On Supervised Learning of Sliding Observer

A sliding observer for a high-order nonlinear uncertain system is examined from the machine learning perspective. The supervised learning mechanism embedded in the sliding observer system, first introduced by Slotine in 1987, is explored in details by integrating a master-slave learning concept between the subsystems of the sliding observer. In particular, the master system acts as a coordinator that coordinates the slave systems to achieve finite-time convergence. During the learning process, the slave systems are forced to learn the finite error convergence properties of the closed-loop error dynamics of the master system by injecting the switching component in all subsystems. Finite-time error convergence of the sliding observer is proved by adopting the idea of modulation transfer function into the closed-loop error dynamics. The simulations are conducted to verify the theoretical analysis.