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.
