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

Rongjie Liu () and Shihua Li ()
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Rongjie Liu: Southeast University
Shihua Li: Southeast University

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 3, No 13, 877-904

Abstract: 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.

Keywords: Integral sliding mode; Suboptimal control; Extended Theta-D method; Affine systems (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0312-x

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