Mathematical Sciences: Stability, Time-Optimal, Minimum Effort Control Theory of Hereditary Systems and Applications

该项目将发展大规模遗传系统的稳定性、时间最优和最小努力控制理论。主要的研究人员将集中在两个大的领域：每个孤立系统的量化行为和考虑内部联系时大系统的整体行为。其目的是根据大系统的子系统及其相互关联的性质来分析大系统的动力学。对于孤立系统，有四个方面的问题：稳定性，控制小时的可控性，时间和精力最小时的最优控制形式，以及所有最优反馈控制的构造。所提出的结果可能包括：如果每个子系统都是可控的，并且相互作用“良好”，则大系统是可控的。当某个子系统不可控时，如果施加一定的外部控制冲击，大系统仍然是可控的。对全球经济这样的大型组织的控制的影响将被研究。将寻求最优控制策略。

This project will develop stability, time optimal, and minimum effort control theory of large scale hereditary systems. The principal investigator will focus on two broad areas: the quantitative behavior of each isolated system and the overall behavior of the large scale systems when the inter-connections are accounted for. The aim is to analyze the dynamics of large scale systems in terms of their subsystems and the properties of their interconnection. For the isolated system there are four aspects of the problem: stability, controllability when the controls are small, the form of optimal control when time and effort are minimum, and all the construction of optimal feedback controls. Proposed results may include: If each subsystem is controllable and the interaction "nice" then the large scale system is controllable. If some subsystem is not controllable the large scale system can still be controllable if some external control impact is brought to bear. The implications to the control of large organizations like global economics will be studied. Optimal control strategies will be pursued.