Scalable Methods for Approximating and Optimizing Robust Stability Functions

鲁棒稳定性函数在科学和工程的许多领域具有广泛的重要性。对于线性动力系统，用无反馈控制的常微分或差分方程描述时，rsf是系统系数矩阵的实值函数。最重要的例子是伪谱横坐标和半径函数以及到不稳定性的距离。首席研究员正在开发和分析新的高效迭代方法，以比目前更快地近似RSFs。在许多应用中，为了优化系统的鲁棒稳定性，系数矩阵依赖于可能变化的参数。由于rsf不是凸的，并且在优化器上通常是不可微的，因此必须使用考虑到这一点的非光滑、非凸优化（NNO）方法。新方法的效率将为计算和优化比以前可能的更大系统的RSFs开辟道路，包括偏微分方程的离散系统。在实践中，大多数动力系统都包含反馈控制。然后我们感兴趣的rsf变得更加复杂一个重要的推广就是h∞范数。PI参与了可以在工程社区中广泛使用的软件的开发。该奖项由国家科学基金会网络基础设施办公室的一个促进网络基础设施（CI）元素重用的项目提供部分资金。该项目的目标是为广大的科学家和工程师社区带来新的优化工具，用于许多不同类型的应用。研究者的开源软件已经在各种应用中使用，包括飞机控制器的设计，质子交换膜燃料电池系统，电力系统控制器和弹性网材料缠绕系统的设计。所有这些系统都需要控制器有效地工作：像飞机或发电厂这样的复杂系统需要自动控制器安全有效地工作，此外还需要知道如何使用这些系统的熟练操作员。然而，这些计算目前仅限于小型或中等规模的系统，不能非常准确地模拟真实的物理系统。新的可扩展方法将允许为比以前可能的更大的系统设计控制器，包括在整个自然科学和工程中应用的偏微分方程离散系统的控制。该奖项由国家科学基金会网络基础设施办公室的一个促进网络基础设施（CI）元素重用的项目提供部分资金。

Robust stability functions (RSFs) have broad importance in many fields in science and engineering. In the case of linear dynamical systems, described by ordinary differential or difference equations with no feedback control, RSFs are real-valued functions of system coefficient matrices. The most important examples are the pseudospectral abscissa and radius functions and the distance to instability. The principal investigator is developing and analyzing new efficient iterative methods to approximate RSFs much more quickly than is currently possible. In many applications the coefficient matrices depend on parameters which may be varied in order to optimize robust system stability. Because RSFs are not convex and are typically not differentiable at optimizers, it is essential to use nonsmooth, nonconvex optimization (NNO) methods that take this into account. The efficiency of the new methods will open the way to computing and optimizing RSFs for much larger systems than was previously possible, including discretized systems of partial differential equations. In practice most dynamical systems include feedback control. Then the RSFs of interest become more complex and an important generalization is the H-infinity norm. The PI is involved in the development of software that can be widely used in the engineering community. This award was selected for partial funding by a program which promotes the reuse of Cyberinfrastructure (CI) elements through the Office of Cyberinfrastructure at the National Science Foundation.The goal of the project is to bring new optimization tools to a wide community of scientists and engineers, for use in many different kinds of applications. The investigator's open-source software is already in use in a variety of applications, including the design of aircraft controllers, a proton exchange membrane fuel cell system, power systems controllers and the design of winding systems for elastic web materials. All of these systems require controllers to work effectively: a complex system such as an airplane or a power plant requires automatic controllers to function safely and effectively, in addition to skilled operators who know how to use such systems. However, these computations are currently limited to small or moderate-sized systems, which cannot model real physical systems very accurately. New scalable methods will allow the design of controllers for much larger systems than was previously possible, including control of discretized systems of partial differential equations, which have applications throughout the natural sciences and engineering. This award was selected for partial funding by a program which promotes the reuse of Cyberinfrastructure (CI) elements through the Office of Cyberinfrastructure at the National Science Foundation.