Sliding Mode Control to Stabilization of an ODE-Schr¨odinger Cascade Systems Subject to Boundary Control Matched Disturbance

LIU Jun-Jun

系统科学与复杂性(英文) ›› 2018, Vol. 31 ›› Issue (5) : 1146-1163.

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系统科学与复杂性(英文) ›› 2018, Vol. 31 ›› Issue (5) : 1146-1163. DOI: 10.1007/s11424-018-6286-x

Sliding Mode Control to Stabilization of an ODE-Schr¨odinger Cascade Systems Subject to Boundary Control Matched Disturbance

    LIU Jun-Jun
作者信息 +

Sliding Mode Control to Stabilization of an ODE-Schr¨odinger Cascade Systems Subject to Boundary Control Matched Disturbance

    LIU Jun-Jun
Author information +
文章历史 +

Abstract

This paper is concerned with the boundary feedback stabilization of a coupled ODESchr ¨odinger system cascades with the external disturbance flowing the control end. The author uses the sliding mode control (SMC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the “reaching condition” is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system. Some numerical simulations is presented to illustrate the effectiveness of the proposed control.

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LIU Jun-Jun. Sliding Mode Control to Stabilization of an ODE-Schr¨odinger Cascade Systems Subject to Boundary Control Matched Disturbance. 系统科学与复杂性(英文), 2018, 31(5): 1146-1163 https://doi.org/10.1007/s11424-018-6286-x
LIU Jun-Jun. Sliding Mode Control to Stabilization of an ODE-Schr¨odinger Cascade Systems Subject to Boundary Control Matched Disturbance. Journal of Systems Science and Complexity, 2018, 31(5): 1146-1163 https://doi.org/10.1007/s11424-018-6286-x
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