CAREER: A New Computational Framework for Control of Complex Systems

这个教师早期职业发展（CAREER）计划项目的目标是为聚变反应堆中的等离子体控制创建可靠的算法。 该方法可以推广到与流体或结构相互作用的系统和/或具有延迟的系统。该项目创建了一个新的框架，用于基于多项式变量的凸优化的延迟或偏微分方程（PDE）描述的系统的最优控制。首先将时滞偏微分系统的最优控制问题表示为正算子的凸优化问题，然后利用正多项式对正算子锥进行参数化，最后利用平方和和半定规划对正多项式进行优化.其结果是一系列易于处理的算法，用于分布参数系统的直接控制，具有减小的误差bounds.Structural或流体组件的偏微分方程（PDE）建模，可以包括在核聚变反应堆中的等离子体，动脉瘤周围的血液流动，或在飞机机翼的振动。延迟的来源可以包括对诸如因特网之类的网络的控制。由于其复杂性，由偏微分方程建模的系统的控制可能是具有挑战性的。 该项目考虑控制核聚变等离子体-尚未在实验上维持正的净能量生产-由此产生的效率提高可能对未来全球能源生产产生长期影响。 该项目将通过NSF国际科学与工程办公室（OISE）全球风险基金（GVF）共同资助并与当地初中和高中课程整合，以促进能源教育，并建立对高能磁约束聚变及其在国家和全球能源讨论中的作用的支持和公众意识。

The goal of this Faculty Early Career Development (CAREER) program project is to create reliable algorithms for the control of plasma in a fusion reactor. The approach can be generalized to systems that interact with fluids or structures and/or systems with delay. This project creates a new framework for optimal control of systems described by delayed or partial differential equations (PDEs) based on convex optimization of polynomial variables. A three-step approach is used: First, optimal control of delayed and partial-differential system is expressed as convex optimization of positive operators; Second, positive polynomials are used to parameterize the cone of positive operators; Finally, Sum-of-Squares and semi-definite programming are used to optimize the positive polynomials. The result is a sequence of tractable algorithms for direct control of distributed-parameter systems with decreasing error bounds.Structural or fluid components are modeled by partial differential equations (PDEs) can include plasma in a nuclear fusion reactor, blood flow around an aneurysm, or vibration in an aircraft wing. Sources of delay can include control over a network such as the Internet. Control of systems modeled by PDEs can be challenging due to its complexity. This project considers the control of nuclear fusion plasma - which has yet to experimentally sustain a positive net energy production - the resulting improvement in efficiency may have long-term implications for future worldwide energy production. The project will leverage international collaboration through NSF Office of International Science and Engineering (OISE) Global Venture Fund (GVF) co-funding and integrate with local middle and high school programs to promote energy education as well as building support and public awareness for high-energy magnetic confinement fusion and its role in the national and global energy discussion.