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Suboptimal Integral Sliding Mode Controller Design for a Class of Affine Systems

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Abstract

This paper proposes an nth-order suboptimal integral sliding mode controller for a class of nonlinear affine systems. First, a general form of integral sliding mode is given. An extended Theta-D method is developed for the optimal control problems characterized by a quadratic cost function with a cross term. Then the extended Theta-D method is employed to determine a suboptimal integral sliding mode. Rigorous proof shows that the controller guarantees semi-global asymptotical stability of affine systems. To verify the accuracy of the extended Theta-D method, a numerical example is provided. To verify the effectiveness of the proposed suboptimal integral sliding mode controller, a numerical example and an application example of an overhead crane system are provided.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (61074013), and the Program for New Century Excellent Talents in University (NCET-10-0328).

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  1. School of Automation, Southeast University, Nanjing, 210096, China

    Rongjie Liu & Shihua Li

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  1. Rongjie Liu
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  2. Shihua Li
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Correspondence to Shihua Li.

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Liu, R., Li, S. Suboptimal Integral Sliding Mode Controller Design for a Class of Affine Systems. J Optim Theory Appl 161, 877–904 (2014). https://doi.org/10.1007/s10957-013-0312-x

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