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A Continuous-Discrete Unknown Input Finite Memory Observer Design for Nonlinear Lipschitz Systems with Process and Measurement Noises

This paper intends to design a continuous-discrete unknown input finite memory observer (CD-UI-FMO) for the dynamical nonlinear systems with unknown input. The nonlinear systems under consideration are at least locally Lipschitz and represented by ordinary differential equations (ODEs) with process noise while measurements are sampled at discrete time instants with measurement noise. Both process and measurement noise configurations guarantee the robustness and stability of state estimation, as well as performances in diagnosis. By an augmented model, the proposed CD-UI-FMO is designed based on least square method together with an iterative prediction-update scheme with the aim to simultaneously estimate system state and unknown input. The unbiased estimation property is proved in deterministic case and demonstrated via Monte Carlo simulations in stochastic case, respectively. Moreover, the presented nonlinear observer is successfully applied to an actuator fault detection and estimation for a single-link joint robotic arm incorporating with the exponentially weighted moving average (EWMA) control chart. Illustrative simulation results highlight the effectiveness of the proposed approach.