Adaptive Estimation of Unknown Inputs with Weakly Nonlinear Dynamics

Unknown inputs are often present in dynamical systems. These inputs may have important analytical or diagnostic information, so it may be valuable to recover their waveform while simultaneously estimating the internal plant states. In this work, we present an adaptive unknown input observer, which is tolerant to known weakly nonlinear plant dynamics, provided they are Lipschitz continuous. While the input is unknown, it is often composed of deterministic waveforms which can be superposed for an estimate of the unknown input. While the waveforms are known, their weighting coefficients are not. Here, we seek to identify these coefficients with an internal model of the known waveforms. Further, a system subject to unknown inputs may incur significant parametric uncertainty in the formulation of its model. For this reason, an adaptive estimator law is included to recover the correct plant dynamics from the synthesized model. A proof of error convergence is shown, and a simple example demonstrating the effectiveness and limitations of the architecture is provided.