Intrinsic Desensitized Optimal Control Progress Report 1

The Desensitized Optimal Control (DOC) approach enables the simultaneous optimization of a physical reference trajectory and the associated transition matrix describing the sensitivity of the physical states in the neighborhood of the optimal reference trajectory. In the context of DOC, the gains appearing in the differential equations for the sensitivity states are treated like additional controls, and are subject to optimization. In the standard DOC approach, the optimization of the DOC gains is performed with no attention paid to the optimality of the continuation of a trajectory after a perturbation is encountered. This limitation is overcome in the present paper by introducing a condition that forces the DOC control gains to become equal to the DOC problem's neighboring optimal control gains. The newly introduced condition cannot be considered an optimality condition since it acts as a constraint, and hence, can never cause an improvement in the DOC problem's performance index. The condition cannot qualify as a state constraint or control constraint either since it involves the DOC problem's costates. The condition is dubbed a “design condition”, since it enforces a desirable behavior of the optimal solution that is not otherwise compelled by the minimization of the DOC performance index alone.