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

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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.