Co-design of sparse output feedback and row/column-sparse output matrix

We consider the co-design problem of sparse output feedback and row/column-sparse output matrix. A row-sparse (resp. column-sparse) output matrix implies a small number of outputs (resp. sensors). We impose row/column-cardinality constraint on the output matrix and the cardinality constraint on the output feedback gain. The resulting nonconvex, nonsmooth optimal control problem is solved by the proximal alternating linearization method (PALM). We show the global convergence of PALM by establishing the Lipschitz conditions of the bilinear matrix function. Furthermore, the proximal operators for sparsity constraints therein admit closed-form expressions. Numerical experiments verify the convergence results and demonstrate the effectiveness of our approach.