Computationally Efficient State and Model Estimation via Interval Observers for Partially Unknown Systems

This paper addresses the synthesis of interval observers for partially unknown nonlinear systems subject to bounded noise, aiming to simultaneously estimate system states and learn a model of the unknown dynamics. Our approach leverages Jacobian sign-stable (JSS) decompositions, tight decomposition functions for nonlinear systems, and a data-driven over-approximation framework to construct interval estimates that provably enclose the true augmented states. By recursively computing tight and tractable bounds for the unknown dynamics based on current and past interval framers, we systematically integrate these bounds into the observer design. Additionally, we formulate semi-definite programs (SDP) for observer gain synthesis, ensuring input-to-state stability and optimality of the proposed framework. Finally, simulation results demonstrate the computational efficiency of our approach compared to a method previously proposed by the authors.