Global/Semi-Global Stabilizing, Local Optimized Gain-Scheduling Control Design for Nonlinear Systems

尽管在过去的十年中，在发展非线性控制理论和数值算法方面取得了重大进展，但这些方法在有效地解决全局稳定性和最优控制性能方面的能力似乎是有限的。一种对非线性系统具有很大潜力的控制设计方法是增益调度控制。随着控制器复杂性的适度增加，多种控制方案(如切换和增益调度)将增强非线性控制系统的能力，并将非线性控制设计任务解耦。从而达到整体非线性控制的设计目标，提高了系统的稳定性和性能。该项目将专注于全球增益调度控制的开发及其在无人机(UAV)中的应用，以及将研究成果整合到北卡罗来纳州立大学(NCSU)的教育计划中。全局增益调度控制框架将提供一种具有优化局部性能和保证全局/半全局稳定性的系统控制设计方法，克服了非线性最优控制问题的计算复杂性。通过利用非线性矢量场的函数依赖性，利用平方和(SOS)分解将极大地改进LPV分析和控制设计技术。更重要的是，强大的SOS工具的应用将为现有领域提供新的见解，如稳健和自适应控制，并导致下一代先进控制技术的发展。将所提出的增益调度控制技术应用于无人机，将显示出无人机能力的增强，并将极大地提高商用、军用和个人飞机的性能和安全性。随着计算机辅助控制设计软件的发展，我们预计由此产生的增益调度控制系统将被广泛用于提高非线性控制系统的性能，包括地面/水下自主机器人、机器人操作手和汽车发动机。创新教育方法的发展将通过为本科生和研究生提供强大的理论背景和实践技能来加强NCSU的教育计划。此外，开发的LPV分析和控制设计工具箱将作为向学生和研究人员传播研究成果的工具，并促进向工业从业者转让技术。将强调与NASA兰利研究中心的积极合作，以实现研究和教育目标。

Although significant progress has been made over the last decade in developing nonlinear control theories and numerical algorithms, it appears that these methods are limited in their abilities to effectively address global stability and optimal controlled performance altogether. One control design approach with great potential for nonlinear systems is gain-scheduling control. With moderate increase in controller complexity, multiple control schemes (such as switching and gain-scheduling) will enhance the capacity of nonlinear control systems and decouple the nonlinear control design task. As a result, overall nonlinear control design objective with improved stability and performance will be achieved. This project will focus on global gain-scheduling control development and its application to unmanned aerial vehicle (UAV), as well as the integration of research results into the educational program of North Carolina State University (NCSU). The global gain-scheduling control framework will provide a systematic control design technique with optimized local performance and guaranteed global/semi-global stability, and overcome the computational complexity of nonlinear optimal control problem. By exploiting the functional dependency of nonlinear vector field, significantly improved LPV analysis and control design techniques will be developed using the sum-of-squares (SOS) decomposition. More importantly, the application of the powerful SOS tool will offer new insights into existing fields, such as robust and adaptive controls, and lead to the development of next generation of advanced control techniques. The application of proposed gain-scheduling control technique to UAVs will demonstrate increased UAV capabilities, and would greatly improve the performance and safety of commercial, military, and personal aircraft. With the development of computer-aided control design software, we envision the resulting gain-scheduled control systems to be widely used to enhance the performance of nonlinear control systems, including ground/underwater autonomous vehicles, robot manipulators, and automotive engines. The development of innovative education approaches will enhance NCSU educational program by providing students at both undergraduate and graduate levels with strong theoretical background and practical skills. Furthermore, the developed toolbox on LPV analysis and control designs will serve as a vehicle to disseminate research outcomes to students and researchers, and facilitate technology transfer to industrial practitioners. Active collaboration with NASA Langley Research Center will be emphasized to achieve research and educational objectives.