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

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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.