Less Conservative Criteria for Analysis and Synthesis of Nonlinear Systems

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。该奖项的研究目标是建立用于分析和综合非线性系统的工具，特别强调原子力显微镜。现有的方法是保守的，即使存在获得性能的潜力，通常也无法实现期望的性能。本研究所依据的主要概念如下：通常，非线性系统需要具有一定的标称行为，而在该系统的标称行为附近，系统通常可以得到精确的表征。然而，有一些外部因素会导致系统偏离标称行为，这可能会导致所需的非线性描述变得复杂。在提出的研究中使用的主要概念之一是首先管理系统行为，当系统远离预期的运行条件。一旦确定系统可以从标称条件下的这种漂移中恢复，就可以采用一种不太保守的非线性表征，将其域限制在较小的区域内。这种两阶段方法在改善非线性系统的性能方面具有很大的潜力。将开发一个框架，系统地利用上述策略，以获得不太保守的工具，以实现绝对稳定性、吸引力域和解决外部输入的影响。研究成果包括用于非线性系统分析和综合的新理论工具，基于AFM成像的新方法，本科和研究生阶段的工程学生教育以及向AFM相关行业转移专业知识。如果成功，将产生一个新的控制理论体系。本研究的创新贡献将直接影响AFM的大多数方面，因为所提出的方法适用于大多数现有的设置。PI与AFM相关行业有着紧密的合作关系。PIs学术机构和AFM行业的技术转移将使美国AFM行业更具竞争力。这项研究将引导研究生和本科生通过从AFM动力学中获得的直觉，更好地了解非线性系统。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The research objective of this award is to build tools for analysis and synthesis of nonlinear systems with particular emphasis on Atomic Force Microscopy. Existing methodologies are conservative and often the desired performance cannot be achieved even if the potential to obtain the performance is present. The main concept on which the research is based is as follows. Often the nonlinear system is desired to have a certain nominal behavior and near the desired nominal behavior the system typically admits a precise characterization. However, there are external agents that cause the system to deviate from the nominal behavior and this might cause the required nonlinearity description to be complex. One of the main concepts utilized in the proposed research is to first manage the system behavior when the system is away from the desired operating condition. Once it is determinable that the system can recover from such excursions from the nominal condition, a less conservative characterization of the nonlinearity with its domain restricted to a smaller region is employed. This two stage approach has large potential to improve the performance of nonlinear systems. A framework to methodically exploit the above strategy for obtaining less conservative tools for absolute stability, domains of attraction and for addressing influence of external inputs will be developed Framework developed will be applied to Atomic Force Microscopy. The research deliverables include new theoretical tools for nonlinear system analysis and synthesis, new ways of AFM based imaging, engineering student education at the undergraduate and graduate levels and transfer of knowhow to the AFM related industry. If successful, a new body of control theoretic work will be produced. The innovative contributions of this research will directly impact most aspects of AFM, as the proposed methods apply to most of the existing setups. The PI has strong collaboration with AFM related industry. The transfer of knowhow from the PIs academic institution and the AFM industry will make the US industry more competitive. The research will lead to graduate and undergraduate students who will obtain better insights into nonlinear systems with the intuition gained from AFM dynamics.