Research Initiation Award: Establishment of an Integrated Analysis, Control Design and Implementation Framework for Hybrid Dynamical Systems with Constraints

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Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at his home institution, and involves undergraduate students in research experiences. The award to Prairie View A&M University has potential broader impact in a number of areas. The goal of the project is to establish an integrated analysis, control design and implementation framework for hybrid dynamical systems with constraints. Such systems contain rich dynamics that can be used to model a large class of physical systems such as robotic systems, advanced manufacturing systems and drug effects to gene networks. Undergraduate students will gain research experiences and the research will be integrated in a number of mechanical engineering courses.The goal of the research is to investigate the theory, engineering, and application of hybrid dynamical systems subjected to various constraints such as actuator nonlinearities, robustness against parameter uncertainties and limitations on hardware when implementing digital controls. Hybrid dynamical systems are characterized by the interaction of continuous system dynamics and discrete event dynamics. Conservatism is often introduced for such complex systems in order to, for example, render convex control synthesis conditions or reduce computational complexity. To avoid introducing such conservatism, efficient analysis and control synthesis algorithms will be created and integrated through exploiting and inventing various modeling and controller structures. A novel underactuated platform will be built to experimentally validate and verify the analysis and control method for a subclass of hybrid dynamical systems. Through this experiment platform, practical issues such as actuator nonlinearities, friction, measurement noise and quantization will also be investigated to enhance and expand the theoretical framework.