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

在这个项目中，研究人员将进一步开发新的控制设计工具，用于紧急控制应用中产生的复杂非线性系统。重点将放在两类复杂的非线性系统，尽管其重要性和相关性的控制应用，还没有被广泛研究，在目前的文献。 第一类系统的研究建议由耦合滞后泛函微分差分方程描述的互联非线性系统。这一主题的进展要求开发新的分析和合成工具，这一类重要的无限维系统。以前介绍的有限维系统的背景下的设计工具是不直接适用和扩展。第二类系统包括非线性和时变MIMO（多输入多输出）系统。现有的大多数工具最初是针对非线性系统的时不变和SISO（单输入单输出）。 目的是通过引入非线性反馈设计工具包来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，从而为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世界上很少有物理和自然系统是线性的，其中许多是强非线性的事实驱动的。近几十年来，这一重要领域取得了惊人的进展，预计在现在和未来会有更令人兴奋的进展。在这项提案中，主要研究人员将进一步开发新的控制设计工具，用于紧急控制应用中产生的复杂非线性系统。拟议的研究的重点将是新的和重要的类复杂的互联非线性系统，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，将来自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.