Sparsity Promoting H-Conic Control

A controller is designed through an alternating direction method of multipliers (ADMM) algorithm to maximize sparsity while providing similar closed-loop $\mathscr {H}_{2}$ performance to an optimal 'target' controller and imposing conic bounds that ensure robust input-output stability for the nonlinear closed-loop system. The invoked sparsity improves implementation feasibility for large scale systems. The optimal target controller problem is reformulated and solved in terms of structured static output feedback. Feasibility and convergence are proved and the design is applied to a chain of mass-spring-dampers.