Building Hybrid Observers for Complex Dynamic Systems Using Model Abstractions

Abstract

Controllers for embedded dynamic systems have to deal with models that combine continuous behavior evolution with discrete mode transitions. These transitions may cause discontinuous changes in the field that defines continuous system behavior and the variable values associated with the continuous state vector. In reality, these discontinuous changes are fast continuous transients. To simplify the analysis of these transients time scale and parameter abstractions are applied to system models causing instantaneous transitions and discontinuities in the state vector. The two abstraction events have very different impacts on the analysis of system behavior. We have developed a systematic modeling approach that introduces formal semantics for behavior generation corresponding to these two abstraction events. This paper discusses the implementation of this scheme in a hybrid observer to track embedded system behavior. The resultant observer is based on piecewise simpler continuous models with mode transitions defined between the piecewise models. Actual mode transitions in the system are provided by a digital controller and directly obtained from measuring physical variables, therefore, the resultant observer system does not deal with complicated mode estimation problems.