Output feedback controller sparsification via H₂-approximation

The problem of optimal sparse output feedback control design for continuous linear time invariant systems is considered. This work adopts the concept of H_p-approximation to develop an optimization algorithm capable of synthesizing a structured sparse static controller gain for which the overall closed loop system exhibits empirical frequency characteristics resembling that of the system controlled with a pre-designed centralized controller. We, moreover, modify our optimization problem so that the control signal generated by the sparse controller falls into the vicinity of the centralized control input, in the sense of L² ₂ norm. Furthermore, we show that our optimization problem can be equivalently reformulated into a rank constrained problem for which we propose to use a tailored version of Alternating Direction Method of Multipliers (ADMM) as a computationally efficient algorithm to sub-optimally solve it. Finally, we illuminate the effectiveness of our proposed method by testing it on randomly generated sample network models.