Nonlinear Control Problems for Underactuated Mechanical Systems

该建议描述了一个研究计划，以调查欠驱动机械系统的控制问题，即为机械系统的独立控制变量比自由度少。 我们提出了一个数学模型，提供了一个框架（1）开发一个概念综合控制的许多例子，欠驱动机械系统已在出版的文献中研究，（2）构建新的控制分析和设计工具，是具体的欠驱动机械系统。 我们的第一个研究目标是开发一个合成或统一的不同的结果在现有的文献控制欠驱动机械系统，从而提供新的见解各种非线性控制方法的适用性。 我们的其他研究目标是开发新的非线性控制的结果，是特定的欠驱动机械系统的类。 这一研究方向将建立在我们目前的NSF研究资助（非线性系统的监督和混合控制）下开发的成功成果以及我们许多研究同事开发的相关非线性控制成果的基础上。 我们确定了具体的研究方向，我们认为有可能是成功的，我们认为，预期的结果可能会提供重要的进展，超出现有的知识基础控制欠驱动机械系统。

This proposal describes a research program to investigate control problems for underactuated mechanical systems, that is for mechanical systems with fewer independent control variables than degrees of freedom. We propose a mathematical model that provides a framework for (1) developing a conceptual synthesis for control of the many examples of underactuated mechanical systems that have been studied in the published literature and (2) constructing new control analysis and design tools that are specific for underactuated mechanical systems. Our first research objective is to develop a synthesis or unification of the disparate results in the existing literature on control of underactuated mechanical systems, thereby providing new insights into the applicability of various nonlinear control approaches. Our other research objective is to develop new nonlinear control results that are specific to the class of underactuated mechanical systems. This research direction would build heavily on the successful results developed under our current NSF research grant (on supervisory and hybrid control of nonlinear systems) as well as on the relevant nonlinear control results developed by many of our research colleagues. We identify specific research directions that we believe are likely to be successful and we suggest that the expected results are likely to provide important advances beyond the existing knowledge base for control of underactuated mechanical systems.