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A synthesis approach of fast robust MPC with RBF-ARX model to nonlinear system with uncertain steady status information

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Abstract

The mechanical model of a plant in real industry is usually difficult to obtain. This paper integrates the data-driven RBF-ARX modeling method and a fast Robust Model Predictive Control (RMPC) approach to achieving output-tracking control of a nonlinear system with unknown steady status information. Considering the large online computational burden of online RMPC, this paper proposes a RBF-ARX model-based efficient robust predictive control (RBF-ARX-ERPC) approach. First, based on the RBF-ARX model, a polytopic uncertain linear parameter varying (LPV) state-space model is built to represent the dynamic behavior of the system; next, two convex polytopic sets are constructed to wrap the globally nonlinear behavior of the system. Then, an optimization problem including several linear matrix inequalities (LMIs) is formulated, which is solved offline to synthesize a sequence of explicit control laws corresponding to a sequence of asymptotically stable invariant ellipsoids in the state space, of which all the optimization results are stored in a look-up table. For the real-time control online, it only involves simple state-vector computation and bisection search. Two simulation examples, i.e. the modeling and control of a widely used continuously stirred tank reactor (CSTR) and a linear one-stage inverted pendulum (LOSIP) system, and the real-time control experiments on an actual LOSIP plant are provided to demonstrate the effectiveness of the proposed RBF-ARX model-based efficient RPC approach.

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Acknowledgments

The authors would like to thank the editors and the anonymous referees for their valuable comments and suggestions, which substantially improved the original manuscript. This work was supported by the National Natural Science Foundation of China (61773402, 51575167, 61540037), and the Fundamental Research Funds for the Central Universities of Central South University (2017zzts132).

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Authors and Affiliations

  1. School of Automation, Central South University, Changsha, 410083, Hunan, China

    Xiaoying Tian & Hui Peng

  2. College of Electronic Information and Electrical Engineering, Changsha University, Changsha, 410003, Hunan, China

    Feng Zhou

  3. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, Hunan, China

    Xiaoyan Peng

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  1. Xiaoying Tian
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  2. Hui Peng
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  3. Feng Zhou
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  4. Xiaoyan Peng
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Correspondence to Hui Peng.

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Tian, X., Peng, H., Zhou, F. et al. A synthesis approach of fast robust MPC with RBF-ARX model to nonlinear system with uncertain steady status information. Appl Intell 51, 19–36 (2021). https://doi.org/10.1007/s10489-019-01555-9

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