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Local Extrema Refinement Based Tensor Product Model Transformation Controller Design with Vary Input Methods

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  • Robot and Applications
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Abstract

Tensor product model transformation could find a convex polytope representation similar to the Takagi-Sugeno (TS) fuzzy model from the given quasi-linear variable parameter (quasi-LPV) system model. TP models have proposed many convex hulls manipulated methods in previous studies, but these convex hulls are designed based on classical sampling methods, and local extrema refinement methods are often ignored by these classical sampling methods. Therefore, this paper proposes a convex hull manipulate method by adding local extremum to refine the partition of the entry functions, and the method is proposed based on vary input quasi-LPV state space models. First, the TP model transformation is extended by linearizing the weighting functions that is obtained via different ways of substituted entry functions, the given TS fuzzy model is converted into an alternative TS fuzzy model, and the converted TS fuzzy models are presented with different number of inputs. The difficulty level of controller design is reduced by changing the antecedents of the fuzzy sets, so the optimized control can be achieved via linear matrix inequalities (LMIs). Secondly, the local extrema refinement strategy is used to implement the TP model transformation, the manipulated method of convex hull is expanded. Finally, the GOOGOL’s two-wheeled self-balancing robot model is employed as the controlled object, and the tracking controller is attached for verification. At the same time, different external disturbances are considered to be added to the left and right wheels of the robot. The simulation results show that, by combining the state-space model with vary input variables and the local extrema refinement strategy, the designed controller achieved better control performance.

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Funding

The authors would like to thank the support of natural science foundation of Inner Mongolia (2019MS01005, 2020MS06016), National Natural Science Foundation of China under number 62141305 and 12161065, and the work is also supported by the Research Foundation for Advanced Talents Research Foundation of Inner Mongolia University (21700-5185130).

Author information

Authors and Affiliations

  1. College of Electronic Information Engineering, Inner Mongolia University, Hohhot, 010021, China

    Bao Shi & Guoliang Zhao

  2. College of Science, Inner Mongolia Agricultural University, Hohhot, 010018, China

    Sharina Huang

Authors
  1. Bao Shi
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  2. Guoliang Zhao
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  3. Sharina Huang
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Corresponding author

Correspondence to Guoliang Zhao.

Additional information

Bao Shi is currently pursuing his master’s degree in Inner Mongolia University. His research interests include fuzzy control and adaptive control.

Guoliang Zhao received his B.S. degree in mathematics from Inner Mongolia Normal University, China, in 2003, an M.S. degree in applied mathematics from Inner Mongolia Normal University, China, in 2006, and a Ph.D. degree from Dalian University of Technology, Dalian, China, in 2015. His research interests include fuzzy control, adaptive control, computational intelligence, and sliding mode control.

Sharina Huang received her B.S. degree in mathematics from Inner Mongolia Normal University, China, in 2003, an M.S. degree in operations research and control theory from Inner Mongolia Normal, China, in 2006, and a Ph.D. degree from Harbin Institute of Technology, China, in 2018. Her current research interests focus on bio-inspired computing and fuzzy optimization.

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Shi, B., Zhao, G. & Huang, S. Local Extrema Refinement Based Tensor Product Model Transformation Controller Design with Vary Input Methods. Int. J. Control Autom. Syst. 20, 1351–1364 (2022). https://doi.org/10.1007/s12555-021-0110-4

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  • DOI: https://doi.org/10.1007/s12555-021-0110-4

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