singular control as part of the optimal s olutions is also observed.