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

在这个项目中，研究人员将朝着为紧急控制应用中出现的复杂非线性系统进一步开发新的控制设计工具迈进一步。重点将集中在两类复杂的非线性系统上，尽管它们对控制应用具有重要意义和相关性，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-差分方程组描述的相互关联的非线性系统。这一主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。以前引入的有限维系统环境中的设计工具不是直接适用和可扩展的。第二类系统由非线性时变MIMO(多输入多输出)系统组成。现有的大多数工具最初都是针对时不变、单输入单输出(SISO)的非线性系统。通过引入非线性反馈设计工具包，旨在解决欠驱动船舶和生物反应器控制中的一些具有挑战性的问题，旨在促进先进的非线性控制理论在MIMO系统中的进一步发展。非线性控制系统的研究是基于这样一个事实，即世界上很少有物理和自然系统是线性的，并且许多系统是强且真正的非线性的。近几十年来，在这一重要领域取得了惊人的进展，预计在现在和未来将取得更令人振奋的进展。在这项提案中，主要研究人员将朝着进一步开发用于紧急控制应用的复杂非线性系统的新控制设计工具迈进一步。建议的研究重点将放在新的和重要的复杂的相互关联的非线性系统上，特别强调在生物反应器中的应用。该项目的应用数学性质，再加上它涉及挑战实际应用的事实，将吸引并非专门在该领域工作的工程师和数学家，从而刺激新的互动。该项目的跨学科性质将对两个研究机构的教育产生重大的直接影响，因为它将几个系的学生聚集在一起。

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.