Interval Observers for Simultaneous State and Model Estimation of Partially Known Nonlinear Systems

We consider the problem of designing interval observers for partially unknown nonlinear systems with bounded noise signals that simultaneously estimate the system states and learn a model of the unknown dynamics. Leveraging affine abstraction methods and nonlinear decomposition functions, as well as a data-driven function over-approximation/abstraction approach to over-estimate the unknown dynamic model, our proposed observer recursively computes the maximal and minimal elements of the interval estimates that are proven to frame the true augmented states. Then, using observed output/measurement signals, the observer iteratively shrinks the intervals by eliminating estimates that are not compatible with the measurements. Moreover, given new interval estimates, the observer updates the over-approximation model of the unknown dynamics. Finally, we provide sufficient conditions for uniform boundedness of the sequence of interval estimate widths, i.e., for the stability of the designed observer.