CAREER: Computational Methods for the Analysis and Design of Stochastic Hybrid Systems

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Recent advances in information and micro-scale technologies are enabling a new generation of embedded systems that are pervading our daily lives, from automobiles and aircrafts to manufacturing plants. Such applications consist of tightly coupled physical and computational processes that dynamically interact with the environment in the presence of uncertainty and variability. This project aims at developing a stochastic hybrid system framework that provides the theories, computational methods, and software tools for analysis and design of such systems. Stochastic hybrid systems are approximated by locally consistent Markov decision processes that preserve local mean and covariance. The project addresses the following critical research challenges: (1) Formal analysis of system properties expressed using probabilistic temporal logics. Stochastic bisimulations are employed to provide equivalent minimal models of the approximating Markov processes and allow the development of scalable algorithms. (2) Design of embedded control systems with high degree of autonomy using stochastic optimal control. Efficient algorithms are designed by utilizing stochastic bisimulations that account for the available controls. Model-based software design is used for building a suite of supporting tools and experimental research is conducted to validate the results. The research advancements are integrated into the undergraduate and graduate curriculum using a series of realistic challenge problems. Technical results, software tools, and the education materials will be made available electronically using an open-source model as well as through publications and conference participation. The broader goal of the project is to establish solid theoretical foundations and computational methods that will impact embedded system design in applications such as mobile sensor networks for homeland security and environmental monitoring, intelligent transportation systems, and electromechanical systems and chemical processes in manufacturing.