Presidential Young Investigators Award

本研究涉及控制理论及其应用。它侧重于当前理论兴趣的两个领域，包括由泛函和偏微分方程控制的系统的振动和鲁棒周期性反馈控制理论，以及此类系统的自适应准则和自适应控制算法。第一个主题涉及以物质和/或能量传输或信息转换为特征的系统。这类系统的模型通常涉及空间导数和时间延迟。这类系统包括等离子体、核反应堆和化学反应堆、传输线、流体机械系统和燃烧系统。对于这类系统，常规的时不变反馈和前馈控制律不能保证理想的控制性能。振动和周期反馈的概念为改进这些系统的控制提供了一些希望。对于第二个主题，使用渐近和几何技术来降低系统复杂性，以及使用基于知识的规则将有助于设计上述系统的有限维自适应控制器。在这两项研究中发展的理论将在一个先进的控制实验室进行测试。

This research is concerned with control theory and its applications. It focuses on two areas of current theoretical interest including vibrational and robust periodic feedback control theory for systems governed by functional and partial differential equations, and adaptation criteria and adaptive control algorithms for such systems. The first topic addresses systems characterized by the transport of matter and/or energy or the transformation of information. Models of such systems typically involve space derivatives and time delays. This class of systems include plasmas, nuclear and chemical reactors, transmission lines, mechanical systems with fluids, and combustion systems. For such systems, conventional time invariant feedback and feedforward control laws cannot guarantee the desired control performance. The concept of vibrational and periodic feedback offers some hope of improved control for these systems. For the second topic, the use of asymptotic and geometric techniques for reduction of system complexity, and the use of knowledge based rules will aid in the design of finite dimensional adaptive controllers of systems described above. The theory developed in both of these studies will be tested in an advanced control laboratory.