Collaborative Research: New Tools for Nonlinear Control Systems Analysis and Synthesis

在这个项目中，研究人员将朝着进一步开发新的控制设计工具迈出一步，这些工具用于由紧急控制应用引起的复杂非线性系统。重点将放在两类复杂非线性系统上，尽管它们对控制应用具有重要性和相关性，但在目前的文献中尚未得到广泛的研究。本文研究的第一类系统是由耦合时滞泛函微分-差分方程描述的相互关联的非线性系统。这一问题的进展要求为这类重要的无限维系统开发新的分析和综合工具。以前介绍的设计工具在有限维系统的背景下不能直接适用和扩展。第二类系统由非线性时变多输入多输出（MIMO）系统组成。现有的大多数工具最初都是针对时不变和单输入单输出的非线性系统的。通过引入非线性反馈设计工具包，旨在解决由欠驱动船舶和生物反应器控制引起的一些具有挑战性的问题，旨在为MIMO系统的先进非线性控制理论的进一步发展做出贡献。非线性控制系统的研究是由于世界上很少有物理和自然系统是线性的，而许多系统是强烈的和真正的非线性。近几十年来，这一重要领域取得了惊人的进展，在现在和未来，预计会有更多令人兴奋的进展。在本提案中，主要研究人员将朝着进一步开发新的控制设计工具的方向迈进一步，用于由紧急控制应用引起的复杂非线性系统。提出的研究重点将放在新的和重要的复杂互连非线性系统的类别上，特别强调在生物反应器中的应用。该项目的应用数学性质，加上它涉及具有挑战性的实际应用，将吸引那些不是专门在该领域工作的工程师和数学家，从而激发新的互动。该项目的跨学科性质将通过将来自几个系的学生聚集在一起，对两个研究机构的教育产生实质性的直接影响。

In this project, the investigators will take a step forward toward the further development of new control design tools for complex nonlinear systems arising from emergent control applications. The focus will be on two classes of complex nonlinear systems which, despite their importance and relevance to control applications, have not been extensively studied in the present literature. The first class of systems to be investigated in the proposal consists of interconnected nonlinear systems described by coupled retarded functional differential-difference equations. Advances on this topic call for the development of new analysis and synthesis tools for this important class of infinite dimensional systems. Previously introduced design tools in the context of finite-dimensional systems are not straightforwardly applicable and extendible. The second class of systems consists of nonlinear and time varying MIMO (multi-input multi-output) systems. Most of the existing tools are targeted originally at nonlinear systems which are time-invariant and SISO (single-input single-output). The aim is to contribute to the further development of advanced nonlinear control theory for MIMO systems, by introducing a toolkit of nonlinear feedback designs geared towards solving some challenging problems arising from the control of underactuated ships and bioreactors.The research in nonlinear control systems is driven by the fact that few physical and natural systems in the world are linear and many of them are strongly and genuinely nonlinear. There has been a phenomenal progress in this important field over the recent decades, and more exciting advances are expected in the present and future. In this proposal, the principal investigators will take a step forward toward the further development of new control design tools for complex nonlinear systems arising from emergent control applications. The focus of the proposed research will be on new and important classes of complex interconnected nonlinear systems with special emphasis on applications in bioreactors. The applied mathematics nature of the project, combined with the fact that it involves challenging practical applications, will attract engineers and mathematicians who are not specifically working in the field, thereby stimulating new interactions. The interdisciplinary nature of the project will have a substantial direct impact upon education at both investigators' institutions by bringing students together from several departments.