Design of dynamic event-triggered interval observer for Euler-lagrange systems under stealthy attack

This paper investigates the problem of interval estimation for Euler-Lagrange systems under stealthy attack based on a dynamic event-triggered mechanism. The measurement error, nonlinear term, and disturbances of the system are all taken into consideration in the design of dynamic event-triggered interval observer. By performing state reconstruction on Euler-Lagrange systems, the state-space equations of the Euler-Lagrange systems are obtained. Then, an observer is constructed to estimate the stealthy attack, and a dynamic event-triggered interval observer frame is designed to estimate the states of the Euler-Lagrange systems by using the method of coordinate transformation. Meanwhile, the ultimate boundedness of the error system is proved and the Zeno behavior is avoided. Finally, the efficiency of the designed interval observer is illustrated by a two-wheel differential drive robot. According to the simulation results, the dynamic event-triggered interval observer can save 0.64% network resources and 0.223s computational time compared with event-triggered interval observer. Moreover, when the disturbances are considered as \(\begin{bmatrix} 0.15 \cos (\pi t)\\ 0.10\sin (\pi t)\nonumber \end{bmatrix}\), \(\begin{bmatrix} 0.25 \cos (\pi t)\\ 0.20\sin (\pi t)\nonumber \end{bmatrix}\) and \(\begin{bmatrix} 0.35 \cos (\pi t)\\ 0.30\sin (\pi t)\nonumber \end{bmatrix}\), the upper and lower estimation errors are 0.122 and 0.223, 0.173 and 0.279, 0.219 and 0.323, respectively.