Sparsity Invariance for Convex Design of Distributed Controllers

Understand

We address the problem of designing optimal linear time-invariant (LTI) sparse controllers for LTI systems, which corresponds to minimizing a norm of the closed-loop system subject to sparsity constraints on the controller structure.

• This problem is NP-hard in general and motivates the development of tractable approximations.
• We characterize a class of convex restrictions based on a new notion of Sparsity Invariance (SI).
• The underlying idea of SI is to design sparsity patterns for transfer matrices Y(s) and X(s) such that any corresponding controller K(s)=Y(s)X(s)^-1 exhibits the desired sparsity pattern.