Zonotopic Kalman filter for stability augmentation and flight envelope estimation

Abstract

This article introduces a novel methodology based on zonotopic Kalman filtering for stabilizing attitude dynamics and estimating flight envelopes of an unmanned helicopter via an observer-based (output) feedback control law and a reachability analysis, respectively. The helicopter dynamics is represented by a linear state-space model, based on which the feedback control law is designed. Since not all state variables are measurable, state information is acquired by applying a zonotopic Kalman filter to yield sets of state-variable estimates of the helicopter in terms of zonotopes. Not only are the resulting zonotopes used for the observer-based feedback control, but also for estimating the flight envelopes of the helicopter based on the reachability analysis. This approach is useful for enhancing pilot's awareness about dynamic responses of the helicopter, which may undergo unsafe flight conditions due to actuator faults triggered by undesirable perturbations. The efficacy of the proposed methodology is demonstrated via an example, where we also expose the benefits of applying the zonotopic Kalman filter as compared with an ordinary stochastic Kalman filter.