A State Bounding Observer for Uncertain Non-linear Continuous-time Systems based on Zonotopes

A state bounding observer aims at computing some domains which are guaranteed to contain the set of states that are consistent both with the uncertain model and with the uncertain measurements. In this paper, the estimated domains are represented by zonotopes. A zonotope is a particular polytope defined as the linear image of a unit interval vector (i.e. unit hypercube). Some results about the validated integration of ordinary differential equations are used to guarantee the inclusion of sampling errors. The main loop of the observation algorithm consists of a one step prediction with a limitation of the domain complexity and a correction using the measurements. The observer is applied to a Lotka-Volterra predator-prey model.