New Controller Design Approaches for Complex, Nonlinear Dynamic Systems

该项目将为确保复杂动态系统的稳定行为和期望的性能创造新的理论和方法。这类系统的一些例子包括发电厂网络、相互连接的电动汽车或生物系统，如正常的细胞生理学和导致人类疾病的变化。该项目将开发新的理论和方法，以更好地了解系统的内在特征与其动态行为之间的内在关系，从而帮助设计此类系统的控制系统。这些理论、工具和方法可以很容易地用于解决广泛的现实世界工程问题，包括预测骨骼损伤的演变，为发电系统开发更节能的控制算法以减少危险排放，或者为电动汽车网络设计更好的协调控制。对于复杂的非线性系统，传统的控制系统设计方法涉及系统的简化模型(线性化)，这固有地限制了这些系统的性能。如果成功，这项工作的结果将是朝着找到更好的非线性系统控制方法迈出的一大步。该项目还产生了重大的更广泛的影响。通过一个有组织的研究活动，这个项目将加强德克萨斯大学圣安东尼奥分校的少数族裔学生的教育，该大学是一家拉美裔服务机构。该项目还将促进美国学生、教师和他们在全球社会的同行之间的国际合作。该项目旨在开展持续和系统的研究，以探索内在非线性动态系统的行为分析和控制器设计的新理论和新方法。多变量同质性的新框架将基于最近定义同质性的新概念而开发。新的广义框架将有助于描述更广泛的非线性动力系统。通过建立齐次中心流形理论，发现系统轨迹的收敛速度与系统的单调齐性之间的内在联系。这些创新的设计工具将为许多本质非线性系统的开放控制问题提供解决方案。该项目的定义、理论和方法将增加急需的组成部分，以完成齐次系统理论，加速控制理论和动态系统的研究，并促进现实世界工程问题的新解决方案。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project will create new theories and approaches for ensuring stable behavior and desired performance of complex dynamic systems. Some examples of such systems include network of power plants, interconnected electric vehicles, or biological systems such as normal cell physiology and the alterations that lead to human disease. This project will develop new theories and methods that can help design control systems for such systems based on better understanding of the intrinsic relationships between inherent characteristics of the system and their dynamic behaviors. The theories, tools and approaches can be readily used to solve a wide range of real-world engineering problems, including predicting evolution of damage in bones, developing more energy efficient control algorithms for power generation systems to reduce hazardous emissions, or designing better coordination control for a network of electric vehicles. The traditional approaches to design of control systems for complex nonlinear systems involve simplified model (linearization) of the system which inherently limits the performance of these systems. If successful, the outcome of the work will be a big leap towards finding better control methods for nonlinear systems. The project also has significant broader impacts. Through a structured research activity this project will enhance minority students' education at the University of Texas at San Antonio, a Hispanic serving institution. The project will also promote international collaboration among U.S. students, faculty, and their peers in the global community. This project aims to develop sustained and systematic research to explore new theories and approaches for behavior analysis and controller design of inherently nonlinear dynamic systems. The new framework of multivariant homogeneity will be developed based on recent new concepts in defining homogeneity. The new generalized framework will be instrumental to characterize a boarder range of nonlinear dynamic systems. By establishing the homogeneous center manifold theory, the intrinsic link between the convergence rate of the system trajectory and the monotone homogeneity of the system will be discovered. The innovative design tools will lead to solutions to many open control problems for inherently nonlinear systems. The definitions, theories, and approaches in this project will add much-needed components to complete the theory of homogeneous systems, accelerate the research of control theory and dynamic systems, and facilitate new solutions to real-world engineering problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.