Directional Input Adaptation in Parametric Optimal Control Problems

This paper deals with input adaptation in dynamic processes in order to guarantee feasible and optimal operation despite the presence of uncertainty. The proposed adaptation consists in using the nominal optimal inputs and adding appropriately designed input variation functions. For optimal control problems having both terminal and mixed control-state path constraints, two orthogonal sets of directions can be distinguished in the space of input variation functions: the so-called sensitivity-seeking directions, along which a small variation will not affect the respective active constraints, and the complementary constraint-seeking directions, along which a variation will affect the respective constraints. It is shown that the sensitivity-seeking directions satisfy certain linear integral equations. Two selective input adaptation strategies are then defined, namely, adaptation in the sensitivity- and constraint-seeking directions. This paper proves the important result that, for small parametric perturbations, the cost variation resulting from adaptation in the sensitivity-seeking directions (over no input adaptation) is typically smaller than that due to adaptation in the constraint-seeking directions.