Fundamental Limitations in Control of Nonlinear Systems with Application to Biology

目的：提出的研究动机来自大脑，其中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具有强大的协同关系。本文为非线性控制系统的基本限制和鲁棒性分析提供了一个完整的研究方案。智力上的优点：智力上的优点来自于对非线性反馈系统的基本限制和鲁棒性分析提出的统一框架。各种系统理论问题可以在提出的框架内，这可以导致对大脑功能非线性动力学的基本理解的变革性进展。该项目将开发用于模型简化的算法和软件，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架构，以及开发用于模拟大脑神经回路的软件工具。更广泛的影响：提出的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，可以在当前和未来的工程应用中找到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。一些教育举措将有助于传播这些方法、成果和跨学科的协同作用。该项目旨在培养大学生对研究的强烈参与，跨学科的外展活动，暴露于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.