CAREER: Hybrid Control of Nonlinear Systems

在过去的几十年里，自动控制理论已经相当成熟。大量的diverseandchallenging问题的解决方案已经获得，许多重要的数学方面的理论是很好地理解。然而，仍然有几类问题，标准控制工具的成功受到限制。这些措施包括：1.不能用连续反馈稳定的系统的控制。 2.具有传感器或执行器约束的系统控制。 3.具有大规模模型不确定性系统的控制。 这里提出的研究和教育发展计划旨在设计混合控制算法。在这个框架中，一个连续时间过程是通过基于逻辑的开关之间的调节器的家庭控制。闭环系统被称为混合动力系统，因为它结合了连续和离散动态。我们研究了几种情况下，这样的控制范式是自然的，并有助于克服各种缺点的更传统的控制methodology.The主要重点是系统的开发工具的混合控制设计，适用于一般和有用的类的非线性动力系统。我们建议通过认识到统一考虑中的问题的不同方面的共同趋势，并通过利用提议者和合作者在非线性干扰衰减和切换系统稳定性分析方面的最新进展来实现这一目标。混合控制技术适合于在许多重要应用的背景下实现，这些应用推动了现代技术，如软件使能控制，网络控制，基于视觉的控制。这些方法有助于弥合数学控制理论与工程实践之间的差距。因此，他们也产生了很高的学生兴趣。我们的研究项目将通过课程开发、学生指导、实验室创建和教程出版物融入伊利诺伊大学厄巴纳-香槟分校电气和计算机工程系的学术课程。

The theory of automatic control has reached considerable maturityin the last few decades. Solutions to a large number of diverseand challenging problems have been obtained, and many importantmathematical aspects of the theory are well understood. However,there remain several categories of problems for which the successof standard control tools has been limited. These include: 1. Control of systems that cannot be stabilized by continuousfeedback. 2. Control of systems with sensor or actuatorconstraints. 3. Control of systems with large-scale modelinguncertainty. The research and educational development planproposed here is aimed at designing hybrid controlalgorithms. In this framework, a continuous-time process iscontrolled by means of logic-based switching among a family ofregulators. The closed-loop system is then called hybridbecause it combines continuous and discrete dynamics. We studyseveral situations in which such a control paradigm is natural andhelps overcome various shortcomings of more traditional controlmethodologies.The primary focus of this research is on systematic development oftools for hybrid control design, applicable to general and usefulclasses of nonlinear dynamical systems. We propose to achieve thisgoal by recognizing common trends that unify different aspects ofthe problems under consideration, and by exploiting recentadvances made by the proposer and collaborators in nonlineardisturbance attenuation and in stability analysis of switchedsystems.Hybrid control techniques are suitable for implementation in thecontext of many important applications that drive the moderntechnology, such as software-enabled control, control overnetworks, and vision-based control. These methods help bridge thegap between the mathematical control theory and engineeringpractice. For this reason, they also generate high studentinterest. Our research program will be integrated into theacademic curriculum of the Electrical and Computer EngineeringDepartment of the University of Illinois at Urbana-Champaignthrough course development, student mentoring, laboratorycreation, and tutorial publications.