Hybrid Systems: A Two-time-scale Approach
Department of
Mathematics
Wayne State
University
Owing to applications in signal
processing, random evolution, telecommunications, financial engineering, and
production planning, there has been renewed interest in understanding hybrid
and large-scalesystems, where the usual dynamics and discrete events coexist.
These discrete events evolve randomly and influence the underlying dynamic
systems by providing a set of regimes; across the regimes, the dynamic behavior
of the systems can be markedly different. In this talk, we summarize some of
our recent work, in which the discrete events are formulated as a finite-state
random jump process. When the state space of the jump process becomes fairly
large, the computational task for obtaining optimal control policies is
difficult or infeasible. Aiming at reduction of complexity, we consider an
alternative approach that uses time-scale separation to reveal the hierarchical
structure of the underlying systems. We first derive basic properties to gain a
comprehensive understanding of the jump process; we then develop near-optimal
controls of the hybrid systems.
3:30 – 4:30
p.m.