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

本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。首席研究员将专注于两个广泛的领域：每个孤立系统的定量行为和大规模系统的整体行为，当相互联系被解释。其目的是分析大型系统的动力学方面的子系统和他们的互连性质。对于孤立系统，有四个方面的问题：稳定性，当控制器很小时的可控性，当时间和精力最小时的最优控制形式，以及最优反馈控制的所有构造。建议的结果可能包括：如果每个子系统是可控的，并且相互作用“很好”，那么大规模系统是可控的。如果某个子系统不可控，那么在受到外部控制冲击的情况下，大系统仍然是可控的。对全球经济等大型组织控制的影响将被研究。将追求最优控制策略。

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.