Developing High Performance, Computationally Efficient Nonlinear Control Techniques for Polynomial Nonlinear Systems

这一建议旨在开发一种新的控制方法，以克服现有非线性控制技术的局限性和计算复杂性。通过功率变换利用多项式非线性矢量场，利用非二次Lyapunov函数和平方和规划技术，可以得到计算上有效的控制技术。系统控制设计方法有可能解决具有挑战性的多项式非线性系统的最优控制和鲁棒控制问题。该研究还有助于实现控制设计过程的自动化和高性能非线性控制律的验证，从而显著降低非线性控制系统的成本和设计周期。可以预见，这种新的非线性控制方法不仅将为多项式非线性系统提供有效的控制设计和计算工具，而且还可能导致竞争性非线性控制理论的发明。将所提出的非线性控制方法应用于航天器控制，可以通过优化其非线性控制策略来增强其鲁棒性，改善航天器的运行性能。由于其一般性，预计拟议的研究还将对其他应用产生重大影响，包括飞机、机器人机械手、汽车发动机和磁悬浮旋转机械等。通过与NASA约翰逊空间中心和外联活动的密切合作，研究成果将传播给航空航天工业/控制界，并将产生自动化非线性控制设计技术。此外，开发在线控制课程和虚拟实验试验台可以提供一个独特的学习平台，并通过吸引非传统学生和为学生提供动手体验来加强北卡罗来纳州立大学的教育计划。这些外展和教育活动也将有力地促进人力资源开发和多样性。

This proposal is aimed at developing a novel control approach to overcome limitations and computational complexity of existing nonlinear control techniques. By exploiting the polynomial nonlinear vector field through power transformation, computationally efficient control techniques could be obtained using non-quadratic Lyapunov functions and Sum-of-Squares programming techniques. The systematic control design approach has the potential to solve challenging nonlinear optimal and robust control problems for polynomial nonlinear systems. The proposed research could also help automate the control design process and verification of high performance nonlinear control laws, thus significantly reducing the cost and design cycle of nonlinear control systems. It is expected that the new nonlinear control approach will not only provide effective control designs and computational tools for polynomial nonlinear systems, it may also lead to the invention of competitive nonlinear control theory. The application of proposed nonlinear control approach to spacecraft control could enhance its robustness and improve spacecraft operating performance by optimizing its nonlinear control strategy. Because of its general nature, the proposed research is also expected to have major impacts on other applications including aircraft, robotic manipulators, automotive engines, and magnetic-levitated rotary machines, etc. Through close collaboration with NASA Johnson Space Center and out-reach activities, the research results will be disseminated to aerospace industry/control community and will result in automated nonlinear control design techniques. In addition, the development of an on-line controls course and a virtual experiment testbed could provide a unique platform for learning, and enhance the educational program at North Carolina State University by attracting non-traditional students and providing students with hands-on experience. These out-reach and educational activities will also strongly promote human resource development and diversity.