Probabilistic Reachability for Stochastic Hybrid Systems: Theory, Computations, and Applications

Probabilistic Reachability for Stochastic Hybrid Systems: Theory, Computations, and Applications by Alessandro Abate Doctor of Philosophy in Electrical Engineering and Computer Sciences University of California, Berkeley Professor Shankar S. Sastry, Chair Stochastic Hybrid Systems are probabilistic models suitable at describing the dynamics of variables presenting interleaved and interacting continuous and discrete components. Engineering systems like communication networks or automotive and air traffic control systems, financial and industrial processes like market and manufacturing models, and natural systems like biological and ecological environments exhibit compound behaviors arising from the compositions and interactions between their heterogeneous components. Hybrid Systems are mathematical models that are by definition suitable to describe such complex systems. The effect of the uncertainty upon the involved discrete and continuous dynamics—both endogenously and exogenously to the system—is virtually unquestionable for biological systems and often inevitable for engineering systems, and naturally leads to the employment of stochastic hybrid models. The first part of this dissertation introduces gradually the modeling framework and focuses on some of its features. In particular, two sequential approximation procedures are introduced, which translate a general stochastic hybrid framework into a new probabilistic model. Their convergence properties are sketched. It is argued that the obtained model is more predisposed to analysis and computations. The kernel of the thesis concentrates on understanding the theoretical and computational issues associated with an original notion of probabilistic reachability for