Selective Input Adaptation in Parametric Optimal Control Problems with Path Constraints

This paper is concerned with input adaptation in dynamic processes in order to guarantee feasible and optimal operation despite the presence of uncertainty. For optimal control problems having mixed control-state constraints, two sets of directions can be distinguished in the input function space: the so-called sensitivity-seeking directions, along which a small input variation does not affect the active constraints, and the complementary constraint-seeking directions, along which an input variation does affect the respective constraints. Two selective input adaptation scenarios can be defined, namely, adaptation along each set of input directions. This paper proves the important result that the cost variation due to the adaptation along the sensitivity-seeking directions is typically smaller than that due to the adaptation along the constraint-seeking directions.