Optimal boundary flow control: Equivalence of adjoint and co-state formulations and solutions

This paper addresses controversial issues fundamental to the optimal control of aerodynamic flows. Aerodynamic flows being external to wings, the significant region of the flow is in the interface region. In assessing the closedloop performance the relevant performance index must therefore be evaluated exclusively on the wing boundary which is the most significant region for the development of both lift and drag. When this is done the controller may be synthesised relatively easily as it can be shown that the associated optimising co-state equations are identical to the adjoints, which can then be solved by the same methods employed for the Navier-Stokes equations. The control laws may then be deduced by comparing the open and closed loop pressure distributions.