Distributed Optimization Design for Computation of Algebraic Riccati Inequalities

This article proposes a distributed optimization design to compute continuous-time algebraic Riccati inequalities (ARIs), where the information of matrices is distributed among agents. We propose a design procedure to tackle the nonlinearity, the inequality, and the coupled information structure of ARI; then, we design a distributed algorithm based on an optimization approach and analyze its convergence properties. The proposed algorithm is able to verify whether ARI is feasible in a distributed way and converges to a solution if ARI is feasible for any initial condition.