Sparse Feedback Controller: From Open-loop Solution to Closed-loop Realization

TL;DR

This paper develops a sparse feedback control method for linear systems that achieves input sparsity through a dynamic linear compensator, ensuring stability and equivalence to open-loop solutions, with demonstrated effectiveness via numerical examples.

Contribution

It introduces a novel sparse feedback control framework that transitions from open-loop solutions to closed-loop realization using a dynamic compensator, ensuring stability and input sparsity.

Findings

Closed-loop sparse control is equivalent to open-loop solutions under a specific basis.

The dynamic compensator extends to feedforward tracking control.

Numerical examples confirm the effectiveness of the proposed approach.

Abstract

In this paper, we explore the discrete time sparse feedback control for a linear invariant system, where the proposed optimal feedback controller enjoys input sparsity by using a dynamic linear compensator, i.e., the components of feedback control signal having the smallest possible nonzero values. The resulting augmented dynamics ensures closed-loop stability, which infers sparse feedback controller from open-loop solution to closed-loop realization. In particular, we show that the implemented sparse feedback (closed-loop) control solution is equivalent to the original sparse (open-loop) control solution under a specified basis. We then extend the dynamic compensator to a feedforward tracking control problem. Finally, numerical examples demonstrate the effectiveness of proposed control approach.