Closed-loop feedback sparsification under parametric uncertainties

We consider the problem of output feedback controller sparsification for systems with parametric uncertainties. We develop an optimization scheme that minimizes the performance deterioration from that of a well-performing pre-designed centralized controller, while enhancing sparsity pattern of the feedback gain. In order to improve temporal proximity of the pre-designed control system and its sparsified counterpart, we also incorporate an additional constraint into the problem formulation such that the output of the controlled system is enforced to stay in the vicinity of the output of the pre-designed system. It is shown that the resulting non-convex optimization problem can be equivalently reformulated into a rank-constrained problem. We then formulate a bi-linear minimization problem to obtain a sub-optimal solution which satisfies the rank constraint with arbitrary tolerance. Finally, a sub-optimal sparse controller synthesis for IEEE 39-bus New England power network is used to showcase the effectiveness of our proposed method.