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

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  • Rongjie Liu

    (Southeast University)

  • Shihua Li

    (Southeast University)

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.

Suggested Citation

  • Rongjie Liu & Shihua Li, 2014. "Suboptimal Integral Sliding Mode Controller Design for a Class of Affine Systems," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 877-904, June.
    • Handle: RePEc:spr:joptap:v:161:y:2014:i:3:d:10.1007_s10957-013-0312-x
    DOI: 10.1007/s10957-013-0312-x
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    References listed on IDEAS

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    1. G. S. Hu & C. J. Ong & C. L. Teo, 2004. "Minimum-Time Control of a Crane with Simultaneous Traverse and Hoisting Motions," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 395-416, February.
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    Cited by:

    1. Yusheng Zhou & Zaihua Wang & Kwok-wai Chung, 2019. "Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 634-652, May.

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