Set-Theoretic Estimation of Hybrid System Configurations

Hybrid systems serve as a powerful modeling paradigm for representing complex continuous controlled systems that exhibit discrete switches in their dynamics. The system and the models of the system are nondeterministic due to operation in uncertain environment. Bayesian belief update approaches to stochastic hybrid system state estimation face a blow up in the number of state estimates. Therefore, most popular techniques try to maintain an approximation of the true belief state by either sampling or maintaining a limited number of trajectories. These limitations can be avoided by using bounded intervals to represent the state uncertainty. This alternative leads to splitting the continuous state space into a finite set of possibly overlapping geometrical regions that together with the system modes form configurations of the hybrid system. As a consequence, the true system state can be captured by a finite number of hybrid configurations. A set of dedicated algorithms that can efficiently compute these configurations is detailed. Results are presented on two systems of the hybrid system literature.