CAREER: A New Computational Framework for Control of Complex Systems

该学院早期职业发展(CALEAR)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和/或具有延迟的系统相互作用的系统。该项目基于多项式变量的凸优化，建立了由时滞或偏微分方程(PDE)描述的系统的最优控制的新框架。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；其次，利用正多项式对正算子的锥进行参数化；最后，利用平方和和半定规划方法对正多项式进行优化。其结果是一系列易于处理的算法，用于直接控制分布参数系统，误差范围越来越小。结构或流体组件由偏微分方程组(PDE)建模，可以包括核聚变反应堆中的等离子体、动脉瘤周围的血液流动或飞机机翼中的振动。延迟的来源可能包括对网络(如Internet)的控制。由于其复杂性，对由偏微分方程建模的系统的控制可能是具有挑战性的。该项目考虑了核聚变等离子体的控制--它尚未在实验上维持正的净能量生产--由此产生的效率改进可能对未来的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)的共同资助利用国际合作，并与当地的初中和高中项目相结合，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.