In a wide range of practical applications (e.g., transportation systems, embedded software design, energy saving of portable electronics, biological systems, etc.), there are two types of uncertainty inherent in the evolution of the systems: small incremental noises caused by environmental perturbations, and abrupt and large changes caused by random discrete events and system reconfigurations. The model and analysis of such systems can be conveniently captured by the recently developed framework of stochastic hybrid systems.
This NSF CAREER research aims to develop the theoretical foundation and the computational platform for the efficient solution of two important classes of problems arising in stochastic hybrid systems: their reachability problems and reachability optimization problems. The reachability problems are particularly relevant in safety-critical applications (e.g. air traffic management): their solutions will give quantitative probabilistic characterizations of the system safety under the presence of uncertainty. Such information can not only be used in monitoring the safe operation of the system, but can also serve as the intermediate results in an overall effort to optimize the system performance, resulting in reachability optimization problems. A key obstacle to the efficient solution of these two problems is the explosive increase of computational complexity with the problem dimension. Hierarchical multi-level computational algorithms are being developed in this project to overcome this obstacle. Software tools developed based on these algorithms are expected to enable the real-time solution of the two problems for many practical applications of great societal importance. In addition, the developed theory, algorithms, and software are being validated on a multi-robot experimental testbed.
