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We study the problem of designing interval-valued observers thatsimultaneously estimate the system state and learn an unknown dynamic model forpartially unknown nonlinear systems with dynamic unknown inputs and boundednoise signals. Leveraging affine abstraction methods and the existence ofnonlinear decomposition functions, as well as applying our previously developeddata-driven function over-approximation/abstraction approach to over-estimatethe unknown dynamic model, our proposed observer recursively computes themaximal and minimal elements of the estimate intervals that are proven tocontain the true augmented states. Then, using observed output/measurementsignals, the observer iteratively shrinks the intervals by eliminatingestimates that are not compatible with the measurements. Finally, given newinterval estimates, the observer updates the over-approximation of the unknownmodel dynamics. Moreover, we provide sufficient conditions for uniformboundedness of the sequence of estimate interval widths, i.e., stability of thedesigned observer, in the form of tractable (mixed-)integer programs withfinitely countable feasible sets.

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