Sparse Topology Estimation for Consensus Network Systems via Minimax Concave Penalty

This letter proposes an optimization method to estimate the network topology in continuous-time consensus systems. Assuming the network topology is non-negative weighted and undirected, we formulate an optimization problem based on the sparse maximum likelihood estimation using the minimax concave penalty function as the sparsity promoting term. We show that the problem belongs to the class of difference of convex functions (DC) optimization problems and quote the best-known DC algorithm for the computation. The effectiveness of the proposed method is demonstrated through numerical simulations and experiments using flight data measured from a multi-agent system of drones. We confirm that our method outperforms the conventional $\ell ^{1}$ regularization methods.