A bottom-up approach for searching for sparse controllers with a budget

Abstract

In this paper, we propose a bottom-up approach for designing sparse static output-feedback controllers for large-scale systems. Starting from an existing sparse controller, we iteratively add feedback channels using a gradient-based predictor, optimizing the closed-loop $H_2-$norm within a predefined budget constraint. The proposed method significantly reduces the computational burden compared to traditional top-down approaches, which rely on pruning centralized controllers. We prove the convergence of our method and demonstrate its scalability through benchmarks, achieving comparable or better performance with significantly less computation time. This approach paves the way for efficient and scalable control design in distributed systems.