System Level Synthesis with State and Input Constraints
For distributed control systems, this work addresses the practical challenge of incorporating constraints into SLS, offering a distributed computation method and stability guarantees under saturation.
This paper incorporates state and input constraints into the System Level Synthesis (SLS) framework using robust optimization, showing that dual variables preserve sparsity for distributed computation. It provides stability analysis for SLS with input saturation and proposes a saturation compensation scheme that improves performance over naive SLS design.
This paper addresses the problem of designing distributed controllers with state and input constraints in the System Level Synthesis (SLS) framework. Using robust optimization, we show how state and actuation constraints can be incorporated into the SLS structure. Moreover, we show that the dual variable associated with the constraint has the same sparsity pattern as the SLS parametrization, and therefore the computation distributes using a simple primal-dual algorithm. We provide a stability analysis for SLS design with input saturation under the Internal Model Control (IMC) framework. We show that the closed-loop system with saturation is stable if the controller has a gain less than one. In addition, a saturation compensation scheme that incorporates the saturation information is proposed which improves the naive SLS design under saturation.