A novel adaptive sliding-mode based interval observer for a class of uncertain nonlinear systems*

In this paper, we propose a novel interval observer scheme for a class of uncertain unobservable nonlinear systems. Existing works on interval observers require the system to be observable in order to ensure positivity and convergence of estimation errors. Hence it is very challenging to design interval observer for unobservable systems. Firstly, we introduce linear state transformations to partition the original system into three subsystems. We then propose a novel adaptive sliding-mode based interval observer for the subsystem whose states are measurable, from which finite-time state estimates, as well as an approximation of uncertainty (based on the equivalent output injection) are obtained. Using these information, interval observers are designed for the other subsystems. Positivity and convergence are ensured simultaneously, without the observability of the system, as well as relaxing the requirement to the tight lower and upper bounds of uncertainty. Finally, simulations are conducted to verify the effectiveness of the proposed scheme.