Performance Output Tracking for an ODE Cascaded with Schrodinger Equation Subject to Disturbances

In this paper, we are concerned with the performance output tracking for a Schrodinger PDE-ODE cascaded system with external disturbances enter in all possible channels. The main challenge of the problem is the fact that the disturbances are non-collocated to the controller. By proper trajectory planning approach, this difficulty can be overcome by converting non-collocated configurations into the collocated ones. Then a state observer is designed in terms of the tracking errors. Finally, the feedback control is proposed by applying the backstepping technique. The stability of the closed-loop system and the exponential convergence of the regulation error are proved. Some numerical simulations illustrate that the proposed approach is very effective.