Robust Optimization of Nonlinear Dynamical Systems

对制造、国防和能源等应用的稳健系统设计的日益重视，促使设计工程师使用高保真模型，这些模型考虑了复杂的非线性行为和参数值的不确定性。这项研究项目将为工程师开发新的方法和易于使用的软件，以解决设计阶段的不确定性。这些产品将极大地提高几乎每个行业的设计能力，从而产生更安全、更可靠、更坚固和更具成本效益的工程系统设计。作为这项研究项目的一部分，一名研究生将接受尖端研究方面的培训。此外，还将开发一个新的关于动态系统稳健设计的模块，通过一个关于不确定性分析、稳健设计和优化的研究生在线课程，向来自行业的系统工程师介绍不确定情况下的正式动态系统。本研究项目的目标是解决将系统建模为初值问题的稳健设计问题，该问题被描述为一个双层、最大/最小和/或半无限优化问题。解决这一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。提出了一种基于McCormick的隐函数松弛方法，用于确定全局边界信息的全局优化框架中。这些开发将在用Julia编程语言编写的软件库中实施，以实现高速和可访问性。改进的系统设计带来更大的安全和保障，减少或完全消除灾难性操作故障的影响，从而造福社会。改进的设计还通过降低产品成本(例如，商品、能源、消费品、运输等)的效率改进来降低生产成本和减少对环境的影响，从而直接造福社会。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。

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.