CAREER: Modeling, Analysis, and Control of Hybrid Systems with Applications to Nanoprocesses

混合系统的建模、分析和控制在纳米过程中的应用鉴于需要控制的动态系统日益复杂的性质，现代工程系统控制律设计的主要考虑因素集中在一般的分层非线性切换控制体系结构上，以最大限度地减少控制律的复杂性，从而实现整体系统的稳定性和性能。这些系统被归类为混合动力系统，包括动态切换系统、非光滑冲击机械系统、生物系统、采样数据系统、离散事件系统、智能车辆/公路系统、约束机械系统和飞行控制系统，仅举几个例子。提出的研究计划侧重于一般混合动力系统的稳定性和控制。在本研究中，首先，我们将重点发展一种统一的动力系统方法来解决混合/脉冲动力系统的稳定性分析、耗散性理论、最优控制、鲁棒稳定性和性能问题。接下来，将开发一个由脉冲微分方程描述的机械冲击系统的通用建模框架。此外，基于正在进行的研究工作，我们将开发一种基于被动的控制框架，用于稳定机械冲击系统，更广泛地说，涉及冲击的欧拉-拉格朗日系统。最后，为了将提出的理论发展转化为尖端的工程技术，我们建议在一个非常重要的工程问题上验证我们的结果；也就是说，主动控制纳米过程。作为他的教育活动的一部分，我们建议在本科控制教育中引入一种新颖的基于网络的数值实验组件。具体地说，我们建议使用新的多媒体技术，开发几个数值实验，以训练学生将分析技能应用于计算机生成的模型。最后，受生物过程最优控制方法的启发，我们提出了一种教学理念/模型来研究并希望最大限度地提高新生保留率。

Modeling, Analysis, and Control of HybridSystems with Applications to NanoprocessesIn the light of the increasingly complex nature of dynamical systems requiring controls, the predominant considerations in control law design for modern engineering systems have focused on general hierarchical nonlinear switching control architectures that minimize control law complexity subject to the achievement of overall system stability and performance. These systems, classified as hybrid dynamical systems, include dynamical switching systems, nonsmooth impact mechanical systems, biological systems, sampled-data systems, discrete-event systems, intelligent vehicle/highway systems, constrained mechanical systems, and flight control systems, to cite but a few examples. The proposed research program focuses on stability and control of general hybrid dynamical systems. In this research, first, we will focus on the development of a unified dynamical systems approach for solving the problems of stability analysis, disspativity theory, optimal control, robust stability and performance of hybrid/impulsive dynamical systems. Next, a general modeling framework for mechanical impact systems described by impulsive differential equations will be developed. Furthermore, based on an ongoing research effort, we will develop a passivity-based control framework for stabilization of mechanical impact systems, more generally, Euler-Lagrange systems involving impacts. Finally, to transition the proposed theoretical developments to cutting-edge engineering technology, we propose to validate our results on a very important engineering problem; namely, active control of nanoprocesses.As part of his educational activities, we propose to introduce a novel web-based numerical experimental component in the undergraduate control education. Specifically, using the new enabling multimedia technology, we propose to develop several numerical experiments to train students in applying the analytical skills on computer generated models. Finally, inspired by an optimal control approach for biological processes, we propose a teaching philosophy/model to study and hopefully maximize freshmen retention.