论文标题
具有非负稀疏控件的线性系统的可控性
Controllability of a Linear System with Nonnegative Sparse Controls
论文作者
论文摘要
本文使用非负和稀疏输入研究离散时间线性动力学系统的可控性。这些对控制输入的限制自然出现在许多现实生活中，这些系统对系统的外部影响是单向的，并且激活每个输入节点会增加控制成本。我们为系统的可控性提供了必要和充分的条件，而无需对系统矩阵施加任何约束。与众所周知的基于卡尔曼等级的可控性标准不同，本文中介绍的条件可以在多项式时间内进行验证，并且验证复杂性与稀疏度无关。结果的证明是基于有关凸锥特性的分析工具。我们的结果还提供了每次瞬间要激活的最小控制节点数量的封闭式表达式，以确保使用阳性对照的系统可控性。
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.
