Addressing incremental backstepping control limitations with direct online Gaussian process adaptation

Abstract

Sensor-based incremental control is a recently developed technique that reduces dependency on precise model knowledge. This approach uses measurements or estimates of current state derivatives and actuator states to linearise the dynamics with respect to the previous time instant, albeit at the expense of increased sensitivity to measurement quality. Unknown system behaviour due to unforeseen malfunctions in measurement or actuation systems can lead to significant performance degradation. The novelty of this paper lies in a new method that combines the reduced model dependency of sensor-based Incremental Backstepping (IBKS) control with the adaptive capabilities of data-driven Gaussian Processes (GPs). The resulting controller exhibits significantly reduced sensitivity to model and measurement uncertainties. A theoretical proof of the global uniform ultimate boundedness of the IBKS tracking error is provided. The direct GP-based adaptation reduces the error bound and offers both long-term dependency learning and noise filtering capabilities. The effectiveness of the proposed approach is demonstrated through a missile flight control example.