Riccati-less optimal control of bluff-body wakes

In this paper we propose a new method to solve the optimal control problem in which the feedback matrix K is computed in an efficient way for complex flows, with large number of degrees of freedom, using an approach similar to adjoint-based control optimization. The idea is to consider the direct-adjoint system as an input-output problem where the input is given by the current state and the output is the control. Since the control has much smaller dimension than the state, the feedback matrix K can be efficiently obtained from the solution of the adjoint of the direct-adjoint system. It can further be shown using the symplectic product that the direct-adjoint system is self adjoint. As a consequence the new adjoint system is equivalent to the direct-adjoint system with suitable initial and terminal conditions. With this method the optimal control problem can be solved efficiently for any value of the control penalty l 2. Results are presented of this novel technique as applied to suppressing the vortex shedding behind a circular cylinder, and compared to the minimal-energy feedback control presented in [4]. © 2010 Springer Science+Business Media B.V.