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It is well-known that the Schrödinger equation plays an important role in physics and applied mathematics as well. Variational formulations have been one of the hottest topics. This paper suggests a simple but effective method called the semi-inverse method proposed by Ji-Huan He to construct a variational principle for the nonlinear Schrödinger equation with high nonlinearity.

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This study first proposes an observer-based feedback linearization control of nonlinear multi-input multi-output systems with the input-to-state stability and almost disturbance decoupling characteristics, and summarizes an efficient algorithm for deriving the almost disturbance decoupling control. The state variables for the nonlinear dynamic equations generally are not available, and a state observer is applied to estimate the state variables. The existing approach solves the almost disturbance decoupling problem under the difficult sufficient conditions including the nonlinearities which are not globally Lipschitz and disturbances which appears linearly but multiplied nonlinearities. On the contrary, this problem can be easily solved via the proposed approach without those difficult conditions in this study. The generality of this approach and implications, due to the fact that unlike Jacobian linearization feedback linearization is not only locally valid, are also shown. The double rotor multi-input multi-output system mechanical structure is a laboratory equipment for some flying viewpoints and is investigated in this study to demonstrate the practical value of the proposed results.