Fundamental Limitations in Control of Nonlinear Systems with Application to Biology

目的：这项研究的动机来自大脑，在那里，非线性动力学被认为是计算、信号处理和控制的核心。大脑表明，非线性动力学和控制有一种强大的、协同的关系。这一建议为具有控制的非线性系统的基本极限和鲁棒性分析提供了一个综合的研究方案。智力的优点：智力的优点来自于建议的非线性反馈系统基本限制和稳健性分析的统一框架。各种系统理论问题可以在建议的框架内提出，这可能导致对大脑功能中非线性动力学的基本理解的变革性进展。该项目将开发模型降阶的算法和软件，阐明最适合利用非线性动力学和控制之间的协同作用的控制体系结构，并开发用于对大脑中的神经电路进行建模的软件工具。广泛的影响：拟议研究的理论方面解决了非线性系统控制的基本限制，具有广泛的适用性。大脑本身提供了一个独特的范例，可以导致在当前和未来的工程应用中利用非线性动力学的新方法。此外，研究计划与教育计划紧密结合。若干教育举措将有助于传播方法、成果和跨学科协同效应。该项目旨在培养本科生对研究、跨学科外展活动的强烈参与，接触动态和控制的核心作用，并促进大学研究与行业之间的共生关系。

Objective: The motivation for the proposed research comes from the brain, where nonlinear dynamics are believed to be at the heart of computation, signal processing and control. The brain suggests that nonlinear dynamics and control have a robust, synergistic relationship. This proposal offers an integrated research program for the fundamental limitations and robustness analysis of nonlinear systems with control. Intellectual Merit: The intellectual merit derives from the proposed unified framework for fundamental limitations and robustness analysis of nonlinear feedback systems. A variety of system theoretic problems can be cast within the proposed framework, which can lead to transformative advances in the fundamental understanding of nonlinear dynamics in brain functions. The project will develop algorithms and software for model reduction, enunciation of control architectures that are best suited to exploit synergies between nonlinear dynamics and control and development of software tools for modeling the neural circuits in the brain.Broader Impacts: The theoretical aspects of the proposed research address fundamental limitations in control of nonlinear systems, which have broad applicability. The brain itself offers a unique paradigm that can lead to novel ways to leverage nonlinear dynamics in current and future engineering applications. In addition the research plan is closely integrated with an educational plan. Several educational initiatives will help disseminate the methods, outcomes and the interdisciplinary synergies. This project seeks to develop a strong undergraduate involvement in research, interdisciplinary outreach activities, exposure to the central role of dynamics and control and to foster symbiotic relationships between university research and the industry.