Mathematical Sciences: Global Decompositions of Nonlinear Control Systems

大规模非线性控制的分解问题 系统分解成一个小规模子系统的互连族 这是一个自然的问题， 研究人员在这个问题上所做的绝大多数工作 到目前为止，主要集中在局部分解上。通过 分解一通常意味着变量的变化， 产生至少具有两个独立的等效系统， 而是相互连接的部分。分解是非常重要的， 这是一个实用的观点，因为它简化了分析， 复杂的系统 研究者提出了全球系统的概念 从概念的角度来看是合理的分解 并有可能产生可以应用于 具体的例子。他将尝试把已知的结果推广到 局部分解到全局设置。必须而且 全局分解存在的充分条件将 被寻找。控制对称群的研究 系统将构成本研究的一部分。应用 的全局分解的研究的全局可控性 也将研究非线性控制系统。 本研究试图进一步发展的应用 微分几何控制系统如果成功，它可以 产生对这些应用相当重要的结果 机器人和直升机 自动驾驶

The problem of decomposing a large-scale nonlinear control system into an interconnected family of smaller-scale subsystems is a natural one and has received the attention of many researchers. The vast majority of the work done on this problem thus far has concentrated on local decompositions. By decomposition one usually means a change of variables that produces an equivalent system that has at least two independent but interconnected parts. Decomposition is very important from a practical point of view, because it simplifies the analysis of complex systems. The investigator proposes a notion of global system decomposition which is reasonable from a conceptual point of view and has potential of producing results that can be applied to specific examples. He will attempt to extend known results on local decompositions to a global setting. Both necessary and sufficient conditions of existence of global decompositions will be sought. A study of symmetry groups associated with a control system will constitute a portion of this research. Applications of global decompositons to the study of global controllability of nonlinear control systems will also be pursued. This research attempts to develop further the applications of differential geometry to control systems. If succesful, it could produce results of considerable importance for such applications of control theory as robot manipulators and helicopter autopilots.