H₂ Controller Synthesis for Compartmental Systems via ADMM

This letter addresses the problem of optimal state feedback controller design of compartmental systems under H-2 performance. The main challenge of this problem is that both the objective function and its domain are non-convex, and meanwhile, the close-loop system has to be compartmental. This letter addresses this problem from an optimization perspective. By leveraging the coercive property of the objective function, we show that by including the boundaries, the feasible region is reduced to a convex polyhedron. For the technical details, we transform the inequality constraints into equality constraints by introducing non-negative variables. The H-2 controller is designed using the alternating direction method of multipliers (ADMM) and we show that the slack variables can be updated analytically. We prove that the solution returned by the algorithm will always be a KKT point. Finally, a numerical example is provided to show the superior performance of our algorithm.