Robust Optimization of Nonlinear Dynamical Systems

对制造、国防和能源等应用的鲁棒系统设计的日益重视，促使设计工程师使用高保真模型来解释复杂的非线性行为和参数值的不确定性。该研究项目将开发新的方法和易于使用的软件，供工程师在设计阶段考虑不确定性。 这些产品将极大地提高几乎每个行业的设计能力，从而使工程系统的设计更安全、更可靠、更强大、更具成本效益。 作为这个研究项目的一部分，研究生将接受尖端研究的培训。 此外，还将开发一个新的动力系统鲁棒设计模块，通过一个关于不确定性分析、鲁棒设计和优化的研究生在线课程，向工业界的系统工程师介绍不确定性下的正式动力系统。本研究项目的目标是解决建模为初始值问题的系统的鲁棒设计问题，该问题被表述为一个双层，最大/最小，和/或半无限优化问题。解决这个问题需要建立新的理论数学、数值分析和高速软件实现，以结合动态模拟和确定性全局优化。基于McCormick的松弛隐函数的发展，提出了用于确定性全局优化框架内的全局边界信息。这些开发将在Julia编程语言编写的软件库中实现，以实现高速和可访问性。改进的系统设计可以提高安全性和保障性，通过减少灾难性操作故障的影响或完全消除这些故障，使社会受益。改进的设计还通过效率的提高降低了生产成本并减少了对环境的影响，这通过降低产品成本直接造福于社会（例如，商品、能源、消费品、运输等）。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估的支持。

The increasing emphasis on robust system designs for manufacturing, defense, and energy applications, among others, is motivating design engineers to use high-fidelity models that account for complex nonlinear behavior and uncertainty in parameter values. This research project will develop novel methods and easy-to-use software for engineers to account for uncertainty at the design stage. These products will dramatically improve the design capabilities in nearly every industry, resulting in safer, more reliable, more robust, and more cost-effective designs of engineered systems. As part of this research project a graduate student will be trained in cutting edge research. Also, a new module on the robust design of dynamical systems will be developed to introduce formal dynamical systems under uncertainty to systems engineers from industry through a graduate online course on Uncertainty Analysis, Robust Design, and Optimization.The objective of this research project is to solve the robust design problem for systems modeled as initial value problems which is formulated as a bi-level, max/min, and/or semi-infinite optimization problem. Solving this problem requires establishing new theoretical mathematics, numerical analysis, and high-speed software implementations for combining dynamic simulation and deterministic global optimization. The development of McCormick-based relaxations of implicit functions is proposed for use within deterministic global optimization frameworks for global bounding information. These developments will be implemented in a software library written in the Julia programming language for high speed and accessibility. Improved systems design results in greater safety and security which benefits society by reducing the impacts of catastrophic operational failures or eliminating them altogether. Improved designs also result in reduced production costs and reduced environmental impact through efficiency improvements which directly benefit society by reducing costs of products (e.g., commodities, energy, consumer goods, transportation, etc.).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.