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Numerical optimization method for HJI equations derived from robust receding horizon control schemes and controller design

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Abstract

This paper addresses how to numerically solve the Hamilton-Jacobin-Isaac (HJI) equations derived from the robust receding horizon control schemes. The developed numerical method, the finite difference scheme with sigmoidal transformation, is a stable and convergent algorithm for HJI equations. A boundary value iteration procedure is developed to increase the calculation accuracy with less time consumption. The obtained value function can be applied to the robust receding horizon controller design of some kind of uncertain nonlinear systems. In the controller design, the finite time horizon is extended into the infinite time horizon and the controller can be implemented in real time. It can avoid the on-line repeated optimization and the dependence on the feasibility of the initial state which are encountered in the traditional robust receding horizon control schemes.

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Authors and Affiliations

  1. School of Information Science and Engineering, Northeastern University, Shenyang, 110004, China

    ChongHui Song, ChunYuan Bian, Xie Zhang & ChengLong Shi

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  1. ChongHui Song
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  2. ChunYuan Bian
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  3. Xie Zhang
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  4. ChengLong Shi
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Correspondence to ChongHui Song.

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Song, C., Bian, C., Zhang, X. et al. Numerical optimization method for HJI equations derived from robust receding horizon control schemes and controller design. Sci. China Inf. Sci. 55, 214–227 (2012). https://doi.org/10.1007/s11432-011-4403-8

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  • DOI: https://doi.org/10.1007/s11432-011-4403-8

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