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Robust Control of Uncertain Nonlinear Switched Systems: A Dissipativity-Based Integral Sliding Mode Control Redesign Approach

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Abstract

This paper considers the redesign control problem based on integral sliding control theory for a class of uncertain nonlinear switched systems where the primary control law is designed based on the dissipativity of the unperturbed system. Unlike the existing works, the model is considered nonlinear with different input channels and matched and unmatched perturbations. The dissipativity-based redesign strategy includes an integral sliding mode control with a common sliding surface with smooth changes in the switching instances. The sliding surface depends on the initial value of states such that the controlled system operates on the sliding mode from the initial time and the sliding dynamics are stable. Moreover, the reachability of the specified sliding surface in finite time is guaranteed, and the designed control law preserves the stability of the perturbed system with the same characteristics of the unperturbed system. In addition, these results are further extended to the cases that the initial values of states are not exactly known. By including an additive term in the sliding surface equation, the resulting sliding mode controller guarantees the dissipativity of the closed-loop system in the neighborhood of the sliding surface. This control law improves the behavior of the controlled switched system in the partial reaching phase and during the chattering. The proposed technique eliminates the restrictive design conditions on the derivative of storage functions and the switching law required in recent works. Finally, the theoretical results are applied to a nonlinear switched system to illustrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Malek Ashtar University of Technology, P.O. Box 84145-115, Isfahan, Iran

    B. Shahriari

  2. Intelligent Control Systems Laboratory, School of Electrical and Computer Engineering, Tarbiat Modares University, P.O. Box 14115-194, Tehran, Iran

    V. J. Majd

  3. Faculty of Electrical and Computer Engineering, Graduate University of Advanced Technology, P.O. Box 76318-194, Kerman, Iran

    H. Moradi Shahrebabaki

Authors
  1. B. Shahriari
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  2. V. J. Majd
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  3. H. Moradi Shahrebabaki
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Correspondence to B. Shahriari.

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Shahriari, B., Majd, V.J. & Moradi Shahrebabaki, H. Robust Control of Uncertain Nonlinear Switched Systems: A Dissipativity-Based Integral Sliding Mode Control Redesign Approach. Iran J Sci Technol Trans Electr Eng 43 (Suppl 1), 325–337 (2019). https://doi.org/10.1007/s40998-018-0148-3

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  • DOI: https://doi.org/10.1007/s40998-018-0148-3

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