Adaptive control for nonlinear non-autonomous systems with unknown input disturbance

In this paper, an input disturbance estimator using the time receding optimisation principle is firstly proposed for nonlinear non-autonomous systems. The estimated disturbance at present instance is computed from the current state of the system and that of a corresponding model and it will be used to compensate the input disturbance during the next time interval. Then, an adaptive controller is proposed for the nonlinear non-autonomous systems with the proposed input disturbance estimator. An attractor set of the closed-loop system is also obtained and its size can be decreased by reducing time receding step. Finally, numerical simulations for two examples are carried out to support the proposed. The simulation results show that all the estimated disturbances converge to the unknown disturbances and the proposed controller guarantees stability.