Matrix Pontryagin principle approach to controllability metrics maximization under sparsity constraints

This study considers optimization problems for time-varying network topologies that maximize the controllability of linear network systems under sparsity constraints. The major theoretical differences from the existing findings on control node scheduling problems is that our method is based on the matrix-valued Pontryagin maximum principle applied to the controllability Lyapunov differential equation. This allows us to handle various controllability metrics that can only be approximated by existing methods. Finally, we perform a numerical evaluation of our proposed method and compare results with those of our previous approximation method.