论文标题
边界近似可控性在线性系统的阳性约束下
Boundary approximate controllability under positivity constraints of linear systems
论文作者
论文摘要
本文着重于在广泛的无限维控制系统的阳性约束下的边界近似可控性。我们开发频域可控性标准。首先，我们在此类系统的控件上的积极限制下得出了可控结果。然后，更重要的是，我们为控制和状态的积极限制提供了必要和充分的条件，以实现可控性。 获得的结果应用于运输和热传导网络的可控性。特别是，只要基础图是密切相关的，则在运输网络系统控制/状态状态的阳性约束下的可控性将完全以卡尔曼型等级条件为特征。对于在类似路径的网络上具有罗宾边界条件的热方程系统，我们在阳性状态构成下建立了近似的可控性，并通过启动节点单个正输入。但是，我们证明在单方面控制构成下缺乏可控性。
This paper focuses on boundary approximate controllability under positivity constraints of a wide range of infinite-dimensional control systems. We develop frequency domain controllability criteria. Firstly, we derive a controllability result under positivity constraints on the control for such systems. Then, and more importantly, we provide a necessary and sufficient condition for controllability under positivity constraints on the control and the state. The obtained results are applied to the controllability of transportation and heat conduction networks. In particular, provided that the underlying graph is strongly connected, the controllability under positivity constraints on the control/state of transport network systems is fully characterized by a Kalman-type rank condition. For a system of heat equations with Robin boundary conditions on a path-like network, we establish approximate controllability under positivity state-constraint with a single positive input through the starting node. However, we prove the lack of controllability under unilateral control-constraint.
