Output Controllability of a Linear Dynamical System with Sparse Controls

TL;DR

This paper investigates conditions for ensuring output controllability in discrete-time linear systems with sparse controls, providing computationally efficient criteria and bounds on sparsity levels for control design.

Contribution

It extends the Kalman rank test to sparse control inputs and derives polynomial-time verifiable conditions for output controllability.

Findings

Derived non-combinatorial conditions for sparse controllability

Provided bounds on minimal sparsity levels needed for control

Ensured polynomial-time verification of controllability conditions

Abstract

In this paper, we study the conditions to be satisfied by a discrete-time linear system to ensure output controllability using sparse control inputs. A set of necessary and sufficient conditions can be directly obtained by extending the Kalman rank test for output controllability. However, the verification of these conditions is computationally heavy due to their combinatorial nature. Therefore, we derive non-combinatorial conditions for output sparse controllability which can be verified with polynomial time complexity. Our results also provide bounds on the minimum sparsity level required to ensure output controllability of the system. This additional insight is useful for designing sparse control input that drives the system to any desired output.