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We study the problem of designing interval-valued observers that simultaneously estimate the system state and learn an unknown dynamic model for partially unknown nonlinear systems with dynamic unknown inputs and bounded noise signals. Leveraging affine abstraction methods and the existence of nonlinear decomposition functions, as well as applying our previously developed 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 estimate intervals that are proven to contain 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. Finally, given new interval estimates, the observer updates the over-approximation of the unknown model dynamics. Moreover, we provide sufficient conditions for uniform boundedness of the sequence of estimate interval widths, i.e., stability of the designed observer, in the form of tractable (mixed-)integer programs with finitely countable feasible sets.
We address the problem of designing simultaneous input and state interval observers for Lipschitz continuous nonlinear systems with rank-deficient feedthrough, unknown inputs and bounded noise signals. Benefiting from the existence of nonlinear decom
A simultaneous input and state interval observer is presented for Lipschitz continuous nonlinear systems with unknown inputs and bounded noise signals for the case when the direct feedthrough matrix has full column rank. The observer leverages the ex
In this paper, we study the problem of designing a simultaneous mode, input, and state set-valued observer for a class of hidden mode switched nonlinear systems with bounded-norm noise and unknown input signals, where the hidden mode and unknown inpu
In this paper, we propose fixed-order set-valued (in the form of l2-norm hyperballs) observers for some classes of nonlinear bounded-error dynamical systems with unknown input signals that simultaneously find bounded hyperballs of states and unknown
Parameters of the mathematical model describing many practical dynamical systems are prone to vary due to aging or renewal, wear and tear, as well as changes in environmental or service conditions. These variabilities will adversely affect the accura