A novel concurrent learning‐based sliding‐mode observer for second‐order multivariable systems with a time‐varying coefficient: An application to machine vision

Abstract The problem of finite‐time state recovery for multivariable second‐order systems with a time‐varying coefficient is considered in this study. The key challenge lies in the time‐varying nature of the regressor coefficient, which possibly results in the lack of a well‐defined relative degree, and renders the synthesis of a finite‐time state observer difficult for such systems. In order to overcome this challenge, a novel multivariable sliding‐mode observer is developed that relies on an information‐rich term based on concurrent learning to ensure observer convergence. In particular, the concurrent learning‐based augmentation term leverages information contained in prior data, which is recorded over a sliding time window in the recent past, so that the resulting observer structure need only satisfy a relaxed observability condition for ensuring finite‐time convergence. A Lyapunov‐based stability analysis is undertaken to demonstrate finite‐time convergence of the observer estimates to a small uniform ultimate bound around the ground truth for a sufficiently large choice of observer gains. The observer is then applied to accomplish the task of structure and motion recovery from machine vision that involves tracking of a single stationary object feature by a moving camera across the image sequence. Numerical results are used to validate accurate observer performance in the presence of model uncertainty and measurement noise for weakly persistently exciting systems. Furthermore, a detailed comparison study with leading alternative designs is also included that demonstrates the superior performance of the proposed scheme. As the current approach precludes any reliance on a restrictive persistency of excitation condition that is difficult to satisfy apriori , an important advantage of the proposed scheme is its suitability to practical applications such as visual servo control.