This paper studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems where the external influence on the system is unidirectional, and activating each input node adds to the cost of control. We derive the necessary and sufficient conditions for controllability of the system, without imposing any constraints on the system matrices. Unlike the well-known Kalman rank based controllability criteria, the conditions presented in this paper can be verified in polynomial time, and the verification complexity is independent of the sparsity level. The proof of the result is based on the analytical tools concerning the properties of a convex cone. Our results also provide a closed-form expression for the minimum number of control nodes to be activated at every time instant to ensure controllability of the system using positive controls.

中文翻译：

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具有非负稀疏控制的线性系统的可控性

本文研究了使用非负和稀疏输入的离散时间线性动力系统的可控性。这些对控制输入的约束在许多实际系统中自然出现，其中对系统的外部影响是单向的，激活每个输入节点会增加控制成本。我们推导出系统可控性的充分必要条件，而不对系统矩阵施加任何约束。与众所周知的基于卡尔曼秩的可控性准则不同，本文提出的条件可以在多项式时间内验证，验证复杂度与稀疏度无关。结果的证明基于有关凸锥特性的分析工具。