  Flow control has been the subject of numerous experimental and theoretical
works. In this numerical study, we analyse full-order, optimal controllers for
large dynamical systems in presence of multiple actuators and sensors. We start
from the original technique proposed by Bewley et al. (2016), the adjoint of
the direct-adjoint (ADA) algorithm. The algorithm is iterative and allows
bypassing the solution of the algebraic Riccati equation associated with the
optimal control problems, typically unfeasible for large systems.
  We extend ADA into a more generalized framework that includes the design of
multi-input, coupled controllers and robust controllers based on the H_{\infty}
framework. The full-order controllers do not require any preliminary step of
model reduction or low-order approximation: this feature allows to pre-assess
the optimal performances of an actuated flow without relying on any estimation
process or further hypothesis.
  We show that the algorithm outperforms analogous technique, in terms of
convergence performances considering two numerical cases: a distributed system
and the linearized Kuramoto-Sivashinsky equation, mimicking a full
three-dimensional control setup. For the ADA algorithm we find excellent
scalability with the number of inputs (actuators) in terms of convergence to
the solution, making the method a viable way for full-order controller design
in complex settings.
