Collaborative Research: Hybrid small-gain theorems for nonlinear networked and quantized control systems

这个项目涉及的混合系统被视为反馈互连的简单子系统的连续和离散动态。这种观点的一个优点是，在非线性系统理论中开发的工具，用于分析系统互连，最显着的小增益定理，成为适用于一般的混合动力系统。该项目将系统地探索和应用这一思想，以发展非线性混合系统的稳定性和鲁棒性的新成果，重点是在网络化和量化系统设计和合作非线性控制设计中的应用。本研究的理论核心是输入-状态稳定性和构造关联系统的李雅普诺夫函数（沿沿着轨迹严格或非严格递减），主要应用领域是通信约束系统的控制策略分析和设计。这类系统的具体类别是网络控制系统和量化控制系统，以及结合两种类型的效果及其大规模变体的系统。小增益的方法，预计将提供有见地的解释现有的结果，使泛化，并允许一个统一的治疗问题，到目前为止已被studiedseparately.智力优点：这项工作将带来现代工具的非线性系统理论承担的重要和具有挑战性的问题所产生的混合动力系统的分析。通过以自然和协同的方式将这两个领域连接起来，它将产生新的成果，丰富这两个领域，促进每个领域的进一步发展。更广泛的影响：由于混合系统在应用中的普遍性，该项目的结果预计将在许多领域有用。超越控制理论和工程的应用，如预测生物分子振荡器和生化反应网络的动力学模型的行为的混合模型，将被探索。该项目包括研究生和本科生教育，课程开发和推广活动。

This project deals with hybrid systems regarded as feedback interconnections of simpler subsystems with continuous and discrete dynamics. An advantage of this viewpoint is that tools developed in nonlinear system theory for analyzing system interconnections, most notably small-gain theorems, become applicable to general hybrid systems. The project will systematically explore and apply this idea to develop new results in stability and robustness of nonlinear hybrid systems, with strong emphasis on applications in networked and quantized systems design and cooperative nonlinear control design. The technical tools that will form the theoretical core of this research are input-to-state stability and constructions of Lyapunov functions (strictly or nonstrictly decreasing along trajectories) for interconnected systems.The main application domain for these results will be the analysis and design of control strategies for systems with communication constraints. Specific classes of such systems are networked control systems and quantized control systems, as well as systems combining both types of effects and their large-scale variants. The small-gain approach is expected to provide insightful interpretations of existing results, enable generalizations, and allow a unified treatment of problems that so far have been studied separately.Intellectual Merit: This work will bring modern tools of nonlinear system theory to bear on important and challenging problems arising in analysis of hybrid systems. By connecting the two domains in a natural and synergistic way, it will generate new results and enrich both fields, facilitating further progress in each.Broader Impacts: Due to the pervasive nature of hybrid systems in applications, the results of the project are expected to be useful in many areas. Applications that go beyond control theory and engineering, such as hybrid models for predicting the behavior of bio-molecular oscillators and kinetics models of biochemical reaction networks, will be explored. The project includes graduate and undergraduate student education, curriculum development, and outreach activities.