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

Bao Shi, Guoliang Zhao*, and Sharina Huang
International Journal of Control, Automation, and Systems, vol. 20, no. 4, pp.1351-1364, 2022

Abstract : Tensor product model transformation could find a convex polytope representation similar to the TakagiSugeno (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 twowheeled 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.

Keyword : Convex hull manipulation, local extrema refinement (LR), tensor product (TP) model transformation, TS fuzzy model, vary input (VI).

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