Computational Methods for the Analysis and Design of Stochactic Hybrid Systems

Sponsored by NSF CAREER Award CNS-0347440


Summary

Recent advances in information and micro-scale technologies are enabling a new generation of embedded systems that are pervading all aspects of our daily lives, from home appliances and automobiles to aircrafts and 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. The goal of this project is to contribute to the foundations of a stochastic hybrid system framework that provides the theories, computational methods, and software tools for analysis and design of embedded software.

The proposed project aspires to lay a foundation for progress in the area of stochastic hybrid systems by establishing a novel direction based on Markov approximation methods. Hybrid systems are approximated by locally consistent Markov decision processes that preserve local mean and covariance. The approach provides a unified framework to analyze and reason about both the physical and computational processes of embedded systems. Methods based on the approximations are directly related to the original processes through the notion of local consistency.

The following four primary tasks address the intellectual challenges of the proposed approach: (i) Formal analysis methods based on stochastic bisimulations that provide equivalent minimal models of the approximating Markov decision processes and allow the development of scalable algorithms. This task will follow two complementary directions for defining hybrid system specifications, a probabilistic logic and a real-valued logic framework that enable robust reasoning techniques. (ii) Stochastic optimal control methodologies for designing embedded control systems with high degree of autonomy. This task will focus on extending stochastic bisimulation techniques to take into consideration the available control actions and cost functions and will emphasize the development of efficient algorithms utilizing numerical methods based on dynamic programming. (iii) Model-based software design for building a suite of tools that support modeling of stochastic hybrid systems, computation of the approximating Markov processes, formal analysis and verification based on stochastic bisimulations, stochastic optimal control, integration with simulation languages, and tools for embedded code generation. (iv) Experimental research in order to motivate problems that are relevant to realistic applications, evaluate the developed methodologies, and engage students. The proposed experimental platforms are a multi-robot team, a highly-coupled articulated robotic system, and a three-tank system.



Personnel

Graduate Students Undergraduate Students - Summer 2007 Undergraduate Students - Fall 2006 Undergraduate Students - Summer 2006 Undergraduate Students - Summer 2005 Undergraduate Students - Summer 2004

Publications

Updated list of publications and preprints can be found at http://www.vuse.vanderbilt.edu/~koutsoxd/www/publications.html


Experimental Platforms

Multi-Robot Team Three-Tank System






















Summer Research Opportunities for Undergraduates

The project offers multiple research opportunities for undergraduate students. Details about the research positions can be found at: http://frontweb.vuse.vanderbilt.edu/vuse_web/summerResearch/index_home.htm

For additional information or if you are interested for undergraduate or graduate student research positions, contact me at: Xenofon.Koutsoukos@vanderbilt.edu

Xenofon Koutsoukos's Home Page