Parametric sensitivity of path-constrained optimal control: Towards selective input adaptation

In the context of dynamic optimization, plant variations necessitate adaptation of the input profiles in order to guarantee both feasible and optimal operation. For those problems having path constraints, two sets of directions can be distinguished in the input space at each time instant: the so-called sensitivity-seeking directions, along which a small input variation does not affect the active path constraints; the complementary constraint-seeking directions, along which a variation affects the path constraints. Hence, three selective input adaptations are possible, namely, adaptation along each set of input directions and adaptation of the switching times between arcs. This paper considers parametric variations around a nominal optimal solution and quantifies the influence of these variations on each type of input adaptation.