Probabilistic output admissible set for systems with time-varying uncertainties

This paper considers time-varying uncertain constrained systems, and develops a method for computing a probabilistic output admissible (POA) set. This set consists of the initial states probabilistically assured to satisfy the constraint. The time-invariant counterpart has already been investigated in Hatanaka and Takaba Computations of probabilistic output admissible set for uncertain constrained systems, Automatica 44 (2) (2008), to appear]. We first define the POA set for time-varying uncertainties with finite dimensional probability space. Then, we show that an algorithm similar to Hatanaka and Takaba Computations of probabilistic output admissible set for uncertain constrained systems, Automatica 44 (2) (2008), to appear] provides the POA set also in the time-varying case, as long as an upper bound of a what we call future output admissibility (FOA) index is available. We moreover present two methods for computing the upper bound of the FOA index: probabilistic and deterministic methods. A numerical simulation demonstrates the effectiveness of our algorithm.