Collaborative Research: Hybrid Small-Gain Theorems for Nonlinear Networked and Quantized Control Systems

本课题将混杂系统视为具有连续和离散动态的较简单子系统的反馈互连。这种观点的一个优点是，在非线性系统理论中发展起来的用于分析系统互联的工具，尤其是小增益定理，变得适用于一般的混杂系统。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稳定性和鲁棒性方面的新成果，重点是在网络化和量化系统设计以及协作非线性控制设计中的应用。构成本研究理论核心的技术工具是互联系统的输入-状态稳定性和Lyapunov函数的构造(严格或非严格沿轨道递减)，这些结果的主要应用领域将是分析和设计具有通信约束的系统的控制策略。这类系统的具体类别是网络控制系统和量化控制系统，以及结合了这两种类型的效应及其大规模变体的系统。小增益方法有望对现有结果提供有洞察力的解释，使推广成为可能，并允许对迄今单独研究的问题进行统一处理。智力上的优点：这项工作将使现代非线性系统理论工具对混杂系统分析中出现的重要和具有挑战性的问题产生影响。通过以自然和协同的方式将这两个领域联系起来，它将产生新的成果，丰富两个领域，促进每个领域的进一步进展。广泛的影响：由于混合系统在应用中的普及性质，该项目的成果预计将在许多领域有用。将探索超越控制理论和工程的应用，例如预测生物分子振荡器行为的混合模型和生化反应网络的动力学模型。该项目包括研究生和本科生教育、课程开发和外联活动。

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.